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

Abstract

This chapter is a discrete-time analog of Chapter 8. That is we formulate here an output regulation problem which seeks to achieve simultaneously the infimum (or arbitrarily close to the infimum) H₂ norm of a closed-loop transfer function. Such a problem can equivalently be viewed as an H₂ optimal (or suboptimal) control problem with the output regulation constraint. As we discussed in the previous chapter, although a suitable controller which solves the posed problem for the given system can be constructed via the construction of a controller that solves an H₂ optimal (or suboptimal) control problem without the output regulation constraint for a certain auxiliary system, one fundamental question still needs to be answered. Namely, whether the added output regulation constraint in a problem compromises the achievable performance. In this regard, we will show again, as in the previous chapter, that there is no loss at all in the achievable performance because of the added output regulation constraint whenever proper (or strictly proper) controllers are used. However, although the achievable performance is not compromised because of the added output regulation constraint, as well known in H₂ optimal control theory, the achievable performance for discrete-time systems is different over the class of proper controllers compared to that over the class of strictly proper controllers. This chapter is based on the recent research work of authors [77].