Decentralized control of finite state systems: A game theoretic approach

In this paper we consider a pair of interconnected, nondeterministic and metric finite state systems and address a control problem where controllers are designed for enforcing local specifications expressed in terms of regular languages, up to a desired accuracy. The control architecture considered is decentralized, that is each controller can only communicate with the corresponding plant. Since plant systems are interconnected, the part of the specification that can be enforced on one system depends on the part that can be applied on the other one. We show how this dependency can be formalized in terms of equilibria, by extending game theory to the present framework. We introduce notions of equilibria, Nash equilibria and dominant equilibria. When controlled plants are at an equilibrium, they satisfy a part of their specification; when they are at a Nash equilibrium, deviation of each plant from its control strategy may correspond to a loss in terms of the part of specification enforced; when they are at a dominant equilibrium, there is no other equilibrium where plants can achieve larger parts of the corresponding specifications. A characterization of these notions is derived and checkable conditions are discussed. An example in the context of multi-agent systems with shared resources is also included. (c) 2025 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).