Minimax controller design

Given a system with uncertain parameters, a performance index, and a controller structure, it is sometimes appropriate to determine the controller parameters by minimaximizing the performance index. In many of the cases where such a controller is too pessimistic it is appropriate to minimaximize a performance sensitivity. Some properties of these two types of controllers are presented. Since the minimax problems that arise do not in general have a saddle point, they must be solved by an iterative or search procedure. A new algorithm for solving algebraic minimax problems with or without a saddle point is presented and proved to converge. The rate of convergence is discussed. The algorithm is applied to the design of a controller for a string of three vehicles.