A convex programming approach to the multiobjective H2/H∞ problem

Abstract

In this paper, Banach space duality theory for the multiobjective H2/H∞ problem developed recently by the authors, is used to develop algorithms to solve this problem by approximately reducing the dual and predual reperesentations to finite variable convex optimizations. The Ellipsoid algorithm is then applied to these problems to obtain polynomial-time, non-heuristic programs which find "nearly" optimal control laws. These algorithms have been implemented numerically to compute an example.