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Controlling “Emergelent” Systems

Explore the concept of controlling emergent systems through interconnected units with sensing and actuation capabilities. Design decentralized and distributed control strategies for robust and reconfigurable systems. Use hierarchical decomposition and relaxation techniques for high-performance control in uncertain environments.

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Controlling “Emergelent” Systems

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  1. Controlling “Emergelent” Systems Raffaello D’Andrea Cornell University

  2. INTERCONNECTED SYSTEMSExample: Formation Flight Use upwash created by neighboring craft to provide extra lift

  3. Formation Flight Test-bed

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

  5. 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

  6. BASIC BUILDING BLOCK: ONE SPATIAL DIMENSION

  7. PERIODIC CONFIGURATION

  8. BOUNDARY CONDITIONS

  9. SPATIALLY CAUSAL SYSTEM

  10. “INFINITE” EXTENT SYSTEMS

  11. 2D, 2D BOUNDARY CONDITIONS

  12. 2D, 1D BOUNDARY CONDITIONS

  13. 2D, NO BOUNDARY CONDITIONS

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

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

  16. PERIODIC CONFIGURATIONS

  17. PERIODIC CONFIGURATION

  18. SPATIALLY CAUSAL SYSTEMS

  19. SPATIALLY CAUSAL SYSTEMS

  20. INFINITE EXTENT SYSTEMS

  21. INFINITE EXTENT SYSTEMS

  22. BOUNDARY CONDITIONS

  23. BOUNDARY CONDITIONS

  24. 2D, 2D BOUNDARY CONDITIONS

  25. Theorem: There exists a controller which satisfies theperformance condition if and only if there exists

  26. Properties of design • Implementation: distributed computation, limited connectivity • Finite dimensional, convexoptimization problem • Optimization problem size isindependent of the number of units • Allows for real-time re-configuration

  27. Decentralized Control Distributed Control

  28. Simulation results Worst Case L2 Design time (P3, 1.2GHz) • Distributed 0.24 60 seconds • Decentralized 1.10 15 seconds • Fully centralized 0.22 20 hours (4 wings)

  29. Intelligent Vehicle Systems

  30. Example: RoboCup • 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

  31. Objective: Develop hierarchy-based tools for designinghigh-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

  32. System Level Decomposition Vehicle Vehicle Low levelcontrol Low levelcontrol Motion planning Motion planning High-levelreasoning High-levelreasoning INFORMATION EXCHANGE

  33. Example of bottom up design Relaxation and Simplified Dynamics: Low levelcontrol Motion planning Restrict possible motions, design lower level systemsto behave like simplified dynamical model

  34. BACK-PASS PASS-PLAY

  35. Highlights

  36. 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

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