Minimax observers

Abstract

AbstractThis paper discusses the design of the regulator using output feedback, and describes a method of control using the observer. In the regulator using the observer, the evaluation function is increased, compared with the state‐feedback control. In this paper, the minimax evaluation is adopted, which considers the worst case in regard to the initial state. Consequently, the optimal observer, i.e., the minimax observer can be determined by the proposed method, in the sense that the worst value in regard to the initial state is minimized. Since the initial state is not known in the regulator problem using the output feedback control, the minimax evaluation is practically very important. This paper discusses first the discrete‐time system, and the design of the minimax observer is discussed for the linear quadratic form and the model‐following control problems. Then, the result of applying the idea to the continuous‐time system is shown. It is also possible to design the minimax observer for the continuous‐time system, in the same way as for the discrete‐time system. The proposed method can be applied, not only to the observer with the minimum dimension but also to the observer with the same dimension. As the numerical example, a solution of the minimum problem is presented using the proposed method.