A Framework for Coordination in Distributed Stochastic Systems: Perfect State Feedback and Performance Risk Aversion

This research article considers a class of distributed stochastic systems where interconnected systems closely keep track of reference signals issued by a coordinator. Much of the existing literature concentrates on conducting decisions and control synthesis based solely on expected utilities and averaged performance. However, research in psychology and behavioral decision theory suggests that performance risk plays an important role in shaping preferences in decisions under uncertainty. Thus motivated, a new equilibrium concept, called “person-by-person equilibrium” for local best responses is proposed for analyzing signaling effects and mutual influences between an incumbent system, its coordinator, and immediate neighbors. Individual member objectives are defined by the multi-attribute utility functions that capture both performance expectation and risk measures to model the satisfaction associated with local best responses with risk-averse attitudes. The problem class and approach of coordination control of distributed stochastic systems proposed here are applicable to and exemplified in military organizations and flexibly autonomous systems.