A Study On The Application Of Support Vector Regression With Different Kernel Function In Model Predictive Control

In recent decades, model predictive control(MPC) algorithm has been developing rapidly and it has been greatly implements in both theoretical research and practical application. However, it could not get expected results in nonlinear model predictive control(NMPC), for the perfect nonlinear model is difficult to obtain and the globally optimal solution to nonlinear optimization is hard to find.Proposed by Vapnik and Cortes in 1995, SVR could well solve the problems that are with few samples. SVR's putting forward brings the dawn for people to apply model predictive control to nonlinear systems, so the combine of SVR and MPC has become a focus of research.For the problems of the SVR which applied on model predictive control are with quadratic polynomial kernel function, off- line SVR is popular and the difficulty in solving objective function in the predictive control of the nonlinear system model, this paper will mainly study on the prediction and generalization ability of the SVR model depends greatly on a proper setting of its kernel function and model mismatch in nonlinear model predictive control. SVR with different kernel function and online SVR in nonlinear model predictive control are proposed, and multi-Agent Particle Swarm Optimization Algorithm(MAPSO) is introduced to optimize the solution of rolling optimization in model predictive control. The main research works are as follows:(1)Having taken factors, such as the prediction and generalization ability of the SVR model depends greatly on a proper setting of its kernel function, SVR with quadratic polynomial kernel function is an approach popular in NMPC, and polynomial kernel function has gradually been replaced in recent years, in account, model predictive control based on polynomial SVR and mode l predictive control based on RBF-SVR are put forward. In addition, because of polynomial kernel function's and RBF kernel function's complex expression, MAPSO is used to optimize the solution of rolling optimization in MPC. For nonlinear system, the simulation results show that both of the proposed methods is effective and has demonstrated excellent adaptive ability and robustness. Compared with the model predictive controllers based on SVR with quadratic polynomial kernel and inverse model control based o n SVR(SVR-IM), both of the two methods is superior to other methods.(2)For the problems of the off-line model is difficult to adapt to the real nonlinear system and the system state's contact is not close, a new method of multi- step model predictive control based on online SVR optimized by multi-agent particle swarm optimization algorithm(MAPSO-OSVR) is put forward on the basis of research on the off- line SVR. For nonlinear systems, the simulation results show that the proposed method has better control capability, compared with the model predictive controllers based on SVR and online SVR optimized by genetic algorithm(GA-OSVR).