Decentralized chance-constrained finite-horizon
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Williams-2010-Decentralized chance-constrained finite-horizon.pdf
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238.64 KB
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Author(s)
Williams, Brian Charles
Ono, Masahiro
Date Issued
December 2010
Journal
49th IEEE Conference on Decision and Control (CDC), 2010
Publisher
Institute of Electrical and Electronics Engineers
Citation
Ono, Masahiro, and Brian C. Williams. “Decentralized Chance-constrained Finite-horizon Optimal Control for Multi-agent Systems.” 49th IEEE Conference on Decision and Control (CDC). Atlanta, GA, USA, 2010. 138-145. © 2011 IEEE
Version
Final published version
Abstract
This paper considers finite-horizon optimal control for multi-agent systems subject to additive Gaussian-distributed stochastic disturbance and a chance constraint. The problem is particularly difficult when agents are coupled through a joint chance constraint, which limits the probability of constraint violation by any of the agents in the system. Although prior approaches can solve such a problem in a centralized manner, scalability is an issue. We propose a dual decomposition-based algorithm, namely Market-based Iterative Risk Allocation (MIRA), that solves the multi-agent problem in a decentralized manner. The algorithm addresses the issue of scalability by letting each agent optimize its own control input given a fixed value of a dual variable, which is shared among agents. A central module optimizes the dual variable by solving a root-finding problem iteratively. MIRA gives exactly the same optimal solution as the centralized optimization approach since it reproduces the KKT conditions of the centralized approach. Although the algorithm has a centralized part, it typically uses less than 0.1% of the total computation time. Our approach is analogous to a price adjustment process in a competitive market called tatonnement or Walrasian auction: each agent optimizes its demand for risk at a given price, while the central module (or the market) optimizes the price of risk, which corresponds to the dual variable. We give a proof of the existence and optimality of the solution of our decentralized problem formulation, as well as a theoretical guarantee that MIRA can find the solution. The empirical results demonstrate a significant improvement in scalability.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1109/CDC.2010.5718144
