A practical method for constrained-optimization controller design: H2 or H/spl infin/ optimization with multiple H2 and/or H/spl infin/ constraints

Abstract

This paper presents a practical algorithm for multi-input multi-output control law synthesis with an H/sup 2/- or H/sup /spl infin//-norm minimization criterion and multiple H/sup 2/- and/or H/sup /spl infin//-norm constraints. The plant is described by its discrete-time impulse response matrix, which can be determined directly from measurements. The control law design parameters are the tap weights of an FIR discretization of the Q-parameter. The multi-constraint H/sup 2//H/sup /spl infin// control law synthesis is written as a convex constrained optimization problem and solved as a structured semi-definite program. As a design example, we control the acoustic radiation from a (mathematically modeled) submerged spherical shell. The plant-model impulse response matrix has McMillan degree 800. We specify, synthesize, and compare three controllers: one designed by standard H/sup 2/ techniques; one designed by H/sup /spl infin// minimization with three H/sup /spl infin// and three H/sup 2/ constraints; and one designed by H/sup 2/ minimization with the same constraints. In a single design iteration, the multi-constraint H/sup 2//H/sup /spl infin// controllers achieve the best possible performance given the constraints; after several design iterations, the standard H/sup 2/ controller achieves slightly worse performance with several constraint violations.