Abstract
In this article, the output feedback-based direct model reference adaptive control of piecewise affine systems and its parameter convergence are investigated. Under the slow switching assumption, it is shown that all the closed-loop signals are bounded and the output tracking error is small in the mean square sense. Built upon this result, the estimation error of controller parameters is proved to converge to a residual set if the input signal is sufficiently rich. The relationship between the size of this residual set and the switching frequency is established. Moreover, the convergence of the estimated controller parameters to their nominal values can be achieved for a certain subsystem given that this subsystem is activated for infinitely long time. Simulation results validate the effectiveness of the proposed approach.
Highlights
T HE Systems in the real world are mostly hybrid and highly nonlinear
We investigate the output feedback model reference adaptive control (MRAC) for Piecewise affine (PWA) counterparts with special focuses on the analysis of controller parameter convergence
We prove that the controller parameter estimation error converges to a bounded set given a persistently exciting (PE) reference signal
Summary
T HE Systems in the real world are mostly hybrid and highly nonlinear. The mixture of the continuous states and discrete modes as well as the system nonlinearity complicates the analysis and control design. Due to the hybrid nature of PWA systems, both the switching hyperplane estimation and the subsystem parameter identification have been explored in [5] and [6], respectively We first extend the controller proposed in [15] to the context of PWA systems and prove that the tracking error is small in the mean square sense under slow switching. Based on this result, we prove that the controller parameter estimation error converges to a bounded set given a PE reference signal.
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