A Game-Theoretic Approach to Hybrid System Design

We present a design and verification methodology for hybrid dynamical systems. Our approach is based on optimal control and game theory. 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 unmodeled environmental disturbances. The second player is the control, which is to be chosen by the designer. The two players compete over cost functions that encode 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. These safe sets can be used to construct an interface that guarantees the safe operation of the combined hybrid system. Extensions of this approach can also be used for verification of hybrid systems as well as the generation of abstractions of the lower layer behavior (e.g. timed abstractions).