Improvement of the LMI change of variables for multi-objective control design problems


Correspondence to: Emile Simon, Department of Mathematical Engineering, ICTEAM Institute, Université Catholique de Louvain, 4 avenue Georges Lemaître, 1348 Louvain-la-Neuve, Belgium.



The aim of this paper is to propose an improvement of a classical change of variables useful to solve multi-objective control design problems that can be formulated with LMIs. For multi-objective problems, the only approach guaranteed to converge to global optima is to use an iterative approach where the order of the design parameter grows (until no improvement is obtained to some relative decrease). The issue is that the order of the design parameter and the size of associated LMIs may easily grow to unacceptably large values (computationally and/or for implementation in practice). The change of variables considered here was proposed to mitigate that issue, that is, to reduce the inflation of number of variables of the corresponding optimization problems. Here, we propose a method exploiting this change of variables further in order to obtain a sequence of increasing order design parameters converging faster towards the global optimum. Copyright © 2012 John Wiley & Sons, Ltd.