Projection/Reflection-based Techniques for Multi-objective Control Synthesis under information structure constraints

This paper deals with multi-objective static feedback synthesis under potentially information structure constraints. The proposed approach relies on a triptych : the geometry of Hurwitz-stable matrices set, the projection techniques onto convex/non-convex closed-matrix sets and Douglas-Rachford's (DR) like reflection methods for finding a point in the intersection of two (or more) closed sets. The original method, proposed in this paper, aims to emulate the generic behaviour of the Linear/Bilinear Matrix Inequalities (LMI/BMI) framework while keeping the output feedback gain separated from any matrix with direct or indirect connection to the Lyapunov function. It can be considered as an alternative method, easy to implement and modifiable at will by any user, to existing optimization based methods. Moreover, the connection between the sequence of iterates generated by the algorithm and a continuous dynamical model are given. Thereby, the convergence and the behaviour of the proposed algorithm are analysed by using the direct method of Lyapunov from dynamical systems stability theory. Several examples are given to prove the validity of the proposed techniques and results.