Optimal Decentralized Control of Finite Nondeterministic Systems

A control problem with a system modeled as a nondeterministic finite state machine is considered. Several agents seek to optimize the behavior of the system under a minimax criterion, with each agent having different information about the system state. The nondeterministic model of uncertainty, combined with the minimax criterion, lead to equivalence relations on the past input/output histories of each agent which generate simple sufficient statistics for the optimal control laws. This sheds light on the basic nature of decentralized control and permits complete solution of a particular class of problems.