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

2. INTERCONNECTED SYSTEMS Example: 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. Performance theorem: if there exists such that Semi-definite Programming Approach

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

20. INFINITE EXTENT SYSTEMS

22. BOUNDARY CONDITIONS

24. 2D, 2D BOUNDARY CONDITIONS

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

26. 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

27. Decentralized Control Distributed Control

28. Simulation results Distributed0.24 60 seconds Decentralized1.10 15 seconds Fully centralized0.2220 hours (4 wings) Design time (P3, 1.2GHz) Worst Case L2

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. 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 Objective:

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

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

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