Input constrained linear control

The presence of input constraints is ubiquitous in control systems. As soon as higher performance-eg., faster response-is demanded of the system, limitations imposed by input constraints are more than likely to be encountered. This thesis focuses on various aspects of control system design for linear plants subject to input constraints. For such problems, a number of the results of the well known theory of linear systems still apply, but yet there are many aspects which are of a definitive nonlinear nature, making these problems highly nontrivial. This explains the fact that, despite considerable past work on the topic, there still remain many interesting unsolved research problems. In this thesis we study different control methodologies aimed at dealing with this problem. The main methodologies considered are: model predictive control, time optimal control and switching strategies. Insight is gained through the analysis of the solutions provided by these control formulations. In the case of model predictive control, a technique traditionally implemented via an on-line optimisation, our approach leads us to investigate closed-form solutions to this problem. By obtaining closed-form analytical solutions to model predictive control of limited horizons, we are able to elucidate aspects of the underlying structure of its solution. We also obtain a closed-form solution for arbitrary horizon model predictive control which is, in general, valid locally, in a closed region of the state-space. A common observation that is made in the various control formulations considered in the thesis is that they can be implemented by switching strategies which have similar underlying features. These features are of crucial importance for the achievement of high performance. The specific features of interest are the shape of the switching surface and the degree of effective use of the available control authority. This insight is used to devise switching strategies aimed at achieving high performance. Robustness issues associated with the switching strategies are also addressed.