Model Reference Adaptive Control of Piecewise Affine Systems and Applications
Montanaro, Umberto (2009) Model Reference Adaptive Control of Piecewise Affine Systems and Applications. [Tesi di dottorato] (Inedito)
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An increasing number of devices in engineering and applied science is modelled by piecewise affine (PWA) sets of ODEs changing configuration according to the phase space region (or domain) visited by their trajectories. Given the wide range of applications of PWA systems, several strategies have been proposed to analyze their properties and control their dynamics. From a control viewpoint, several techniques have been presented to stabilize and control the dynamics of systems described by PWA ODEs based on a number of different approaches. Typically, these strategies extend to this class of systems methodologies previously developed for smooth dynamical systems. As is typical in control, an important issue is for the control action to provide a certain amount of robustness with respect to time-varying parameter uncertainties and unmodelled dynamics. Traditionally, in the case of smooth dynamical systems, adaptive controllers have been used in order to achieve this objective. Surprisingly, despite the wide range of potential applications, little attempts have been made in the existing literature to develop a generic adaptive control framework for PWA systems. The aim of this thesis is to develop adaptive switched control strategies for both piecewise affine systems and LTI systems characterized by uncertain parameters. Different approaches based on more traditional adaptive laws and new hybrid strategies will be proposed and tested on different case studies in applications.
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