Output feedback adaptive command following for nonminimum phase uncertain dynamical systems

Abstract

In this paper, we develop an output feedback adaptive control framework for continuous-time nonminimum phase multivariable systems for output stabilization and command following. The approach is based on a nonminimal state space realization that generates an expanded set of states using the filtered inputs and filtered outputs of the original system. Specifically, a direct adaptive controller for the nonminimal state space model is constructed using the expanded states of the nonminimal realization and is shown to be effective for multi-input, multi-output nonminimum phase systems with unstable dynamics. The adaptive controller does not require any model information except for an expanded compatibility condition involving the nonminimal model which is far less restrictive than standard matching conditions for model reference adaptive control involving the actual system dynamics. Two illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach.