Parameterization of Outputs which Track to Reference Asymptotically and Are Achievable by Bounded Input

Abstract

This paper deals with trajectory tracking control for non-minimum phase systems. We first consider to characterize output such that it tracks to a given reference signal asymptotically and that the corresponding input is bounded. In particular, we parameterize the error signals between the reference and the achievable output by using Q-parameters in the frequency domain. Since the parameterized set consists of rational functions which are analytic in the closed right half plane, we can solve easily the problem to minimize theL₂norm of the error and the analytic solution of the optimal error is obtained. The optimal output is the projection of the reference to the space of achievable outputs. By using the parameterization, the simultaneous optimization of the error and the input deviation from the steady state input can be also solved. The effectiveness of the proposed method is examined by numerical examples.