A hybrid gradient-LMI algorithm for solving BMIs in control design problems

This paper presents an algorithm for solving optimization problems with bilinear matrix inequality constraints. The algorithm is based on a combination of gradient-based optimization and LMIs, which makes it fast and enables it to handle a large number of decision variables. It is applied to two controller synthesis problems: static output feedback controller synthesis and robust controller synthesis for linear parameter varying (LPV) systems using the idea of quadratic separation. Since the second problem has large number of decision variables, a hybrid approach is applied, in which LMI solvers are used for the evaluation of the cost function. The algorithm is applied to two examples, and results are compared with some existing approaches.

Subjects

Algorithms and software

Optimization based controller synthesis

Robust controller synthesis

DDC Class

600: Technik

620: Ingenieurwissenschaften

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A hybrid gradient-LMI algorithm for solving BMIs in control design problems