Research Of Robust Stability For Constrained Nonlinear Predictive Control Algorithms

Optimization control of constrained nonlinear systems has increasingly been a hot topic of research in the field of nonlinear control. Model predictive control (MPC) has an ability to deal with system constraints and the optimization of costs explicitly, and then is one of the most effective, advanced control techniques to be selected for optimization control of constrained systems. However, for highly nonlinear processes with disturbances or large operating regions, linear predictive control (LMPC) or linearization models-based predictive control, in general, does not meet the requirement of control performances. Hence, the research on constrained nonlinear model predictive control (NMPC) is of great significance theoretically and practically.Due to the complexities of nonlinear systems, the research of NMPC has lagged behind that of LMPC both in theoretical and practical ways. Especially, the issues of stability, robustness and the computational burden of online optimization on NMPC have been still the focuses of the researchers for both predictive control and optimization algorithms. Based on the existing theoretical results on NMPC, this dissertation investigates the basic 5 topics of NMPC for constrained nonlinear systems, that is, feasibility of optimization, stability, robustness, computational burden and estimate of stability region. The goal of the work is to obtain some theoretical results and algorithms with more practical value. To achieve the goal, the relevant theory and approaches are exploited, such as differential game, (robust) invariant set theory, input-to-state stability, control Lyapunov function, backstepping method, etc. The main contribution of this dissertation includes:(1) A suboptimal, minimax robust NMPC algorithm is proposed for discrete-time nonlinear systems subject to constraints and uncertainties, the goal of which is to reduce the on-line computational load of robust NMPC schemes. By introducing the differential game theory and the concept of input-to-state stability, the closed-loop robust stability for this suboptimal NMPC algorithm is achieved in the vector norm way.(2) The problems of disturbance rejection and implementation of H_∞NMPC is systematically investigated for discrete-time nonlinear affine systems subject to constraints and uncertainties. Based on the results in (1), the robust stability of H_∞NMPC is studied in both cases of optimal and suboptimal solutions, respectively. By introducing L₂-gain of nonlinear systems, the problem of disturbance rejection of H_∞NMPC is investigated quantitatively in the signal norm way. In order to lessen the computational burden of online optimization in NMPC, finite dimension parameterizations are incorporated into the design of the NMPC algorithm.(3) A novel NMPC guaranteed closed-loop stability——constructive NMPC is proposed for continuous-time, constrained nonlinear systems. The main idea of this algorithm is to derive a stable control class off-line via the design of construction, and then to calculate its adjustable parameters on-line via the optimization of costs. The desire goal is to lessen the on-line computational load of NMPC and to decouple the stability of closed-loop systems from the Optimality of performance indexes.(4) Based on the NMPC scheme addressed in (3), a NMPC algorithm is presented for constrained, strict-feedback nonlinear systems, where the stable control class is constructed by using backstepping method. Then the NMPC algorithm is employed to optimize the control of nonholonomic wheeled mobile robots.