Output Feedback Control for Uncertain Variable Structure Systems with Resets

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Discontinuous systems are studied in very different research fields such as economics, electrical circuit theory, mechanical engineering (impact theory, plasticity theory), biosciences, systems and control theory. Such systems are typically viewed as a simple model of hybrid systems, consisting of a finite family of subsystems, equipped with rules determining how to switch between them. The literature on robust control of complex nonlinear systems with set-valued equilibrium such as discontinuous systems using output information is very sparse. This project seeks to extend a framework that has been developed for output feedback control of continuous systems to robust control of complex discontinuous systems using only measured output information. The practical need for such a framework has been demonstrated by recent applications to biped robots, for example, from Chevallereau et al. (2003) and Westervelt et al. (2007) and is also supported by the needs of industry where tighter controls on efficiency are producing increasing levels of monitoring. Incorporating this information in the control loop is a natural next step and discontinuous systems often result. Theoretical developments will be facilitated by interaction between the proposed Visiting Researcher, Professor Orlov, who is a recognised expert on stability analysis and robust control synthesis of uncertain discontinuous systems within the framework of methods of nonsmooth Lyapunov functions and the PI, who is recognised for her work on robust sliding mode control and observation. The applied research will focus on the production of significant implementation studies relating to control of impact mechanical systems and the control of industrial production processes to demonstrate the efficacy of the underlying philosophy and the new design algorithms. These are pertinent design studies to inform the development of the theoretical research programme as well as being used to illustrate the research outcomes.