An adaptive controller based on disturbance attenuation

This paper discusses the control of linear systems with uncertain parameters in the control coefficient matrix, under the influence of both process and measurement noise. A disturbance attenuation approach is used, and from this a multiplayer game problem is generated. First, the minimax formulation is presented, which represents an upper bound on the game cost criterion. Second, a dynamic programming approach is used to solve the game. It is shown that for this class of problems, the controller determined from the dynamic programming approach is equivalent to the minimax controller. Therefore the minimax controller is also a saddle point strategy for the differential game. Controller development appears to be much simpler from the dynamic programming standpoint. A simple scalar example is presented