Bound Computation for Adaptive Systems VV Giampiero Campa
Bound Computation for Adaptive Systems V&V Giampiero Campa September 2008 West Virginia University September 2008 1
Relevance to NASA • Adaptive Control Systems will be needed to improve: – Autonomy/Self Reliance – Performance in unforeseen conditions – Fault Tolerance September 2008 2
Problem • DESIGN PROBLEM: Can a given adaptive dynamical systems ever exceed certain working limits as a result of its online learning mechanism ? Or in other words, can we trust adaptive systems ? • Theoretical tools to answer the above question are usually system-specific or not general enough • Limits are shown to exist but are never calculated • No software tool exist to help the control system designer in the involved tradeoffs. September 2008 3
Approach • Calculate as-general-as-possible boundedness conditions as well as bounds expressions • Perform a detailed analysis of the inherent trade offs among systems parameters and boundedness • Develop software to calculate and visualize such conditions and bounds, given a general adaptive control system. • Develop software to help the designer within the simulation and implementation phases of the adaptive control system. September 2008 4
Importance & Benefits By producing: • Clear stability and performance metrics • Computation and visualization software • Simulation and Implementation software • A of Documented Examples This research encourages a more formal design approach for adaptive systems, and has the potential of being leveraged to the next generation of aerospace vehicles, allowing more autonomy, self-reliance, and safety. September 2008 5
Accomplishments (Year 1) • The development of a Simulink Neural Network Library and preliminary analysis on the Lyapunov function have been completed. Adaline Multi Layer Perceptron Extended RBF Extended DCS September 2008 Demo 6
Accomplishments (Year 2) • Existing bound calculation procedures were considerably improved so that more accurate bounds can be calculated Tracking without adaptive control for simpler adaptive systems. 2 • A simulation involving adaptive 1 control of a simple system has 00 2 4 6 8 10 12 14 16 18 been developed: Tracking with adaptive control 2 Bounds calculated with existing formulas September 2008 Bounds calculated with new formulas 20 1 00 8 6 4 2 0 -2 -4 -60 2 4 6 8 10 12 14 16 18 20 Systems bounds with adaptive control Ellipse Center System Evolution 100 200 300 400 500 600 7
Accomplishments (Year 3) • An analysis on the variation of the parameters for bounds calculation was performed. • A new formulation was developed that allows placing separate limits for each variable in the state space as opposite of having a limit on the norm of the state vector September 2008 8
Accomplishments (Year 3) • A more complete case of study based on the dynamics of F -18 aircraft was studied. • Software for the computation of the bounds was developed. September 2008 9
Next Steps • Complete the study for the most complete case in which an observer is placed before the adaptive element. • Complete the report with the case of study. • 2 Journal papers & 1 book chapter submission. • Upload the final report along with the software. September 2008 10
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