Continuous-time retrospective cost adaptive control for nonminimum-phase systems

Abstract

We present a continuous-time output-feedback direct adaptive control method to deal with command following or disturbance rejection problem for systems that are possibly nonminimum phase and exponentially unstable. The adaptive control algorithm requires knowledge of the nonminimum-phase zeros of the transfer function from the control to the output. However, the knowledge of the characteristics or measurement of the reference command and disturbance is not required. The closed-loop stability is analyzed and the convergence of tracking error is proved under assumptions. The proposed adaptive control method is an extension of discrete-time retrospective cost adaptive control to continuous-time. Interpretation of retrospective cost adaptive control is provided, which is applicable for both discrete-time and continuous-time version. Numerical examples show that the proposed adaptive control method is effective for command following problem with unmeasured reference command and, in addition, robust to errors in the nonminimum-phase zero estimates.