MULTIPLE OBJECTIVE OPTIMAL-CONTROL OF LINEAR-SYSTEMS - THE QUADRATIC NORM CASE

Most control system design problems involve making trade-offs among competing objectives. In this paper, we consider a control system synthesis problem that arises when the objective is to find a controller such that several closed-loop transfer functions are small in an appropriate sense. To be more precise, given a linear time-invariant plant, the objective is to find all stabilizing compensators that are Pareto optimal (equivalently noninferior) with respect to a vector-valued H2 performance criterion. It is shown that this multiple criteria optimization problem can be reduced to a simultaneous model matching problem in a Hilbert space. Moreover, state-space formulas are given to solve this model matching problem. We also show that in some particular cases, Pareto optimal controllers have the same order as that of the given plant and in these cases, the aforementioned state-space formulas can be further simplified.