Linear Matrix Inequalities in Control [控制中的线性矩阵不等式]Linear Matrix Inequalities in Control [控制中的线性矩阵不等式].pdf

Linear Matrix Inequalities in Control Carsten Scherer Delft Center for Systems and Control (DCSC) Delft University of Technology The Netherlands Siep Weiland Department of Electrical Engineering Eindhoven University of Technology The Netherlands 1/23 Introduction • Overview: What can be expected from LMI techniques? • What are LMI’s and what are they good for? • Example: Truss topology design • Software • Some aspects of linear algebra 2/23 Carsten Scherer Siep Weiland Merging Control and Optimization In contrast to classical control, H∞-synthesis allows to design controllers in an optimal fashion. However the H∞-paradigm is restricted: • Performance spec in terms of complete closed-loop transfer-matrix. Sometimes only particular channels are relevant. • One measure of performance with clear interpretation in frequency domain. Often particular time-domain specs have to be imposed. • No incorporation of structured time-varying/nonlinear uncertainties. • Can only design LTI controllers. View controller as decision variable of optimization problem. Desired specifications are constraints on controlled closed-loop system. 3/23 Carsten Scherer Siep Weiland Major Goals for Optimization and Control • Distinguish easy from difficult problems: Convexity is key. • What are the consequences of convexity in optimization? • What is robust optimization