Robust Model Predictive Control For Discrete-time Constrained Uncertain Linear Systems

Almost all physical systems are subject to some constraints. Predictive control, which is the most popular control strategy for constrained systems, has ever-increasing wide application in industry. This results from its notable capability of handling constraints and optimization over some performance index in a systematic way during both the controller design and implementation stage. On the other hand, the model, which is used to describe the dynamics of controlled system, always has some uncertainty. In order to guarantee the specified performance, model uncertainty must be taken into account properly. Robust model predictive control is referred to the predictive control method which can make the performance index within the acceptable range in the presence of model uncertainty.Based on the existing theoretical results on model predictive control, this thesis is devoted to the development of the framework of robust model predictive control with guaranteed robust feasibility, roboust stability and real-time applicability. To achieve this goal, the relevant theory and approaches, such as linear matrix inequalities (LMI), robust controllable invariant set, robust controllable contractive set and multi-parameter linear programming, are employed in the research work. Specifically, the main contribution of this thesis includes.1. "Multi-step predictive sequence trajectory tree", which respects the so-called "casual constraints", is used to formulate the online optimization problem. And a framework is presented for a novel min-max robust model predictive control approach cf constrained linear time-varying systems with polytopic uncertainty. In this framework, the optimizer of online optimization is the predictive input sequence with the length exceeding predictive horizon. Thus more freedom is introduced to the optimization problem with the enlarged feasible domain. Moreover, the corresponding online optimization problem is converted to the generalized eigenvalue problem in terms of LMIs. And the robust feasibility and robust stability are converted to the feasibility of a set of LMIs;2. A robust feasible predictive control scheme is put forward vhich adoptsnominal model and applies for constrained linear systems with polytopic uncertainty. Set invariance is the theory which underlies this control profile. And the key point to this predictive control paradigm is to append robust feasible constraint in the online optimization problem. In contrast to the similar robust model predictive control approach, the feasible domain of optimization can be remarkably enlarged with the application of set invariance theory. Furthermore, a sufficient condition for robust stability is given for closed-loop uncertain system, which is based on the convexity of optimization and can provide a guide to the choice of cost function to guarantee robust stability.3. A robust model predictive control method is presented with an appropriately constructed robust contractive set as the terminal set of its optimization problem and with the cost function formulated from the gauge function of this set regarding state variable. And the online optimization problem also takes on min-max form and can be reformulated as a linear programming. Multi-parameter linear programming is utilized to obtain the explicit model predictive control law and the online computation associated with optimization can be removed completely. Thus better real-time applicability is obtained in the presented predictive control profile.In addition to the above main result, some interesting results in this thesis are also listed as follows1. Based on Lyapunov stability theorem and LMIs approach, a control profile, including both static state feedback control and dynamic output feedback control, is presented for norm-bounded uncertain discrete-time linear systems with actuator sector nonlinearity;2. A fast computation algorithm is put forward for the exact determination of the specified Step controllable region of constrained discrete-time LTI sys...