The Research On Online Optimization Strategy In Model Predictive Control

As a category of control algorithm adopting online receding horizon optimization, model predictive control (MPC) attracts much attention of industrial and theoretical researchers due to its good control performance and capability of handling constraints explicitly. Over the past decade, qualitative synthesis of model predictive control rapidly develops and many important results are proposed. As an important issue of qualitative synthesis of model predictive control, the guaranteed stability of MPC was particularly addressed. However, many other issues such as control performance, online computation burden and feasible region of a MPC controller, which are important in practical applications, are still expected to be further studied.For a MPC controller, the issues such as stability or control performance are dependent on the online optimization strategy adopted. So this dissertation will focus on the online optimization strategy of MPC. With the guaranteed stability as the precondition, for the open-loop and closed-loop MPC respectively, the control performance, feasible region and online computation burden of MPC are studied in this dissertation and the following contributions are obtained.●A general aggregation framework is proposed to overcome the weakness of the previous framework and can more easily formulate other aggregation strategies . Based on the general framework, a method to analyze the stability of aggregation based MPC controller is developed. And then an algorithm to estimate its feasible region with guaranteed stability is proposed.●In order to guarantee the control performance of aggregation based MPC, two new concepts, the equivalent aggregation and quasi-equivalent aggregation, are proposed. Making use of the characteristic of MPC, i.e. at each time, only the first control input in the optimal solution is acted on the practical plant, the problems of equivalent aggregation and quasi-equivalent aggregation of MPC are studied for four cases and the corresponding algorithms are developed.●For linear systems with additive disturbance, two design methods of RMPC (robust MPC) are presented. Based on the disturbance invariant set, an improved ERPC (efficient robust predictive control) and the aggregation strategy are adopted in the two design methods respectively to improve the control performance and reduce the online computation burden.●For uncertain systems with polytopic description, the concept of multi-step control set is proposed. Based on the concept, the feedback robust MPC controller with single or parameter dependent Lyapunov function is developed. Making use of the characteristic of the method, the design of a sequence of feedback control laws can be completed offline and then a feedback robust MPC controller with lower online computation burden can be obtained.●For LPV systems (linear parameter varying system) with limited rates of parameters varying, two algorithms to predict the models in the future are developed. The future system is predicted to belong to a sequence of polyhedral sets with the same number of models as the original one. To determine these sets, only algebra calculation is concerned. Based on the two algorithms, the feedback robust MPC for this kind of LPV systems are developed. Compared with the design without considering the limited rates of parameter varying, the design here can reduce the conservativeness and lead to better control performance.●Although LMI (linear matrix inequalities) is widely used in a number of previous literatures on robust MPC, it makes the online computation burden of robust MPC too heavy for practical applications. For uncertain systems with polytopic description, the min-max optimization problem of a closed-loop robust MPC is converted into a QP (Quadratic Programming) problem and then the online computation burden is reduced greatly. Meanwhile the extended general interpolation is proposed. Based on it, the closed-loop robust QP-MPC with varying feedback control law is also developed to reduce the design conservativeness.