Research On Robust Model Predictive Control For Nonlinear Systems Based On T-S Model

Model Predictive Control(MPC)can use the historical information and model information to continuously optimize the target function,and can also modify the predictive model based on the actual measured information of plant.MPC is widely used in industrial systems because it can handle and control the hard constraints of the state to ensure the stability of the system.In industrial processes,nonlinearity,time delay,and disturbance are common dynamic characteristics of systems.The phenomena such as time delay and disturbance existing in the nonlinear system may interfere with the prediction of the state.Based on the theory of linear matrix inequality,robust invariant set and Lyapunov stability,this paper studies the robust model predictive control problem based on state feedback control for nonlinear systems with time-delay and disturbance characteristics described by T-S fuzzy model.The main research contents of this paper are as follows:For a class of nonlinear time-delay systems with input constraints described by Wiener model,the stability analysis problem and the design problem of the controller are studied.The state space model is used to describe the linear part of Wiener model,and the T-S model is used to represent the nonlinear part of Wiener model.The Wiener model can be approximated by the weighted sum of multiple local linear models.The state feedback control law is designed based on the Lyapunov-Krasovskii function and the parallel distribution compensation principle,and the optimization problem of minimizing the worst case of the objective function is solved.The optimization problem is represented by a linear matrix inequality.The sufficient conditions for asymptotic stability and less conservation is presented.Finally,the effectiveness of the algorithm is verified by simulation.For a class of nonlinear systems with norm-bounded uncertainties described by T-S fuzzy models,the stability analysis and controller design problems of nonlinear systems with input constraints and output constraints are studied.By using a T-S model to represent a nonlinear system,the nonlinear system can be approximated by the weighted sum of multiple local linear models.By using the Lyapunov function and the parallel distribution compensation principle,the optimization problem of minimizing the objective function of each subsystem in the worst case is solved,and the state feedback control law of each subsystem is obtained,and then the control law of the entire nonlinear system is also obtained by the weighting of each subsystem control law,and the asymptotic stabilityfor the system under the control law is satified.Finally,the effectiveness of the algorithm is verified by simulation.For a class of nonlinear discrete systems with time-delay and disturbance,the nonlinear local T-S fuzzy model with norm-bounded uncertainty is used to approximate the nonlinear system,and the robust model predictive control problem is studied.The terminal constraint set is designed by the concept of robust invariant set,and the fuzzy controller is designed in the terminal constraint set,so that the state of the system finally enters the terminal constraint set.The algorithm guarantees that the system is input-state stable and achieves better control performance.Finally,the effectiveness of the algorithm is verified by simulation.