H₂ optimal control with an output regulation constraint — continuous-time systems

Abstract

In Chapter 7, we dealt with the problem of achieving a desired performance subject to an output regulation constraint. We showed how one can solve such a problem without solving directly a constrained optimization problem. The method we developed there basically amounts to transforming the constrained optimization problem for a given system to an unconstrained optimization problem, however, for a certain auxiliary system. The development in Chapter 7 is general i.e. it does not consider explicitly any specific performance measure; typically any performance measure can be used. In this chapter, we will use the H₂ norm of the closed-loop transfer function matrix as the performance measure.