Czech Technical University in Prague Faculty of Transportation

Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics Hybrid Uncertain Systems Zdeněk Votruba 10 March 2009

The author is with the Czech Technical University, Faculty of Transportation Sciences, Konviktská 20, Praha (Prague) 1, CZ 110 00; E - mail: votruba@fd. cvut. cz; zdevo@ieee. org Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Hybrid Systems System Model of the object owing the relation of isomorphism or “controlled homomorphism“ with the object in the subjectively chosen set of variables OR parts AND their relations Complex System the role of Information / organization / “transcomputability“ Complex Heterogeneous System Hybrid System 1. Min 2 parts / subsystems with different nature of variables; mostly: continuous / discrete; (e. g. discrete / continuous time) 2. Min 2 parts / subsystems with different Identities, e. g. man – machine; driver – car; vehicle – infrastructure; def. of Identity Ø Role of Interface Ø Role o incomplete identification Systems Alliance Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Uncertainty Missing information – see G. J. Klir “Sources“ of Uncertainty: ü Shortage of resources (time, energy, money…) on the sites of Subject or Super-System ü Neighborhood (non – structured, far…) ü Fragmentation of Processes „turbulent“ neighborhood - insufficient dynamics of System ü Inability of Systems Identification Nature of Object Tools / Methodologies of tackling a problem of Uncertainty: Probability Theory (Stochastic) Automata Theory Decision Trees / Forests Time Series Fuzzy Systems Theory Neural Networks (specific lectures) Genetic Algorithms Mix Soft Systems Methodologies (see: Systems Analysis) Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Motivation Transportation ( Communication) is probably the most complex, both heterogeneous and significantly interconnected artificial whole in the Earth, often with non-negligible degree of chaotic behavior. Almost any citizen in any bigger city has a daily experience that the level of understanding and control of transportation processes is not satisfactory. Systems Science and Systems Engineering are the branches of science and technology intended to study and control complex heterogeneous and strongly interconnected wholes, to some extent also with non - negligible degree of uncertainty, via smart systems models identification, construction and manipulation. Are we able to utilize “some pieces“ of Systems Science, theoretical concepts or at least specific theoretical ideas in Transportation? Is Transportation a “generator“ of Systems Ideas and Tasks? Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Motivation Presented “pieces of theory“ are mostly of constructive, task oriented nature, nevertheless Systems Science has its deep holistic backgrounds. Each component of (well - designed) theory owes the power of generalization. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

THEORY Complex Interfaces - Foreword Complex system interfaces (IF), for example “human – machine” IF within the complex hybrid systems or system alliances 3 , are often recognized as the weakest points of the system from the reliability point of view. On the other hand complex neuron synapse in the brain[2] seems to be quite a reliable object. The aim of this Chapter is to utilize model tools suitable for analyzes of IF regularity within the framework of Systems Science 2, 1 , taking into account: (i. ) dimension of relevant IF, and (ii. ) degree of uncertainty. Final goal is better understanding of a nature of Complex IF irregularity. [2] for many systems analytics the prototype of complex interface Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Complex Interfaces - Models of Interface (IF) Several types of models are discussed in detail in 15 : 1. Basic model of IF 2. IF as a fictitious system element 3. IF as a conversion element (CA) 4. Language description of IF 5. Systems Alliance Interfaces 6. Models of neuron synapse. Models ad 2) and 5) are utilized within this Chapter. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Complex Interfaces Interface - fictitious system element For complex IF seems to be advantageous to introduce the IF as a fictitious system element (AFIF). The advantage of this approach is anchored in the richness of the concept of system element, which is generally defined as an automaton. For the sake of simplicity the finite deterministic automaton (FDA) is usually chosen. FDA can be described by triple of sets IN, Z, OUT – inputs, internal states and outputs, respectively (Within the set of internal states Z is further defined a specific subset – initial internal state Z 0. ), and double of (mapping) functions: , . Function transforms the Cartesian product (IN x Z) into the set of internal states Z. Function transforms Cartesian product (IN x Z) into output set OUT. FDA : = (IN, Z, Z 0, OUT, , ) : (IN Z)[1] Z) Z, : (IN Z) OUT) _____________ [1] (IN Z), etc. , means Cartesian product of respective sets. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Complex Interfaces - Interface - fictitious system element The fictitiousness of IF element reflects important features: No demands on systems resources, and No transform of base variables or parameters, i. e. no consumption of time to carry out the functions, as well. It is worth to mention, that these features are strictly valid for regular IF, while any disturbances of regularity can harm these features. Probably the simplest introduction of a regular IF as a fictitious systems element [1] AFIF could be: Z is empty set, is any arbitrary function without demands to system resources (in fact is meaningless), transforms IN into OUT, : IN OUT, the transform being an equivalence for all the parameters (components) of the sets (vectors) IN, OUT respectively : OUT = IN. [1] (i. e. fictitious finite deterministic automaton) Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Complex Interfaces - Interface - fictitious system element To describe the impact of irregularities and uncertainties, slightly modified model of IF is more suitable: Let OUT = ai. OUT be a set of parameters ai. OUT ; Let IN = aj. IN be a set of parameters aj. IN; Let Z = ak. Z be a set of parameters ak. Z ; Z 0 = z 0 k ; : Z : = Z 0 : OUT: = IN Z For regular IF the respective AFIF has of course the features: i = j = k; Z 0 = z 0 k = 1 ; (i. e. : z 0 k = 1 for k); Regular interface: AFIF: Z 0 = 1 ; : Z 0 Z; : IN x Z = OUT; dim(IN) = dim(Z)= =dim(OUT) UN IN OUT A 1 A 2 AFIF Z Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Complex Interfaces - Systems Alliance Interfaces The concept of Systems Alliance has been recently introduced 3 to cope with the emergence of synergic effects even for the groups of systems that do not share Common System Identity[1]. The principle of Systems Alliance[2] (for which the role of IF seems to be crucial) has been explained utilizing the concepts of Information Power (IP) and multilingual translation efficiency, respectively 3, 4. Simplified illustration of basic phenomena[3] resulting in the emergence of Alliance could be based on the concepts of Interface Sharing, and Irregularities Conjugation, as well. The case can be illustrated on a simple constructive example ______________ [1] (as is true for the category of Hybrid Systems) [2] and the emergence of synergic effect, as well [3] (within the Alliance and especially in Alliance IF) Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Complex Interfaces - Systems Uncertainty An uncertainty (in complex systems substantial and almost omnipresent) 1, 2, 10, 12 has many “resources” and aspects. Any effective analysis of complex systems reliability can hardly be done without careful evaluation of the impact of uncertainty to the system. In the beginning of the further study methodological problems arise how to “incorporate“ uncertainty into the system? The significant majority of authors localize uncertainty into: Systems (or system elements) functions / processes or systems structure, eventually to systems neighborhood. The localization of uncertainty into the IF is not frequent. Nevertheless, the author is convinced that just this approach could help us to illustrate some nontrivial aspect of the task. To model IF I have primarily chosen an attempt described in previous paragraph (Interface as a fictitious system element) in which uncertainty “enters” the initial state Z 0. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Complex Interfaces - Specification of the Task The aim of the further part of this Chapter is to analyze combined effect of the dimension and uncertainty of chosen IF within the system with respect to the reliability of defined [1] processes. The task is structured to the following main steps: A. Reliability of a single (non-interacting) IF B. Reliability of interacting interfaces. [1] (usually strong or goal – seeking) Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Complex Interfaces - Reliability of the non-interacting IF is directly connected with the regularity of this interface. The respective relation is as follows. Reliability of regular IF is equal to 1. Rel (Reg (IF)) = 1; To specify the impact of irregularity we have to turn back to the chosen model of interface. Assume further the same dimension of sets IN, OUT and Z, (i = j = k). To simplify the following discussion let us transform the task to the “quasibinary world”. Suppose Z 0 is vector the components of which can be alternatively 1 or 0. For regular IF the vector Z 0: = 1, 1, 1, …. 1. The impact of uncertainty (resulting in possible IF irregularity) could then be expressed by the simplest possible way as the existence of zero components in Z 0. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Complex Interfaces - Reliability of the non-interacting IF : ai. Z : = z 0 i i. e. Z : = Z 0 : ai. OUT : = ui ai. IN; ui =1 for i, for that ai. Z=1, else ui = , where is the number of undefined real value[1] in interval 0 1[2]. Verbally: All the components of input vector IN for which the corresponding components of initial internal state Z 0: z 0 i = 1 are directly mapped into the respective components of output vector OUT: ai. IN (zoi = 1) ai. OUT, while these components of input vector IN for which the corresponding components of Z 0 : z 0 j 1 are mapped into the component aj. OUT which has value , uncertain without any a priori knowledge within the interval 0, 1. _______ [1] is real number with undefined value in the strong sense, i. e. neither the probability density function, nor membership function within the interval 0, 1 are known. [2] (in purely binary case: alternatively 0 or 1 with unknown probabilities / expectancies) Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Complex Interfaces - Reliability of the non-interacting IF IN ai. IN OUT ai. IN ai. Z Z 0 z 0 i Z ai. Z Model of IF function (IF represented by fictitious finite deterministic automaton) : ai. Z : = z 0 i i. e. Z : = Z 0 : ai. OUT : = ui ai. IN; ui =1 for i, for that ai. Z=1, else ui = , where is the number of undefined real value in interval 0 1. For example: For IN: = a 1, a 2, a 3… an , and Z 0: = 0, 1, 0…. 1 OUT = a 1, a 2, a 3…. an. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Complex Interfaces Reliability of the non-interacting IF Assuming the length of vectors IN, OUT, Z, Z 0 is n and there is m[1] components of Z which are not equal to 1, then m could naturally be an absolute measure of IF irregularity, while the relative measure of IF irregularity can then be introduced as rir : = m/n. Reliability of irregular IF could be expected to be monotonous non-increasing function of the rir. As the reliability from its definition is probability, it must be defined within the interval 0, 1. Rel (Irreg (IF) = Rel(rir) ______ [1] (m n; m, n : 0, 1, 2…) Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Complex Interfaces - Acceptable degradation of IF This consideration does not take into account concept of “acceptable degradation of IF” which is quite often used within the body of Systems Analysis. This concept reflects the experience of analytics that minor irregularities of IF could often have (in real or interpreted systems) no measurable effect on the reliability of respective processes. The nature of this phenomenon can be linked with the redundancy of input parameters/variables (IN), and consequent possibility to reconstruct the correct values of the disturbed vector components in OUT. To introduce this aspect of the task into the model the threshold parameter [1] can be defined and the impact of uncertainty is then quantitatively expressed assuming z 0 i 0, 1 [2]. The function in the model is modified, as well: : If (z 0 i + ) 1 then ai. Z: = 1, else ai. Z: = (z 0 i + ), while remains unchanged: : ai. OUT : = uiai. IN; ui =1 for i, for that ai. Z=1, else ui = , where is undefined real number[3] in interval 0 1. The further results of the previous chapter remain unchanged. _________ [1] 0, 1). An obvious generalization could be done assuming vector character of ( n), but this generalization is not reasonable for our purposes. [2] (not only the binary values 0/1) 1, 2 , . . i. . [3] is real number with undefined value in the strong sense, i. e. neither the probability density function, nor membership function within the interval 0, 1 are known. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Complex Interfaces - Generalization of the model for interacting interfaces This model of IF could be further generalized assuming that certain (neighboring) interfaces within the respective system interact. The interaction means for our purposes that the measure of irregularity rir of the IF under study can be modified by irregularities of another[2] system interfaces. The generalization is based on the idea that instead of taking into consideration only the initial state vector Z 0 of the IF under study (as is done in the chapter 4. 1. ) the analogical vectors of neighboring IF in the same system are to be considered as well. The function is in this case of significantly more complex nature, mapping Cartesian product of initial internal states vectors of all the interacting IF into the internal state Z of IF under study. Let the index of IF under study be p 1, q and e =1, 2…. q. Then: p: (Z 0)e Zp; where q means Cartesian product of q sets and the arrow “ ” means certain mapping rule; i. e. : (z 01 z 02 …. . z 0 q) z 1, etc. [2] (neighboring) Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Complex Interfaces - Generalization of the model for interacting interfaces Simplified version of this case should illustrate the nature of the generalized task: Assume two interacting interfaces, IF 1 and IF 2. The first one let be under the study. Z 01: = (1, 0); Z 02: = (1, 0, 1)[1]; The relations let be two-valued ones. Respective (degraded) Cartesian product (Z 01 Z 02) = ((1 -1), (0 -1), (1 -0), (0 -0), (1 -1), (0 -1)); Let us further define 1: (1 -1): = 1, (0 -0): = 0, (0 -1): = 0, (1 -0): = 0 , then (Z 01 Z 02)´: = (1, 0, 0, 0, 1, 0), and (Z 01 Z 02)´´ : = max dim Z 1 (comp((Z 01 Z 02)´)[2] = (1, 1). Then Z 1= (1, 1) and therefore this IF is regularized. For slightly different definition of 1: Z 1: = Z 01 AND(max (comp(Z 01 Z 02)´) the IF remains irregular one. This generalization makes possible to utilize proposed model of IF for both interacting and externally controlled interfaces. This feature is important especially in complex hybrid systems and system alliances. [1] (Therefore the dimension of IF [2] 1 is 2 and dimension of IF 2 is 3. ) vector of the length of Z 1 , components of which are the maximum components of the vector (Z 01 Z 02)´ Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Complex Interfaces - Approaches to the uncertain IF regularization An intuitive approach how to increase the reliability of any IF[1] is: “Identifying and tight control of the all interface variables / parameters”. This, at the first sight quite natural and smart approach could turn to be quite often counterproductive, if the significant uncertainty enters the playground[2]. _____________ [1] i. e. how to tune regularity of the respective interface and subsequently to increase reliability of the system as a whole [2] (So called : “Curses of dimensionality“) Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Complex Interfaces - A homogeneous impact of uncertainty to the all dimensions of the IF This case has been studied in 15 utilizing geometrical reinterpretation of the presented model. The prerequisites of this study are: Analyzed IF consists of n mutually independent variables / markers. All the variables of IF are renormalized. Then, in geometrical view, IF could be supposed to form n dimensional compact body[2]. Uncertainty “enters” solely the studied IF, not the system as a whole. It modifies m = n variables/parameters of Z 0. The results of this study are straightforward: In the presence of uncertainty the increase of the dimension of the IF significantly reduces the relative weight of its regular core. This effect impairs the conditions for regularity, i. e. reliable function of IF as well. For n 10 the IF (for quite moderate renormalized uncertainty 0. 1) has relatively too high potential (renormalized) irregularity (0, 651) for any practical purposes. [2] cube or sphere (or, taking into account the weights of variables, an n – dimensional cuboid or ellipsoid) Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Complex Interfaces - A homogeneous impact of uncertainty to the all dimensions of the IF This notion has also some remarkable links with epistemology, for example with the old, famous and in science very useful principle of “Occam's razor”: “Frustra fit per plura, quod potest fieri per paociora“, or later his successors: “Entia non sunt multiplicanda praeter necessitatem“ William Occam (Ockham) (1285(? )– 1349) Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Complex Interfaces - A homogeneous impact of uncertainty to the all dimensions of the IF - 2 That is probably the reason why scientists and systems analytics on the experience and intuitive background try to keep the number of markers (and therefore the dimension of the IF) on as low as possible value[1]. The basic and to some extent universal way how to improve the conditions for achieving regularity of the IF in this case is to (re)construct it as robust as possible. It means that an acceptable degradation of regularity of respective IF, (expressed by the coefficient ) must be sufficiently high. Within the artificial part of system it should be quite easily done. The redundancy in codes or artificial system elements should be utilized, as well as contextual sensitivity[4], time redundancy, or sophistical means of predictive diagnostics. But this way is of controversial value for human – machine IF, as it often assumes in fact the reconstruction[5] of both interfacing parts of the respective system. [1]They can do it (to some extend), utilizing some known simplification methods 2. [4] (for our purposes also the specific case of redundancy) [5] The “reconstruction “of human component of certain human – machine IF implies for example demanding specific training of the operator, or multiplication of the number of human operators. Such measures could be only rarely met. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Complex Interfaces - IF Conjugation Intrinsically different approach is the utilization of synergic interactions among neighboring IF within the same system. This phenomenon is in fact of the similar nature as Systems Alliances origination 3, 4. Generalized model, described in the previous part of this Chapter is a suitable tool for these purposes. Let us present a simplified example: Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Complex Interfaces - IF Conjugation - Construction of the Example Let A and B be two synchronous binary digital systems. Both A and B consists of three elements. a b c d A 1 A 2 RA A 3 B 1 B 2 RB B 3 Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Complex Interfaces - IF Conjugation - Construction of the Example The elements with the subscript 1 perform either logic function OR, or logic function AND of max. 4 inputs. The choice of the respective logic function is controlled by the (binary) parameter R[1]. The elements with subscript 2 are shift registers of pre-defined length. The elements with subscript 3 identify the total number of zeros in respective shift-registers, and eventually generate the control parameters R. Goal of the system A is to fill dynamically the shift-register A 2 with ones only. Goal of the system B is to fill dynamically the shift-register B 2, 1: 1 with ones and zeros. Goal (seeking) processes are evidently different for A and B. As a result, the system Identities are different, as well. Consequently, any composition of these (sub)systems A, B cannot compose Hybrid System. _______________ [1] ( i. e. RA, RB, respectively; R = 0 means function OR, et vice versa) Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Complex Interfaces - IF Conjugation - Construction of the Example (1) In the beginning of our consideration let A 1 utilizes the inputs a and b, while B 1 utilizes the inputs c and d. There is no a priori information about the state of any input. a A 1 A 2 RA A 3 b c d B 1 B 2 RB B 3 An optimum choice of logic function of element A 1 has to be permanent OR, no control R 1 has to be generated. That is not the case of B, where R 2 must be zero for more then 50 of ones inside B 2, et vice versa. Both systems A and B can dynamically seek their goals, but generally both are not able to reach the goals permanently. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Complex Interfaces - IF Conjugation - Construction of the Example (2) The situation quantitatively changes, if both system A and B start to share all the inputs a-d[1]. In such a case the frequency of reaching both goals dynamically probably arises[2]. a A 1 A 2 RA b c d B 1 B 2 RB A 3 B 3 ______________ [1] IF is shared. [2] There is higher probability that for mutually independent and a priori unknown inputs a, b, c, d the function OR (a, b, c, d) = 1, in comparison with the function OR (a, b) = 1 (and similarly the same is valid for: AND (a, b, c, d) = 0). Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Complex Interfaces - IF Conjugation - Construction of the Example Irregular IF More significant changes occur if some (of many possible) uncertainties of respective IF are taken into account. (1) Consider again the original case. (1), but now let inputs a and c be affected by uncertainty[1]. For OUTA = (0, b) System A is dynamically far from reaching the goal, because the long term probability of the content of A 2 is the same as the probability of “ 1” at b[2]. For OUTA = (1, b) System A reaches the goal absolutely[3], but without any control via inputs. Slightly different results are obtained for system B: For both OUTB = (0, d) and OUTB = (1, d) System B can dynamically reach the goal but probably with lower frequency then in the case of regular IF. [1] It means: Z 0 A= 0 A A 2 b 1 d 1 RA B B 2 1 RB A B 3 3 0, 1 , Z 0 B 0, 1 ; OUTA= ( a, b); OUTB= ( c, d); a resp. c are either 0 or 1 with unknown weighs (probabilities) [2] Taking into consideration the Laplacean principle of insufficient evidence, one can expect probability ½. [3] (A trivial case) Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Complex Interfaces - IF Conjugation - Construction of the Example – Irregular IF (2) Significant change of the goal seeking ability of both systems occurs if these systems share their IF in spite of the same uncertainties as in (1). Four possible situations are to be discussed[1]: (i. ) OUTA = OUTB = (0, b, 0, d): For System A the frequency of reaching the goal dynamically[2] is similar as for regular IF (5. 3. 2. (1)) For System B the frequency of reaching the goal dynamically is higher then in the case 5. 3. 3. (1) (ii. ) OUTA = OUTB = (0, b, 1, d): System A reaches the goal absolutely, but without any control via inputs. For System B the frequency of reaching the goal dynamically is higher then in the case (i. )[3] (iii. ) OUTA = OUTB = (1, b, 0, d): 0 A 1 A 2 RA b 1 d B 1 B 2 RB A B 3 3 The same results as in the case (ii. ) (iv. ) OUTA = OUTB = (1, b, 1, d): System A reaches the goal absolutely, but without any control via inputs. For System B the frequency of reaching the goal dynamically is higher then in the case 5. 3. 3. (1)_______ [1] (Both subsystems A and B are binary ones. ) [2] (i. e. the frequency of validity of the expression: b d =1) [3] (stationary state is 0, 5; in fact without any control via inputs) Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Complex Interfaces - IF Conjugation - Construction of the Example - Discussion The implication of this simple example is straightforward: The presented constructive example shows us that there is a nonzero chance to find the doubles of systems[1] for which the sharing of IF improves the efficiency of the goal seeking processes[2]. It could be true even for the IF affected by uncertainty. Such a double of systems can constitute System Alliance, if either self-ordering or controlled ordering[3] processes occur within the respective systems or systems environment. An analogical result could be found when taking into account another important component of the system identity - strong processes, as well. Therefore, it is reasonable to study the shared IF (with conjugate irregularities) in Systems Alliances as a distinguished case, owing to new both quantitative and qualitative aspects. [1] (even with different identities) [2] There is of course also a nonzero chance to find the doubles of systems for which the sharing of IF worsens the efficiency of goal seeking processes. This fact is not any real objection against our result, as the process of IF sharing (the emergence of the conjugate irregularities) originates only if it actually has the positive global (for the Systems Alliance as a whole) effect. [3] (diagnostics and repair subsystems, e. g. ) Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Complex Interfaces - References 1. 2. 3. 4. 5. 6. 7. 8. Vlček J. : System Engineering, ed. CTU in Prague 1999. (in Czech) Klir G. J. : Facets of System Sciences, 2 nd edition, Kluver Academic / Plenum Publ. , New York, 2001 Vlček J. et at. : Reliability of Hybrid System, Research report No. : K 620 163 / 02 (in Czech) , CTU, Faculty of Transportation Sciences (Revised and extended version in English will be published in 2005) Votruba Z. , Novák M. : An Approach to the Analysis and Prediction of the Complex Heterogeneous Systems Evolution, Technical University Košice, Slovak Republic, October 2000 Votruba Z, Novák M, Voráčová Š. : Problem of dimensionality in predictive diagnostics, Neural Network World, 4/03, 2003 Novák M. : Theory of system tolerances, (in Czech), Academia, Prague, 1987 Novák M. , Šebesta V. , Votruba Z. : Safety and reliability , CTU 2004 (in Czech) Novák M. : Theory of Reliable Systems Based on Tolerance Prediction, Dexa'93, Prague, Czech Republic, September 6 -8, 1993 Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Complex Interfaces - References 9. 10. 11. 12. 13. 14. 15. Mitaim S. , Kosko B. : The Shape of Fuzzy Sets in Adaptive Function Approximation IEEE Trans. on Fuzzy Systems, Vol. 9, No. 4, Aug. 2001 Klir G. J. : Uncertainty in System Science, (invited lecture) CTU in Prague, Faculty of Transportation Sciences, Nov. 11, 03. Hopcroft, J. , Ullman, J. : Formal Languages and their Relations to Automata, Addison-Wesley, Reading, Mass. , U. S. A. , 1969. Votruba, Z. et al. : System analysis (in Czech - Systémová analýza) CTU 2004 Veselý, J: System Interface (in Czech) Prague, Academia 1983 Veselý, J: Chaos theory and Synergetics in Transport Engineering Informatics (Research Report CTU, Faculty of Transportation Sciences, May 2003, in Czech) Votruba, Z. , Novák, M. Veselý, J. : Reliability of Interfaces in Complex Systems Transtec Athens, Sept. 2004 Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Reliability of Information Power - Introduction A knowledge of the processes analysis and control in complex systems (for example the ones of transportation or telecommunication nature) remains still unsatisfactory in spite of significant and continuous progress in Systems Sciences and Systems Engineering. There are several factors affecting this situation most significant being the following ones: Unavoidable and omnipresent uncertainty which is marked by different causes and modes. Uncertainty could be identified both on the levels of original / object and system / model 1. Complexity of the effects on systems interfaces 14. Vague identification of the relevant information subsystems and significant (“strong”) information processes. Holistic nature of the systems resulting in poor efficiency or even the non-relevance of available, mostly reductionistic approaches. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Reliability of Information Power - Introduction That is probably the reason why soft methodologies are widely and more or less successfully used 16. On the other hand, soft methodologies are too subject – sensitive and suffer from serious disadvantages: They cannot be expressed in regular algorithmic way. It is very frequently impossible to measure their efficiency or even to mutually compare different results obtained. The results cannot be transferred and generalized. Strong demand for alternative “non – soft” approaches is therefore obvious. Presented Chapter is a contribution to the task of an analysis and control of processes in complex heterogeneous Systems and Systems Alliances. It is focused on a particular problem - Reliability of Information Power. Constructive approach is used. Unavoidable prerequisite is an introduction of the core concepts, i. e. : Reliability, Homogenization, and Information Power. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Reliability of Information Power A. Reliability of the system element or a system as a whole in the finite deterministic automaton[1] (FDA) representation can be defined as a probability of the correct carrying out of the respective FDA mapping functions. An obvious scheme may be determined as follows: Choosing reference FDA functions. Defining / discovering (on the experimental background) the probability of the event the respective FDA function follows this chosen reference. The second step is often a very difficult one. FDA : = (X, Z, Z 0, Y, , ) X, Z, Y are finite, non-empty sets of inputs, internal states and outputs respectively, Z 0 (subset of Z ) is initial (starting) state of the automaton, : transfer function (mapping) Z x X Z, : is output function (mapping) Z x X Y, [1] Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Reliability of Information Power B Reliability of a system can be defined in several ways 1. From the pragmatic point of view the following scheme is often preferred: Choose the process[2] of interest. Choose reference characteristics of this process. Define / discover (on the experimental background) the probability of the event that the chosen process follows the reference characteristics. Strong and goal seeking processes are frequently of interest. Obviously the second and the third steps are both difficult and tedious. Specification of reliability on this level needs the knowledge of: Systems structure] Detailed course of the chosen process Particular reliabilities of the systems elements activated in the course of the process. This concept of Systems Reliability is an equivalent to the Probability of reference carrying - out of certain chosen process. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Reliability of Information Power Extended definition of the system 15. : S : = (A/F, R/P, M, , , I) A/F is a set of systems elements A holding systems functions F; R/P is a set of systems relations R described by parameters P M is the magnitude (cardinality) of the set of systems processes is the set of goal – seeking processes is the set of strong (genetic) processes I is the systems identity Process: = ordered set of events; Event: = transition of system OR transition of systems element OR a change of systems structure OR a step of external time. Systems Structure: St : = (A, (ai, aj )); i , j = 1, 2, . . . . n; Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Reliability of Information Power C. Reliability of Complex Heterogeneous Systems (e. g. Hybrid Systems, Systems Alliances or Virtual Systems) holds some specific features: vague identification of a strong process of reference, difficult determination / measurement of particular systems elements reliabilities, non-regularity of significant systems interfaces, strong coupling among particular systems elements resulting in complex expressions of particular reliabilities as conditional probabilities, significant systems uncertainty. That is the reason why the concept of Systems Reliability being expressed in terms of probabilities becomes unpractical or even useless. Instead of it a distance of two processes in state-space, i. e. the reference process and the actual one, can be used as a measure of reliability. There at least three approaches within the body of Systems analysis how to measure this distance 3. An alternative approach is based on the measuring of the distance of the process from the boundary of the “region of acceptability” in state - space). Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Reliability of Information Power Information exchange is anchored within reality. The reality is a System composed of three entities R (M, E, I) 1. (Stonier) These elements are mutually irreducible, but there are relations of equivalence among all of them. Within the area of competence of informatics the equation: IR = IM IE II is valid. (IM, IE, II are information reflections of M, E, I, respectively while means Cartesian product). Information could act as a trigger of action. The problem of an origin of relation between information and (physical) action resulting alternatively in decrease or increase of system entropy remains unsolved. [1] M…mass; E…. energy; I…. information Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Reliability of Information Power Information power (IP): (measurable entity in state space (M, E, I), in the analogy to the basic type of automaton) IP : = I S 0 Sk, where S 0 : = (M, E, I) Value of IP: S 0 - Sk The alternatives of evaluation of IP In semantics M, E, I : transitions of states in state space changes in the contribution of S 0 to identity changes of knowledge (epistemological scale) IP can also be distinguished in grades of quality I (data / information / knowledge /. . etc. ). Quality of IP lies within the interval between total chaos and ideal order. IP is measurable from the changes of Systems Time: Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Reliability of Information Power – IP measurement Idealized example of the IP of a single Information on System f t 0 t f: mean frequency of systems events. In the time t 0 system “captured“ reference information I (contamination). Blue curve represents time – limited response, while red curve represents either chaotization or triggering of some control process Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Reliability of Information Power IP / ordering Substantial output of IP analysis should be determination of the sign of ordering function of IP. Unfortunately even after more then 4 years of effort, this problem has remained unsolved. Approaches to the IP analysis There have been two basic approaches to the IP study so far: Multilanguage approach Structured approach The Multilanguage approach is based on the notion that there is equivalence between automaton and a certain language 4 The respective chain of thoughts could be as follows: Structured System is composed of ordered (connected) elements The elements are identified as automata Multilanguage composed of particular languages can be associated with the System Structural System relations and relations System – Neighborhood as well define constrains to the syntax of this Multilanguage and to the rules of the semantics transforms. IP is a measure of the efficiency of Multilanguage translation. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Reliability of Information Power This approach is quite universal. The main problem of this approach from the application point of view comes from the fact that incomplete and uncertain grammars of these languages are very often met. Neither a theory, nor a set of typical tasks with these groups of grammars have been elaborated into sufficient depth. Multilanguage interpretation can be complete, incomplete or alternative. IP is mediated in at least two languages: Language of the respective system Language of environment. Structured approach means to dynamically analyze: Functions of elements Structure of System, inclusive respective sensitivities Regularities of Important complex interfaces. Basic Concepts of IP Reliability An analysis of IP means at the basic level the analysis of reliability and efficiency of processes of the System being activated by input information. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Reliability of Information Power Reliability of Complex Heterogeneous Systems In Complex Heterogeneous Systems owing the significant degree of uncertainty neither the Multilanguage, nor the Structural Analysis could be done correctly, eventually real information value of such analyses could be poor. For example it could be impossible to distinguish, if the change of the frequency of system time is the manifestation of the ordering or chaotization. From the engineering point of view it seems to be obvious that reliability of the systems transition to the chaotic processes is nonsense. As a result, either sophisticated concept of structured reliability must be introduced 6 , or the shift to a higher degree of abstraction should be tried. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Reliability of Information Power. - Systems Abstraction System approach to the reliability of information power is more complex. Reliability subjected to the proposed study is the reliability of a model, following the scheme: (M, E, I) I(M, E, I) What kind of a model is? It has to be both the model of the object reliability and the model of system features of the object. Reliability of the model is then introduced as the probability of isomorphic relation: OBJECT MODEL in these systems features. System features of the original (real) object could be determined within the framework of Systems Theory as dynamical goals: Location inside the both specified space - time interval and state –space area (Systems Reliability Theory defines this area as a “Region of Acceptability”. ). Strengthening or at least conservation of the position of the object in (dynamically changing) environment. (H, E, I) I(H, E, I) Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Reliability of Information Power. - Systems Abstraction Identity System identity is the entity, introduced by Vlček et al. 15 to express (in as compact form as possible) the relation of the complex system with the neighborhood. The identity is defined at two basic levels: (A) Internal, (B) External. A Level is constructed in the dimensions of type, uncertainty and relative weight of goal – oriented processes. B Level is expressed in the dimensions that reflect the impact of the system to the neighborhood. Quantitative construction of Identity forms a 7 dimensional vector Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Reliability of Information Power. - Systems Abstraction 1. 2. 3. 4. 5. 6. 7. “Tuning”: Tu = IFR / IF, where IFR means the number of all regular interfaces in the respective system, while IF means total number of interfaces in this system “Type”: Tp = / M, where means the number of strong processes in the system of interest, while M means systems magnitude. “Goal - weight”: Gw = / M, where means the number of goal - oriented processes in the system of interest, while M means systems magnitude. “Goal – stability”: Gs = 1 – D ( ), where D ( ) means the averaged dispersion of goal - oriented processes in the system of interest. “Extrovert orientation” : Ex = OUT / (IN+OUT), where OUT is total number of output states[2] of the system of interest, while (IN+OUT) is total number of the states of the system boundary elements. “Importance” (for the higher system HS) : Im. HS = OUT / HS , where OUT is the number of output states of the strong processes of the system of interest, participating in the same time in the strong processes of the higher system HS, and HS is the total number of strong processes of HS. “Coherence of goals” (with higher system HS) : Cg. HS = OUT / HS where OUT is the number of output states of the goal - oriented processes of the system of interest, participating in the same time on goal - oriented processes of the higher system HS, and HS is the total number of goal - oriented processes of HS. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Reliability of Information Power - Architecture in a general sense could be introduced as a constructed teleological system model of the object of interest with two key features: Existence within specified (abstract) space Carrying – out defined or identified systems function. Architecture can also be constructed as a weighted unification of a triple of system models Object (what) Infrastructure (where, when – in relation with a higher system) Aim (how, why – in relation with the subject – systems analytics). O I Common understanding of architecture prioritizes the second point. A Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Reliability of Information Power - Interoperability This concept is quite frequent in “European” materials. It is defined within European standards as well. Unfortunately, there are many slightly different definitions which are mutually hardly compatible. Evidently the dominant feature of interoperable systems is reliability (of representation) of standard execution of strong systems processes. If the problem is analyzed on the interface level of distinction, interoperability could be understood as a unique feature of the system in which acceptable degradation of all systems interfaces which participate in the execution of strong processes occurs. The concept of interoperability is therefore equivalent to the at least “weak regularity” of interfaces between strong systems elements. The specific European problem is the interoperability of the existing systems (for example of telecommunication or transportation nature). From the existing “menu” of regularization procedures only the insertion of conversion element is feasible. That is probably why the reaching of the interoperability in the European context is so difficult and quite often also uneconomical task. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Reliability of Information Power - Systems Abstraction Construction of Systems Approach to the Reliability of Information Power Systems constrains: ”Location in space-time and state-space” and identity could be integrated into the concept of identity of architecture. Systems constrains: ”Location in space-time and state-space” and interoperability could be integrated into the concept of interoperability of architecture. The respective sequences of representations are then: Object Architecture Identity of Architecture or Object Architecture Interoperability of Architecture Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Reliability of Information Power - Systems Abstraction Reliability of Information Power could be then recognized alternatively as: Reliability (of representation) of the Identity of Architecture Reliability (of representation) of the Interoperability of Architecture. The first construction is more powerful and accurate. It is the consequence of the rich and more accurate semantics of the concept of Identity. Let us accept it. Reliability of IP could be then decomposed into (the representations of) three components: model of space-time. model of the evolution of identity. model of the evolution of strategic state of identity. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Construction of Systems Approach to the Reliability of IP Reliabilities of these models (and also the reliability of their chaining) could then be deduced from reliability of translation (interpretation) of the respective Multilanguage, and this concept could be further related with the completeness of grammars. The reason is obvious: These models originate in the respective system Multilanguage. Gross scale understanding of the problem could be gained if the function is introduced and utilized. function is the difference of (actual) identity and strategic identity of the system of interest. = Id (t) – St. Id (t) From the mathematics point of view is a well defined function. Both actual and strategic identity are vectors of the same dimension. Time evolution of strategic identity is usually slower then the evolution of actual identity. Both these variables depend on time. Ordering effect of IP is expressed in the approaching of function to zero. Lim = 0 t Time evolution of expresses at this higher level of abstraction reliability of IP. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Reliability of IP - References 1. 2. 3. 4. 5. 6. 7. Vlček, J. a kol. : Res. Rpt. : K 620 163 / 02 “ Analysis of Reliability of Large hybrid Systems“ (in Czech) Brandejský T. , Moos P. , Novák M. , Vlček J. , Votruba Z. : Informační výkon (in Czech) – Information Power, ČVUT 2002; (abridged: Votruba, Z. , Moos, P. , Information Power, Proc. CE I Conference Herl'any 1999, Slovak rep. ) Votruba, Z. a kol. : Systémová analýza (in Czech) - Systems Analysis ČVUT 2004 Hopcroft, J. , Ullman, J. : Formal Languages and their Relations to Automata, Addison-Wesley, Reading, Mass. , U. S. A. , 1969. Klir G. J. : Facets of Systems Sciences, Plenum New York, 1991 Novák M. , Šebesta V. , Votruba Z. : Bezpečnost a spolehlivost systémů (in Czech) – Reliability and Security of Systems, ČVUT 2004 Novák M. , Faber J. , Votruba Z. : Problems of Reliability in Interactions between Human Subjects and Artificial Systems, Monographs NNW, Praha 2004 Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Reliability of IP - References 8. 9. 10. 11. 12. 13. 14. 15. 16. Stonier T. : Information and the Internal Structure of the Universe, Springer 1990 Brillouin. L. : Science and Information Theory, Academic Press, New York, 1956 Prigogine I. , Stengers I. : Order out of Chaos, Bantam Books, Toronto, 1984 Novák M. , Votruba Z. : System Theory Approach to the Hybrid System Lifetime Analysis and Prediction. CCSC `99 Multiconference, Athény 1999. Votruba Z. Chaos a jazyk identity objektu( in Czech) – Chaos and the Language of Object Identity Vlček Seminar 13. 3. 2001 (revised 2001 -04 -10). Votruba Z. , Novák M. On Homogenisation of Heterogeneous Whole, Konference CCSC Crete 2001 Votruba Z. , Novák M. Veselý J. Reliability of Interfaces in Complex Systems, Konference TRANSTEC Atheny 2004 Vlček J. Systémové inženýrství (in Czech) – Systems Engineering, ČVUT 1999 Checkland, P. , Scholes, J. : Soft system metodology in action. Chichester. John Wiley 1990. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Scheme of an alliance , P Q NS RP Aliance Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

State – of – the Art An Alliance of (two) Systems originates as follows: A Product of Random Encounter 1 An Outcome of processes of Contamination and Immunity 1, 2 A Construct. The Alliance should be identified as follows: Multi-system (i. e. the Set of Systems; it need not to have either common characteristics of species (genetic code), or common Goals, or common Identity) Hybrid System Virtual System Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

State – of – the Art The principle of the forming of Systems Alliance has been explained utilizing the concepts of Information Power (IP) and Multilingual Translation Efficiency (MLE), respectively. An illustration of basic phenomena resulting in the emergence of Alliance could be based on the concepts of Interface Sharing, and Irregularities Conjugation, as well. Synergic phenomena of Interface Sharing and Irregularities Conjugation are so significant that they could be used as the definition characteristics of the Alliance. An emergence of these phenomena results in the improvement of the regularity of the interfaces either mutually among the systems which take part in the Alliance or between the Alliance as a whole and its neighborhood (or Super – system). The secondary effect is an improvement of the efficiency of the resources utilization 2. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

State – of – the Art Language model of the Alliance makes possible the quantitative evaluation of processes. The basic ideas of the respective construct are as follows: 1. Any system taking part in the Alliance is expressed in respective language with multi - grammar (The relations within these systems are expressed in mutual translations of particular languages of systems elements). 2. The relations of any system participating in Alliance against the Super – system (i. e. the higher system the Alliance exists within) are performed in mutual translation of boundary elements languages into the language of the respective Super – system. 3. The mutual relations of the Systems taking part in Alliance are reflected in mutual translation of the languages of the respective boundary systems elements (the paradigm of generalized Huygens principle 8 ). 4. The Alliance manifests itself in more complete and / or more efficient translation of the Alliance language into the language of Super – system in comparison with the independent translations of the languages of Systems taking part in Alliance. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

State – of – the Art The critical interfaces within the Alliance should be modeled by the fictitious deterministic automaton 16, 17, 22. This model makes possible to take into consideration uncertainties which could be connected with irregularities of interfaces. The same model is capable to present the irregularities conjugation as well. The transform (simplification) of this model into multidimensional, purely geometrical model of interface makes possible to explain (within the frame of the model prerequisites) the well – known phenomenon, the “curse of dimensionality” (e. g. with non - negligible link to the famous principle of Occam s Razor). The problem of Interface dimensionality has been discussed recently in 16 - 22. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

State – of – the Art Alliances and the Information Power: Alliances forming are causally joined with the receiving and processing of information. (The concept of Information field is occasionally introduced in this context. ) In the dissipative environment it is the condition sine qua non for the plain existence of Alliance. The impact of the information received can be measured utilizing the concept of Information Power (IP is defined as the integral response of the Systems time to the information received. ) At this level we cannot distinguish if the resulting effect is the randomizing or ordering one. In Alliances it means if the sharing of interface increases or decreases its regularity. (It can be distinguished at the higher level of abstraction and within the frame of constructive approach only 9, 22 . ) Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

State – of – the Art The results of experiments on various real objects (laser cooling, control of traffic, social preferences…) support the idea that the ordering can easily flip into chaos, et vice versa. The results are very sensitive on “phase” i. e. on the actual time delay with which information received is transformed into the run of system time. This notion resulted in the first trials to construct “phase sensitive” systems modeling methodologies which could be able to respect this effect. There is probably not a matter of chance that this experimental methodology has some similarities with the models of quantum physics. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

State – of – the Art Reliability of Alliances: To solve pragmatic task of Systems Alliances Reliability, specific tools of predictive diagnostics are to be dynamically utilized for: Analyses of external factors affecting the alliance Diagnosis of the actual state of all systems the alliance is composed of Analysis of the limits of acceptability of alliance components Prediction of the state trajectories (life curves) of these components Evaluation of the actual distances of these state trajectories from boundaries of acceptability Execution of the set of corrective processes (if necessary), or the processes of graceful degradation, or even the processes of “apoptosis”. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

State – of – the Art Could the complete information on Alliance be extracted from interfaces? This question is of fundamental pragmatic value. If the answer is positive, then solely the actual state of the alliance interfaces has to be monitored in order to be able to control the alliance processes and fabric (e. g. via virtual diagnostic sensors). The problems, even in the positive case, are foreseen with dynamics of the monitoring and control. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

I. Construction and Verification of the Dynamic Multilingual Model of Systems Alliance Language representation of the Alliance of (two) Systems (P, Q): Any of the particular systems (P, Q) is equivalent to the set of languages of its elements (automata), and respective set of the rules of mutual translations. For the brevity a concept of System Multilanguage is introduced (Relations within both systems are represented by mutual translations of languages of particular systems elements. ). Eventual irregularities of particular interfaces or conflicts in rules, or alternative types of uncertainty result in incompleteness of the System Multilanguage Grammar. Nevertheless, the existence of Generic characteristics of the system (genetic code), Systems Identity, and Systems Architecture, Sets additional prerequisites which could make possible the correct translation, of course at the expense of higher consumption of systems resources (e. g. time, energy, structure redundancy…). Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

I. Construction and Verification of the Dynamic Multilingual Model of Systems Alliance Relations of both particular systems (P, Q) to the higher system (Super –system) SS are reflected in translations of the boundary elements into the language of Super-system SS (if some - probably plausible - limitations of generality are valid). Mutual relations of the systems P, Q are analogically described by mutual translations of respective boundary elements of the both systems. Alliance (P, Q) have generally not to be a System. (Significant feature being in such a case the absence of Systems Identity). That is why the obvious Systems prerequisites and limiting conditions on respective languages cannot be utilized. On the other hand we could expect that the emergence of the Interfaces Irregularities Conjugation results in more efficient and more complete translation of the language of the double systems (P, Q) into the language of Super – system SS, et vice versa, in the comparison with simultaneous translations of languages of systems P SS resp. Q SS. These specific features of the Systems Alliance Languages are to be taken into account in the process of model construction. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

II. Analysis of the Translation Processes of the Alliance Languages owing Incomplete Grammars To construct Dynamic Multilingual Model of Systems Alliance some preliminary analyses are to be carried out. Most important of them is probably a detailed in depth analysis of the dynamics of processes of translation / interpretation of languages with incomplete grammars. Preliminary considerations done in our previous studies indicated that correct translation was often feasible even if the significant incompleteness both in grammars (rules and alphabets) and semantics occurs. Nevertheless, the dynamics of processes of translation / interpretation could be unacceptably poor. Such an adverse example could be the nesting of three iterative processes of the searching of appropriate doubles of mutually corresponding “free” rules, alphabets and “tuning” of the pertinent semantics. To obtain satisfactorily efficiency of these processes, an analysis of potential parallelism or concurrence has to be done. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

III. Working out of the “Phase Sensitive” Model of the Alliance Interface Models of Interface studied till now 17 - 20, 22 , as well as interesting results of many experiments done with real objects indicate surprisingly high sensitivity of interface behavior on “phase” i. e. on the actual time delay with which information received is transformed into the run of system time. That was why initial trials of modeling of these phenomena, till now at the signal-like representation, have been done recently 11 - 14. Further refining or even complete re-construction of these models is planned within the presented project as an important and demanding part of the study of Alliance dynamics. One (rather conservative) approach could stem from the refining of the “Fictitious Deterministic Automaton” (FDA) model of interface 22 via introduction of mapping functions and as the complex ones. An alternative approach should utilize the principles of the Quantum Computation Theory. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

IV. Verification of the Methodologies of Systems Alliances Analysis on the background of Genetic Approaches (GA) and Artificial Neural Networks (ANN) Significant uncertainty originating in missing or unreliable information to disposal in SS or even in the Systems Universe is a quite common situation in System Alliances. The utilization of GA and / or ANN is frequent and quite successful in analogical situations within the Computer Science. That is why the experimental verification of these approaches for the study and modeling of Systems Alliances is the subject of interest and expectation. The methodology based on GA or ANN and /or the fusion of them will be experimentally evaluated and verified. In the case the obtained results would be encouraging the methodology should be utilized as the support, or even the component of the Dynamic Multilingual Model of Systems Alliance (Chapter I. ). Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

V. Formulating the Prerequisites and Conditions of the Systems Alliance Efficiency utilizing the Concept of Information Power. Both dynamics and efficiency are important characteristics of the Systems Alliance. While dynamics is tightly connected with Systems Times (and consequently with the Information Power) of the particular systems composing the Alliance 2, 22 (e. g. P, Q), the situation concerning the efficiency of Alliance is significantly more complex. On the other hand the efficiency as a result of Alliance Synergic Processes is always of high importance, as well. The study of the Alliance existing in the information field (which is able to “generate” Information Power) could result in the deeper understanding of Systems Alliance homeostasis and / or survival. The aim of this study will be the specification of prerequisites and conditions the processes within the Alliance have to fulfill in order to reach both sufficient dynamics and efficiency of the Alliance. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Goals of the Project: 1. 2. 3. 4. 5. Construction and Verification of the Dynamic Multilingual Model of Systems Alliance +UI Analysis of the Translation Processes of the Alliance Languages owing Incomplete Grammars Working out of the “Phase Sensitive” Model of the Alliance Interface Verification of the Methodologies of Systems Alliances Analysis on the background of Genetic Approaches and Artificial Neural Networks +UI Formulating the Prerequisites and Conditions of the Systems Alliance Efficiency utilizing the Concept of Information Power. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

References [1]…Vlček J. : Systémové inženýrství, vydavatelství ČVUT Praha 1999 [2]…Vlček J. a kol. Spolehlivost hybridního systému. Výzkumná zpráva č. K 614 – 01/2001. Katedra automatizace v dopravě a telekomunikacích, ČVUT v Praze, Fakulta dopravní. [3]…Vlček J. : Návrh struktury konstruktivní teorie hybridních systémů, Vlčkův seminář, FD ČVUT, Praha, květen, červen 2001 [4]…Novák M. , Přenosil V. Svítek M. , Votruba Z. : Problémy spolehlivosti, životnosti a bezpečnosti systémů, Monografie Neural Network World, No. 3, Prague, 2005, ISBN 80 -903298 -2 -9 [5]… Novák M. , Votruba Z: Complex Uncertain Interfaces, 7 th WSEAS Int. Conf. on AUTOMATIC CONTROL, MODELLING and SIMULATION (ACMOS '05), March, 13 -15, 2005, Prague [6]… Novák M. , Faber J. , Votruba Z. : Theoretical and Practical Problems of EEG based Analysis of Human – System Interaction, Proceedings of the International Conference on Mathematics and Engineering. Techniques in Medicine and Biological Sciences METMBS´ 03, Las Vegas, Nevada, USA, June 23 -26, 2003, pp. 247 -259 [7]…Vysoký P. : Vestavěné (embedded) systémy v současném automobilu jako alianční systémy, Vlčkův seminář, FD ČVUT, Praha, 3. 11. 2005 8. . Bowden, K. , Huygens Principle, Physics and Computers, International J. of General Systems, 1998, vol. 27, pp. 9 - 32 [9]…Votruba Z. , Systems Ideas for Transportation, plenary invited lecture, WSEAS Malta 2005_09_15 [10]…Votruba Z. , Aliance 05, Vlčkův seminář 12/05 [11]…Svítek M. , Dynamic Systems with Reduced Dimensionality, Monografie NNW, 2005 12 …Svítek, M. Probabilistic theory of multi-models In: Proceedings of the 5 th WSEAS/IASME International Conference on Systems Theory and Scientific Computation [CD-ROM]. Athens: WSEAS, 2005, ISBN 960 -8457 -35 -1. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

References 13 …Svítek, M. System representation by a set of low dimensional models In: Proceedings of the 5 th WSEAS/IASME International Conference on Systems Theory and Scientific Computation [CD-ROM]. Athens: WSEAS, 2005, ISBN 960 -8457 -35 -1. 14 …Svítek, M. The Decomposition Theory of LTI Systems In: Neural Network World. 2004, vol. 14, no. 6, pp. 489 -506. ISSN 1210 -0552. 14 a …Faber, J. Isagogé to Non-linear Dynamics of Formators and Complexes in the CNS 1. ed. Praha: Karolinum, 2003. 125 p. ISBN 80 -246 -0755 -7. 15 …Votruba, Z. - Kopecký, F. Problematika rozhraní v ITS In: Věda o dopravě 2004. Praha: Vydavatelství ČVUT, 2004, pp 93 -100. ISBN 80 -01 -03047 -4. 16 …Votruba, Z. - Novák, M. - Veselý, J. An Example of Interface Irregularities Conjugation In: Proceedings of the Sixth International Scientific Conference Electronic Computers and Informatics ECI 2004. Košice: Department of Computers and Informatics of FEI, Technical University Košice, 2004, pp 61 -65. ISBN 80 -8073 -150 -0. 17 …Votruba, Z. - Novák, M. - Veselý, J. Reliability of Interfaces in Complex Systems In: TRANSTEC 2004 The Transport Science & Technology Congress [CD-ROM]. Athens: Ministerstvo turismu Řecko, 2004, vol. 1, pp. 158 -165. 18 …Votruba, Z. - Novák, M. Dimensionality / Uncertainty Problem of Complex Interfaces In: Digest of the Proceedings of the WSEAS Conferences [CD-ROM]. Athens: Nikos Mastorakis, 2003, vol. 1, pp. 1 -4. 19 …Votruba, Z. - Novák, M. - Voráčová, Š. Problems of Dimensionality in Predictive Diagnostics In: Neural Network World 2003. Piacenta: ICS UNIDO, 2003, vol. 1, pp. 385392. 20 …Votruba, Z. - Novák, M. - Veselý, J. Reliability of interfaces in complex systems In: Neural Network World. 2004, vol. 14, no. 3 -4, p. 337 -352. ISSN 1210 -0552. 21 …Veselý, J. Systémový koncept rozhraní [Výzkumná zpráva]. Praha: ČVUT, Fakulta dopravní, 2005. LSS 224/05. 34 p. 22 …Votruba, Z. Reliability of Information Power [Professor Lecture]. Praha: ČVUT, Fakulta dopravní, 2005. 32 p. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics