Retrospective Cost Adaptive Control with Error-Dependent Regularization for MIMO Systems with Uncertain Nonminimum-Phase Transmission Zeros

In this paper we focus on retrospective cost adaptive control (RCAC), which is applicable to stabilization, command following, disturbance rejection, and model reference control problems for SISO and MIMO plants. RCAC uses limited modeling information, specifically, Markov parameters of the transfer function from the control input to the performance variable. Typically, a small number of Markov parameters are needed, for example, one Markov parameter usually suffices if the plant is minimum phase. If the plant is Lyapunov stable and nonminimum phase, then knowledge of the locations of the nonminimum-phase zeros is not needed as long as an error-dependent regularization term is used to weight the control effort. For plants that are both open-loop unstable and nonminimum phase, knowledge of the locations of the nonminimum-phase zeros may be needed. The goal of the present paper is to further investigate the effectiveness of the error-dependent regularization terms. Furthermore, we remove the intermediate step of reconstructing the retrospective controls and we directly update the controller. Next, we consider channelwise phase-matching conditions for MIMO plants. Finally, we investigate the role of zeros in MIMO nonsquare systems.