On Nash Equilibria for Decentralized Symbolic Control of Interconnected Finite State Systems

In this paper we consider a pair of interconnected nondeterministic and metric finite state systems and address a decentralized symbolic control problem where controllers are designed for enforcing local specifications expressed in terms of regular languages, up to a desired accuracy. The considered control architecture is decentralized, i.e. 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 one on the other system. We show how this dependency can be nicely formalized in terms of equilibria and in particular, of Nash equilibria. When controlled plants 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. Algorithms are proposed which converge, when an equilibrium exists, to Nash equilibria.