Decentralized chance-constrained finite-horizon optimal control for multi-agent systems

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 tâtonnement 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.