Minimum settling time control design through direct search optimization

Abstract

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.