Hybrid controller design for multi-agent systems

A design and verification methodology for hybrid dynamical systems, based on optimal control and game theory, is presented. The hybrid design is seen as a game between two players. One is the disturbances that enter the dynamics. The disturbances can encode the actions of other agents (in a multi-agent setting), the actions of high level controllers or the usual unmodeled environmental disturbances. The second player is the control, which is to be chosen by the designer. The two players compete over a cost function that encodes the 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 sets can be used to construct an interface that guarantees the safe operation of the combined hybrid system.