Multiple objective optimal control of linear systems: the quadratic norm case

Control of a linear system to meet requirements embodied in multiple performance criteria is recognized as the typical design problem. The authors study the design of control when every criterion of interest takes the form of an H₂ norm defined over certain exogenous inputs and controlled outputs of the system. The objective is to find all stabilizing controllers that are noninferior with respect to the defined objectives, that is, to find the set of Pareto-optimal controllers. The novel feature is the use of the Youla parametrization to represent the admissible controllers. This representation enables the authors to show that each criterion, and hence their weighted sum, is convex over the class of admissible controllers. Since the set of admissible controllers is itself convex, the Pareto-optimal controllers can be determined by the standard scalarization technique. It is concluded that, in general, the controller order is higher than the order of the plant