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UBC Theses and Dissertations

A numerical optimization approach to switching surface design for switching linear parameter-varying control Javadian, Moein


This thesis proposes an algorithm to design switching surfaces for the switching linear parameter-varying (LPV) controller with hysteresis switching. The switching surfaces are sought for to optimize the bound of the closed-loop L2-gain performance. An optimization problem is formulated with respect to parameters characterizing Lyapunov matrix variables, local controller matrix variables, and locations of the switching surfaces. Since the problem turns out to be non-convex in terms of these characterizing parameters, a numerical algorithm is given to guarantee the decrease of the cost function value after each iteration, which consists of two steps: direction selection and line search. A hybrid method which is a combination of the steepest descent method and Newton's method is employed in the direction selection step to decide the orientation of proceeding. A numerical algorithm is used to compute the most appropriate length of the proceeding along the selected direction which generates the most decrease in the cost function. To demonstrate the efficiency and usefulness of the proposed algorithm, it will be applied to three examples in control applications: a tracking problem for a mass-spring-damper system, a vibration suppression problem for a magnetically-actuated optical image stabilizer, and an air-fuel-ratio control problem for automotive engines. In these examples, it will be shown that the proposed optimization approach to the design of the switching surfaces and the switching LPV controller is superior to heuristic approaches in closed-loop performances, at the price of higher computational costs. Additionally, it will be shown that the algorithm can be applied to the general n-parameters case.

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