The problem of minimising a quadratic cost functional while regulating a dynamical system with a saturating control has been widely studied, and is known to lead to the use of non-linear controls. This thesis considers two variations on this problem, which might be considered as alternative approaches to optimal regulator problems. After a statement of the general optimal control problem in Chapter II, necessary and sufficient conditions are discussed. Chapter III considers the failure of the major necessary condition (the Maximum Principle), which leads to the idea of singular controls. These singular controls play a major role throughout Chapters IV-VI. Chapters IV and V consider the first alternative approach, in which a non-quadratic cost functional is adopted. It is chosen in such a way as to give certain desirable properties outlined in Chapter IV. This Chapter also considers two second order problems; while Chapter V considers two third order problems, and extends one to nth order systems. Chapter VI then looks at the second alternative, where a non-quadratic state penalty term is added to the quadratic term in such a way as to simplify the resulting behaviour. In this Chapter, multiple control inputs are considered, and two different types of control penalty are applied. The feedback structures obtained in this problem are used to sub-optimally control a quadratic cost problem, with a discussion of the relative merits of the sub-optimal schemes.
|Date of Award||1983|