Multiagent hybrid system design using game theory and optimal control

A methodology for designing hybrid controllers for large scale, multiagent systems is presented. Our approach is based on optimal control and game theory. The hybrid design is seen as a game between two players: the control, which is to be chosen by the designer and the disturbances that encode the actions of other agents (in a multi-agent setting), the actions of high level controllers or the usual unmodeled environmental disturbances. The two players compete over cost functions that encode properties that the closed loop hybrid system needs to satisfy (e.g., safety). The control "wins" the game if it can keep the system "safe" for any allowable disturbance. The solution to the game theory problem provides the designer with continuous controllers as well as sets of safe states where the control "wins" the game. The sets of safe states are used to construct an interface to the discrete domain that guarantees the safe operation of the combined hybrid system. The design methodology is illustrated by means of examples.