### An Approximate Dynamic Programming Approach to Decentralized Control of Stochastic Systems

• R. Cogill, M. Rotkowitz, B. Van Roy and S. Lall.
• Lecture Notes in Control and Information Sciences, Vol. 329. Control of Uncertain Systems: Modelling, Approximation, and Design, p. 243--256, 2006.
We consider the problem of computing decentralized control policies for stochastic systems with finite state and action spaces. Synthesis of optimal decentralized policies for such problems is known to be NP-hard \cite{Tsitsiklis85}. Here we focus on methods for efficiently computing meaningful suboptimal decentralized control policies. The algorithms we present here are based on approximation of optimal \$Q\$-functions. We show that the performance loss associated with choosing decentralized policies with respect to an approximate \$Q\$-function is related to the approximation error.