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To develop the theory and applications of Probability Collectives (PC) for distributed optimization and control.


Complex systems are difficult to control. Distributed control is the programming of loosely coupled individual (or "local") agents to achieve a global goal. Choosing the control laws -- perhaps to satisfy multiple simultaneous objectives -- is a problem in distributed optimization.

This research project is developing a rich new theory of distributed optimization and is applying it to distributed control problems (and other tasks). The work offers major advances in many control problems of interest to NASA, the aerospace industry, and other customers. The results are being published at major conferences, and the community of collaborators is growing.


Researchers are just beginning to apply PC theory, which may have revolutionary applications in game theory and statistical mechanics as well as distributed optimization and distributed nonlinear control. Studies to date have included agent-based approaches to telecommunications, adaptive programming of nanocomputers, dynamic rescheduling, distributed design, and control of constellations of rovers.

The PI has work closely with Stefan Bieniawski at Stanford on flight control with distributed effectors, specifically real-time adaptive control of mini-flaps on trailing edges of airplane wings to minimize turbulence. A future direction for distributed optimization might be toward integrated, task-specific design of aircraft structures, systems, propulsion, aerodynamics, and control.

Other application areas include computational economics, population biology, and nonlinear time series analysis. Potential applications for control of distributed, multi-agent systems are too numerous to list. (Google search for "multi-agent systems" gives about 1.4 million hits.) Applications of gradient-based optimization and machine learning are even more numerous.


Simulation studies of Probability Collectives for machine learning and optimization have included benchmarks such as k-SAT, the N-Queens problem, bin packing, and a modification of Arthur's El Farol Bar problem. Results of the mini-flap optimization for aircraft wing turbulence suppression have drawn interest from a major aircraft manufacturer.


Principal Investigator
David Wolpert

Other Contributors
Nicolas E. Antoine (Airbus/Stanford)
Stefan Bieniawski (Stanford)
Ilan Kroo (Stanford)
Chiu Fan Lee (Oxford)
Bill Macready (Dwave Systems/NASA)
Dave Nicholson (BAE Systems)
Dev Rajnarayan (Stanford)
Charlie E. M. Strauss (LANL)


David Wolpert's Home Page
PhD Thesis on Flutter Suppression
Stanford Probability Collectives Site
Collectives Workshop, 2003
Stanford AA Design Group

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