Mathematics – Optimization and Control
Scientific paper
2011-04-28
Mathematics
Optimization and Control
See the version 2 http://arxiv.org/abs/1104.5369v2 for the 50th CDC-ECC 2011 paper. This third version is the beamer presentat
Scientific paper
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).
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