TABLE OF CONTENTS Many promising optimisation techniques have, in the past, failed to live up to their promise, one of the most important reasons for this failure being the lack of robustness in the methods. In particular, very complex plant models were often produced and then naively assumed to be accurate representations of the real world. The inevitable mismatches between the assumed (let us say, nominal) models and the real-world processes destroyed the viability of many approaches.
H ? approaches, by specifically taking into account modelling uncertainty, and doing so in a worst case sense, allow complex control design problems to be solved in a theoretically rigorous way while guaranteeing robustness of the implemented solutions over a prespecified range of model incorrectness or (equivalently) of process variability.
In this chapter, we review the linear spaces that underlie much of modern operator-based control theory with particular emphasis on the theory underlying H ? approaches. Some of the H ? control design methodology is then introduced in very simple terms to establish the basic ideas. The chapter ends with an introduction to a deeply satisfying and visualisable approach: the v gap metric method, which is firmly embedded within the H ? family but which is both powerful and general as well as intuitive.
Hardy spaces (see Section 16A) are of value in control problem formulation since they provide a rigorous...
