Emile Simon

Emile Simon, Vincent Wertz

The motivation of this work is to illustrate the efficiency of some often overlooked alternatives to deal with optimization problems in systems and control. In particular, we will consider a problem for which an iterative linear matrix inequality algorithm (ILMI) has been proposed recently. As it often happens, this algorithm does not have guaranteed global convergence and therefore many methods may perform better. We will put forward how some general purpose optimization solvers are more suited than the ILMI. This is illustrated with the considered problem and example, but the general observations remain valid for many similar situations in the literature.

Emile Simon

The aim of this paper and associated presentation is to put forward derivative-free optimization methods for control design. The important element, still ignored at the end of 2011 in systems and control (i.e. this element has apparently never been used so far in the systems and control litterature), is that derivative-free optimization methods were relatively recently proven to converge not only on smooth objective functions but also on most non-smooth and discontinuous objective functions. This opens an avenue of posibilities for solving problems unyielding to classical optimization techniques. Original abstract: This paper investigates the performance of using a direct search method to design optimal Static Output Feedback (SOF) controllers for Linear Time Invariant (LTI) systems. Considering the old age of both SOF problems and direct search methods, surprisingly good performances will be obtained compared to a state-of-the-art method. The motivation is to emphasize the fact that direct search methods are too much neglected by the control community. These methods are very rich for practical purposes on a lot of complex problems unyielding to classical optimization techniques, like linear matrix inequalities, thanks to their ability to explore even non-smooth functions on non-convex feasible sets. Again, the key element here are the relatively new strong theoretical convergence guarantees of derivatie-free methods. Thanks to these, using such optimization methods is superior to other methods without convergence guarantees (like most iterative LMI schemes).

Emile Simon

In this presentation, we will develop a short overview of main trends of optimization in systems and control, and from there outline some new perspectives emerging today. More specifically, we will focus on the current situation, where it is clear that convex and Linear Matrix Inequality (LMI) methods have become the most common option. However, because of its vast success, the convex approach is often the only direction considered, despite the underlying problem is non-convex and that other optimization methods specifically equipped to handle such problems should have been used instead. We will present key points on this topic, and as a side result we will propose a method to produce a virtually infinite number of papers.

Emile Simon

The aim of this work is to design controllers through explicit minimization of the settling time of a closed-loop response, by using a class of methods adequate for this objective. To the best of our knowledge, all the methods available in the literature do not minimize directly the settling time but only related objective functions. Indeed, the settling time objective function is not only non-smooth but also discontinuous. Therefore we propose to use direct search methods, which do not use any gradient information. An important reason is a recent result that some direct search methods are guaranteed to convergence on such discontinuous objective functions. The proposed approach is self-standing but can also improve the solutions obtained with the alternatives of the literature, which lead to good solutions but suboptimal in terms of the settling time. Note also that this approach is very flexible and can be adapted to a broad range of objectives as well as nonlinear systems or controllers, as long as the time response can be simulated.