A perspective for optimization in systems and control : from LMIs to derivative-free methods

(eng) In this thesis, we develop an investigation in the framework of optimization in systems and control, following a perspective starting from a very common approach (that of Linear Matrix Inequalities or LMIs), which limitations draw us to consider a seldom used approach (the derivative-free optimization methods). This investigation is motivated by the fact that this framework is currently largely dominated by LMIs and convex optimization approaches even when the underlying problems are non-convex (in their original or less approximated formulations), in which case other optimization alternatives than convexity-based methods may often be more adequate. This work has been built with the intent of keeping a general perspective, where the developments are illustrated with some specific problems. Main motivations for this thesis are the following: - investigate the current main trend for optimization in systems and control, - outline some limitations of convex optimization approaches to solve non-convex problems, - put forward why derivative-free methods should be much more considered in systems and control, - solve (hard) problems of optimization in systems and control (i.e. a useful, and sometimes optimal, solution is obtained in practice). A key interest of this line of investigation is that, while relying on fundamental and necessarily theoretical concepts from academic research, it pays particular attention to practical issues of implementation (i.e. the results could be transferred for use in an industrial context).