Analysis and design of classes of hybrid control systems

Abstract

This thesis considers the problem of designing stabilizing controllers for hybrid systems. Generally speaking, the term hybrid systems refers to systems that exhibit interaction between continuous-time dynamics and logical events. The class of hybrid systems studied here are plants whose dynamics switch between several linear models. Control systems analysis and design is a non-trivial problem as established methods applicable to continuous-time and discrete-time systems cannot, in general, be extended to hybrid systems. This research focuses on two themes: the application of model reference adaptive control (MRAC) to hybrid systems and the stabilizeability of hybrid systems. In the first of these, we study the performance of output feedback against state feedback and free running against resettable adaptive control for single input single output (SISO) systems. Simulations reveal that output feedback and free running adaptive schemes are incapable of producing stabilizing control in some cases of hybrid systems.  Reset-table state feedback MRAC, implemented through a multiple model adaptive control structure, was found to provide very good results where the plant and reference outputs approached convergence, even in the presence of some perturbation. The problem of extending the method to multivariable hybrid systems is also investigated. Here, successful implementation of the scheme was found to depend on the decoupleability of both the plant and reference models. We propose guidelines on how this constraint may be overcome.  In the second theme, the objective was to identify the stabilizeability of hybrid systems through determination of the existence of control parameters such that all subsystems have a common Lyapunov function. Our work focussed on SISO switching systems with two continuous-time states. For systems modelled in continuous-time, we have derived a method from which this is achieved. A similar method for sampled-data systems has also been found, provided that all subsystems are modelled in the Brunovsky form

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