Control & Sy!ems "eory Seminar at # Technion (2007 éìåéá 22) æ"ñùú ,áàá 'æ ,áéáà øèñîñ

Title:

Time-Varying Uncertainties Reconsidered

Speaker:

Carsten Scherer Delft University of Technology, The Netherlands

Time:

Sunday, July 22, 2007, 14:30

Place:

Room 320, Lady Davis Bld (Mechanical Eng.), Technion

Abstract: In many control problems, such as for position-dependent mechanical systems, it is instrumental to design gain-scheduled controllers for pushing performance to its limits. Linear parameter-varying (LPV) system descriptions offer a promising framework for the systematic design of parameter-dependent controllers with guarantees for stability and performance, all within the the computational framework of semi-definite programming. In this tutorial presentation, we sketch concrete engineering applications of gainscheduled controller synthesis, and subsume them to the framework of LPV systems. We recall how scaled small-gain conditions allow to computationally verify robust stability and performance for LPV systems. As a novel ingredient, we discuss how the failure of these sufficient robustness conditions allow to quantify their conservatism. For controller synthesis, we reveal the prominent role of robust linear matrix inequalities and exhibit the need for approximation or relaxations schemes. Based on recently obtained sum-of-squares representations of polynomial matrices, we finally address how to systematically construct relaxations with arbitrarily small conservatism.