Pareto Optimal Generalized H2-Control and Optimal Protection from Vibration

Abstract

A novel multi-objective control problem with generalized H2 criteria is studied for a linear system with a single disturbance input and multiple objective outputs. The generalized H2-norm is the L2 to L∞ gain of the system with the L∞-norm, understood in a broader sense than usual. Necessary conditions for Pareto optimality are derived in this paper. By using Germeyer convolution it is established that Pareto optimal controllers can be synthesized in terms of LMIs as the generalized H2-optimal controllers for the closed-loop system with the single input and the single output consisting of the scaled objective outputs. Vibration isolation and attenuation problems are considered in a novel framework as applications of the approach proposed. Pareto optimal isolators and attenuators are synthesized for two basic models in the problems of optimal protection from vibration.