Robust Stability Of Nonlinear Model Predictive Control And Online Optimization Algorithms

Model predictive control (MPC) attracts much attention of industrial and theoretical researchers due its ability to deal with system constraints and the optimization of costs efficiently. However, most processes in industry have nonlinear properties and Linear Models-Based Predictive Control (LMPC) does not meet the requirement of control performance. Therefore, the research on Nonlinear Models-Based Predictive Control (NMPC) has an important theoretical and practical significance.Due to the complexities of nonlinear systems, the research of NMPC has lagged behind LMPC. Especially, the issue of stability, robustness and online optimization are three difficult but rather important problems of NMPC research. Based on former research, this thesis gives a survey of NMPC robust controller design and online optimization algorithms. Concepts and methods of control theory such as robust invariance set, H∞control and Input-to-State Stability (ISS) theory, Linear Matrix Inequality (LMI) technique are introduced to deal with several basic issues of NMPC such as stability, robustness and computation burden. The goal of the work is to obtain some theoretical results and scheme of controller design with more practical value. The main contributions of this thesis are as follows:1. A robust NMPC scheme is investigated for a class of constrained nonlinear systems which can be described by polytopic uncertainty model. Based on duel-model strategy, invariance set and MPC control law are constructed offline to reduce the online computation burden. Moreover, conservatism can be reduced by addition control move. The notion of Input-to-State Practical Stability (ISpS) is introduced to deal with persistent bounded disturbances and sufficient conditions for the existence of NMPC controller are obtained in form of LMIs. Examples of spring cart and Continuous Stirred Tank Reactor (CSTR) are used to illustrate the effectiveness of the proposed scheme. 2. A robust state-feedback H∞NMPC controller is designed for a class of constrained polytopic description systems. Combining receding horizon principle of MPC with both differential game theory and nonlinear H∞control theory, the sufficient condition to gurantee ISS of closed-loop system is derived. By using matrix transform technique, the non-convex H∞NMPC finite horizon optimal dynamic game problem is converted to a minimization problem in form of LMIs. Feasible solution is used to construct controller with desired control performance, consraints fulfillment and ISS properties. Simulation results illustrate the effectiveness of the proposed scheme.3. To deal with the difficulties in on line receding-horizon optimization problems in NMPC. An efficient MPC algorithm with larger feasible region is presented for discrete-time linear systems subject to input constraints. Firstly, the larger feasible region of MPC is computated by augment state-space models. Then, the line-search optimization algorithm within the MPC framework is designed to solve on-line optimization problem. This algorithm guarantees the early termination and monotonically decreasing properties of the cost performances. Meanwhile, the local convergence of the line-search optimization algorithm in MPC and asymptotic stability of closed-loop system are proved.4. Consider a class of nonlinear systems, whose dynamic can be embedded into a Linear Parameter Varying (LPV) model. The design and conditions for the existence of robust dynamic output feedback MPC for LPV systems are developed. By using matrix transform technique, a receding optimization problem with LMI constraints is constructed to design the desired controllers with an on-line optimal receding horizon guaranteed cost. Simulation results demonstrate the effectiveness of the proposed scheme.5. A closed-loop NMPC scheme for a class of time-varying nonlinear systems subject to input constraints is presented. The linearization idea is employed and time-varying linear dynamic approximation is used to convert the non-convex programming problem into convex optimization problem with LMI constraints. By minimizing the receding-horizon optimization performance index on line, the closed-loop system is able to manage the trade-off between required high performance and satisfying constraints. Futhermore, for energy bounded disturbance, the receding horizon H∞, control law and sufficient condition for its existence are derived by LMIs. Simulation results demonstrate the effectiveness of the design scheme.6. Finally, the main results are concluded and some problems to be solved in the future are presented.