Model Predictive Algorithm Design And Stability Analysis For Constrained Nonlinear Systems

Model predictive control (MPC) is nowadays arguably the most widely accepted control design technique in control of industrial processes. After more than thirty years'research, many synthesis of model predictive control and many important results have been proposed. However, there is still a great gap between theories and applications because of some open problems, such as control performance, online computation burden and so on. Therefore, based on the nonlinear MPC algorithm and the systems'property, this dissertation focuses on the problem of how to reduce the online computational burden while guaranteeing the system stability, and the following contributions are obtained.Consider the nonlinear systems with constaints. An improved trust-region quadratic programming algorithm is proposed based on the nonlinear programming approach. The algorithm is proved to be converged in the sequel. And then the algorithm is used to solve the optimization problem of nonlinear MPC in order to reduce the size of the sub-optimization problem by substituting the nonlinear dynamic programming into quadratic programming problems. In addition, a new Hessian Matrix updating method is also introduced to reduce the complexity of the algorithm. In the end, the simulation results have demonstrated the efficiency of the algorithm.In terms of the model approximation strategy, the dynamics of a nonlinear system can be embedded into a kind of uncertain model with polytopic description. After that, an approach of constructing larger polytopic invariant set based on linear interpolation method is proposed to ensure the stability of the approximate embedding uncertain model in contrast with existing results. Then based on the extended-invariant set, a quasi-min-max robust MPC strategy is used to obtain the stable control law of the original nonlinear system. The algorithm online only needs solve semi-definite programming problems instead of non-convex, non-linear programming, which will greatly reduce the computation burdern.Consider a class of nonlinear systems, whose nonlinear dynamic can be embedded into a linear parameter varying (LPV) model. For the LPV model with limited rates of parameters varying, a feedback control law with less computational effort is proposed analytically. As the uncertain region of such a LPV system in the future changes corresponding to the parameters which can be predicted in the future stage due to the information on the parameters value, magnitude bounds and the variation rate bounds, the control law is presented by solving a min-max MPC problem based on a dynamic programming viewpoint. By exploiting the dynamic nature of the min-max optimal problem and showing the convexity of the dynamic cost-to-go, the intrinsic structure of the feedback control law has been obtained.A min-max model predictive control strategy is proposed for a class of constrained nonlinear system whose trajectories can be embedded within those of a bank of LPV models via piece-wise embedding strategy. For each approximate model, a parameter-dependent Lyapunov function is introduced to obtain poly-quadratically stable control law and to guarantee the feasibility and stability of the original nonlinear system. When the model switches from one to the other, a switching law to guarantee the feasibility of the initial state is introduced by means of the method of constructing elliptical set. And this approach can greatly reduce computation burden in traditional nonlinear predictive control strategy.