The main objective of this work is the study of the inverse positive Linear-Quadratic problem by means of linear matrix inequalities (LMIs). The latter constitute an important tool that can be used to solve numerically different control problems through convex optimization. The considered problem consists of determining the weighting matrix that define an optimal quadratic cost whose the solution (the LQ-optimal control) is beforehand fixed by a feedback matrix that positively stabilizes the system.
Two intermediate problems are first studied and stated under the form of LMIs: the positive stabilization problem and the inverse LQ problem. The synthesis of these two problems and the consideration of the two corresponding LMIs characterize the problem under study. Solving these LMIs requires the introduction of an iterative process in order to make the solution of the first LMI compatible with the second one.
Finally, the theory is illustrated by solving numerically the studied problem for three particular systems, by means of some softwares whose solution algorithms are briefly described.
Le problème linéaire-quadratique positif inverse: analyse et résolution par les inéquations matricielles linéaires
Jacques, A. (Author). 2009
Student thesis: Master types › Master in Mathematics