Einladung zum Vortrag im Kolloquium
Conservatism reduction for output-feedback optimal
control design through a coordinate descent algorithm
Dipl.-Ing Emile Simon
Department of Mathematical Engineering
Université Catholique de Louvain
Tuesday, 5. October 2010, 4:00 p.m.
IST-Seminar-Room 3.243 - Pfaffenwaldring 9 - Campus Stuttgart-Vaihingen
The first part of this talk presents an algorithm to reduce the conservatism of fixed-order output-feedback control design for Linear Time Invariant (LTI) systems with Linear Matrix Inequalities (LMIs)-representable objectives. Using Lyapunov theory and the Schur complement many objectives can be written as Bilinear Matrix Inequalities (BMIs), which in general are hard to solve and have a non-convex space of solutions.
The classical response to this is to use LMIs reformulation of BMIs, therefore using convex subspaces of the non-convex space of all solutions and thus introducing conservatism in general. Here a new use of a change of variables [Scherer 2000] is proposed, so that consecutive convex subspaces are considered iteratively. This algorithm explores further the non-convex space of solutions, leading to improved objectives with reduced conservatism.
The second part of the talk will discuss more widely the topic of coordinate descent methods to solve BMIs, a technique typically not proven to converge in general.
Emile Simon studied Electrical Engineering at the Université Catholique de Louvain, Belgium. He got his Diploma degree in June 2007. In May 2008, he joined the Department of Mathematical Engineering at the Université Catholique de Louvain to work towards his Ph.D thesis, where he is currently a researcher and a teaching assistant. His research interests are focused on optimization-based control design.