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Robustness aspects of Model Predictive Control

Model, Model-based or Receding-horizon Predictive Control (MPC or RHPC) is a successful and mature control strategy which has gained the widespread acceptance of both academia and industry. The basis of these control laws, which have been reported to handle quite complex dynamics, is to perform predictions of the system to be controlled by means of a model. A control profile is then computed to minimise some cost function defined in terms of the predictions and the hypothesised controls. It was soon realised that the first few predictive controllers failed to fulfil essential properties, such as the stability of the nominal closed-loop system. In addition, it was noticed that the discrepancies between the model and the true process, referred to as system uncertainty, can seriously affect the achieved performance. The robustness problem should, thus, be addressed. In this thesis, the problems of nominal stability and robustness are reviewed and investigated. In particular, the accomplishment of constraint specifications in the presence of various sources of uncertainty is a major objective of the methods developed throughout this PhD research. First of all, controllers which guarantee nominal stability, such as the CRHPC and the GPC∞, are highlighted and formulated, and 1-norm counterparts are obtained. The robustness of these strategies in the unconstrained case has been analysed, and it has been concluded that the infinite horizon approach often leads to more convenient performance and robustness results for typical choices of the tuning knobs. Then the constrained case has been undertaken, and min-max controllers based on the global uncertainty approach have been formulated for both 1-norm and 2-norm formulations. For these methods, a band updating algorithm has been suggested to modify the assumed uncertainty bounds on-line. Although both formulations provide similar results, which overcome the classical approach to robustness when constraints are specified, the 1-norm controllers are computationally more efficient, since the optimal control move sequence can be computed with a standard LP problem. Finally, a refinement of the min-max approach which includes the notion that feedback is present in the receding-horizon implementation of predictive controllers, termed as feedback min-max MPC, is shown to overcome some of the drawbacks of the standard min-max approach.