An improved game theory based approach to one type of H-infinity optimal control problems

In this paper we convert H-infinity optimal control problems with linear quadratic objective functions to a regular optimal regulator problem by improving a game theory based approach (Basar and Bernhard, 1991), in which the critical lambda_infin* plays a key role. An alternative and optimal-control-related method of theoretically defining lambdacirc is presented. Instead of solving the H-infinity problem, we solve a regular optimal control problem. The relation between the optimal control strategy of the H-infinity problem and that of the related optimal regulator problem is presented and proved. Given some regularity conditions, the stability of the optimal controller is proved via a Hamiltonian system. In addition, a fast approximate procedure is also provided to calculate lambdacirc