Min-max quadratic cost control of systems described by approximate models

This paper considers the design of output regulators with the use of approximate models. The measure of the approximation between process and model outputs is represented by a bound in norm of the output error signals and it requires the computation of two numbers. The design is achieved with a rain-max approach where control and error signals are the two antagonists. The min-max solution is obtained as a linear function of the model state (open-loop solution). It is shown that no dosed-loop controls can improve the open-loop min-max performance. Conditions are given so as to preserve the min-max performance by means of proportional feedback of the system's output. In this case the min-max feedback law is obtained (closed-loop solution).