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Output feedback optimal guaranteed cost control of uncertain piecewise linear systems. (English) Zbl 1160.93342
Summary: This paper proposes the output feedback optimal guaranteed cost controller design method for uncertain piecewise linear systems based on the piecewise quadratic Lyapunov functions technique. By constructing piecewise quadratic Lyapunov functions for the closed-loop augmented systems, the existence of the guaranteed cost controller for closed-loop uncertain piecewise linear systems is cast as the feasibility of a set of Bilinear Matrix Inequalities (BMIs). Some of the variables in BMIs are set to be searched by Genetic Algorithm (GA), then for a given chromosome corresponding to the variables in BMIs, the BMIs turn to be Linear Matrix Inequalities (LMIs), and the corresponding non-convex optimization problem, which minimizes the upper bound on cost function, reduces to a SemiDefinite Programming (SDP) which is convex and can be solved numerically efficiently with the available software. Thus, the output feedback optimal guaranteed cost controller can be obtained by solving the non-convex optimization problem using the mixed algorithm that combines GA and SDP. Numerical examples show the effectiveness of the proposed method.
93B51Design techniques in systems theory
93C05Linear control systems
90C59Approximation methods and heuristics
93B12Variable structure systems