Identification of Hybrid Bimodal Piecewise Affine Systems via Minimal Control Synthesis Adaptive Control

This paper is concerned with the design of a novel Model Reference Adaptive Control (MRAC) strategy for the control and identification of bimodal Piecewise Affine (PWA) systems. The control strategy is an extension of the family of Minimal Control Synthesis (MCS) adaptive controllers which has been successfully applied to a vast number of real applications. The resulting control strategy consists of a feedforward and a feedback action whose gains switch according to the phase space regions visited by the plant and reference model. The strategy allows for the reference model to be smooth or piecewise-affine and is shown analytically to guarantee asymptotic tracking of the reference model trajectories without requiring a priori knowledge of the plant matrices. The novel MCS approach presented in this paper is also shown to be an effective identification tool to estimate the matrices of a PWA plant by exploiting in reverse the time evolution of the adaptive gains necessary for its control.