How can we improve adaptive control for systems with complex dynamics? This paper introduces a novel model reference adaptive control approach, inspired by Elliot's adaptive pole-placement controller (APPC) and based on retrospective cost optimization. The retrospective cost model reference adaptive control (RC-MRAC) technique is particularly designed for nonminimum-phase (NMP) systems, assuming the knowledge of NMP zeros. The goal is to provide greater control. Under this assumption, RC-MRAC offers a reduced need for persistency compared to APPC. The paper compares the performance of APPC and RC-MRAC under varying levels of persistency in the command for both minimum-phase and NMP systems. This allows an analytical comparement of the two systems. Numerical results demonstrate that RC-MRAC's model-following performance is less sensitive to command persistency than APPC, albeit at the cost of requiring knowledge of the NMP zeros. The work also shows RC-MRAC to be applicable for disturbance rejection under unknown harmonic disturbances. By introducing RC-MRAC, this research contributes to the advancement of adaptive control techniques, offering potential benefits for systems with complex dynamics and reduced persistency requirements.
Published in the International Journal of Adaptive Control and Signal Processing, this paper is precisely aligned with the journal's scope. By presenting a novel approach to model reference adaptive control, it contributes directly to the ongoing research in adaptive control techniques and signal processing, key areas of focus for the journal and its readership.