Multicriteria Optimization of Induced Norms of Linear Operators: Primal and Dual Control and Filtering Problems

This paper considers multicriteria optimization problems of induced norms of linear parameter-dependent operators mapping a linear space into several ones or conversely. In both cases, direct minimization of an optimal objective function as a linear convolution of individual criteria is difficult. As shown below, for each problem mentioned, a suboptimal objective function (an induced norm of an auxiliary linear operator) can be specified and minimized to obtain Pareto-suboptimal solutions. This establishes the possibility to localize the Pareto set in the criteria space and thereby estimate the suboptimality degree of the resulting solutions. Multicriteria optimal control and filtering problems with the generalized H∞ norm-based criteria are studied as an application.