From mixed to multi-objective control

We revisit a technique for solving multiobjective control problems through affinely parameterizing the closed-loop system with the Youla parameterization and confining the search of the Youla parameter to finite-dimensional subspaces. It is known how to solve such problems if the closed-loop specification are formulated in terms of the solvability of linear matrix inequalities. However, all approaches proposed so far suffer from a substantial inflation of size of the resulting optimization problems if improving the approximation accuracy. On the basis of a novel state-space approach to solving static output feedback control problem by convex optimization for a specific class of plants, we reveal how the growth of the size of the optimization problems can be reduced to arrive at more efficient algorithms. As an additional ingredient we discuss how to use a so-called mixed controller as a starting point for a genuine multi-objective design in order to improve the efficiency of the algorithms