Pareto suboptimal H∞ controls with transients

Abstract

In this paper, we consider multi-objective mini-max problems with criteria being maxima of functionals. We determine a domain in the criteria space containing Pareto optimal points. The upper boundary of this domain corresponds to Pareto suboptimal solutions minimizing maxima of weighted sums of these functionals, while the lower one is computed using the same Pareto suboptimal solutions. This domain allows to evaluate a "proximity" of any solutions of the multi-objective problem to Pareto optimal solutions, which minimize weighted sums of the criteria. The proposed approach is applied to multi-objective control designs for continuous and discrete LTV systems and LTI systems over finite and infinite time horizons, respectively. The criteria used are H∞ norms with transients for several controlled outputs. Pareto suboptimal controls in such problems turn out to be H∞ controls with transients for combined outputs. State feedback gains of these controllers are computed in terms of solutions to differential or difference LMIs. Numerical example illustrates the theoretical results.