Controlling Emergelent Systems Raffaello DAndrea Cornell University INTERCONNECTED

Controlling “Emergelent” Systems Raffaello D’Andrea Cornell University

INTERCONNECTED SYSTEMS Example: Formation Flight Use upwash created by neighboring craft to provide extra lift

Formation Flight Test-bed

Interconnected Systems • System consists of many units • Sensing and actuation exists at every unit • Units are coupled, either dynamically or through performance objectives

Some consideration for control design: • Centralized control not desirable, nor feasible. • Need tools for systems with very large number of actuators and sensors • Robustness and reconfigurability

BASIC BUILDING BLOCK: ONE SPATIAL DIMENSION

PERIODIC CONFIGURATION

BOUNDARY CONDITIONS

SPATIALLY CAUSAL SYSTEM

“INFINITE” EXTENT SYSTEMS

2 D, 2 D BOUNDARY CONDITIONS

2 D, 1 D BOUNDARY CONDITIONS

2 D, NO BOUNDARY CONDITIONS

Semi-definite Programming Approach Performance theorem: such that if there exists

BASIC BUILDING BLOCK: CONTROL DESIGN Design controller that has the same structure as plant

PERIODIC CONFIGURATIONS

PERIODIC CONFIGURATION

SPATIALLY CAUSAL SYSTEMS

SPATIALLY CAUSAL SYSTEMS

INFINITE EXTENT SYSTEMS

INFINITE EXTENT SYSTEMS

BOUNDARY CONDITIONS

BOUNDARY CONDITIONS

2 D, 2 D BOUNDARY CONDITIONS

Theorem: There exists a controller which satisfies the performance condition if and only if there exists

Properties of design • Implementation: distributed computation, limited connectivity • Finite dimensional, convex optimization problem • Optimization problem size is independent of the number of units • Allows for real-time re-configuration

Decentralized Control Distributed Control

Simulation results Worst Case L 2 Design time (P 3, 1. 2 GHz) • Distributed 0. 24 60 seconds • Decentralized 1. 10 15 seconds • Fully centralized 0. 22 20 hours (4 wings)

Intelligent Vehicle Systems

Example: Robo. Cup • International competition: cooperation, adversaries, uncertainty – 1997: Nagoya Carnegie Mellon – 1998: Paris Carnegie Mellon – 1999: Stockholm Cornell – 2000: Melbourne Cornell – 2001: Seattle Singapore – 2002: Fukuoka Cornell

Objective: Develop hierarchy-based tools for designing high-performance controlled systems in uncertain environments Approach: • System level decomposition: temporal and spatial separation • Embrace bottom up design • Simplification of models via relaxations and reduction • Propagation of uncertainty to higher levels • Adoption of heuristics, coupled with verification

System Level Decomposition Vehicle Low level control Motion planning High-level reasoning INFORMATION EXCHANGE

Example of bottom up design Relaxation and Simplified Dynamics: Low level control Motion planning Restrict possible motions, design lower level systems to behave like simplified dynamical model

BACK-PASS-PLAY

Highlights

Observations • Useful emergent behavior is the exception, not the norm • Emergent behavior, when useful, is impressive and amazing • Useful emergent behavior tends to be not very robust • Reluctant to build upon emergent behavior without “understanding” it: no notion of reconfiguration and robustness • Hierarchical decomposition, based on temporal and spatial separation, is a powerful paradigm • Good tradeoff between reliability and performance seems to occur at the limits of our knowledge