Minimax design of optimal stochastic multivariable systems

Abstract

A new minimax optimal control problem is considered for a stochastic multivariable system. The cost function involves the trace of a weighted sum of spectral density matrices whose frequency response is to be limited. The H∞-norm of this scalar function is therefor minimised. To obtain the solution of the minimax control problem, an auxiliary lemma is employed. This enables an equivalent LQG optimal problem to be constructed which has the desired controller as its solution. An advantage of the particular cost function employed is that the solution is obtainedmore easily than for the general multivariable H∞ problem. This makes the approach easier to understand and the results simpler.