Research On Control Methods For Discrete Nonlinear Systems Based On Predictive Control

Model predictive control approach is a kind of intelligent approaches which is developed in the industrial production and closely related to the industrial application.It can effectively handle problems with input/output constrain,nonlinearity,uncertainty,time-variance and multivariate and has been attached high importance to by researchers in control field.However,since nonlinear system is a complicated system there are still some existing problems that haven't been well solved.This work focuses on the problems of nonlinear model predictive control.Based on the predictive control theory and some advanced control approaches,by applying the characters of the nonlinear systems,several predictive control problems with uncertainty,disturbance and time delay are systematically studied on the basis of the analysis of research results obtained in the area of model uncertainty system predictive control all over the word.The main research results are as follows:For a class of convex polyhedron uncertain discrete nonlinear systems with disturbance and multiple time-delay,a min-max robust predictive control algorithm is proposed based on predictive control theorem.First,the model prediction control problem is described as a class of min-max problems for infinite time domain.Then the problem is transformed into a constrain problem described by LMI by the LMI technology and a state feedback controller is designed.An improved Lyapunov-Krasovskii functional is constructed using provided information and the optimization problem is solved based on model predictive control theory.At the same time the theory and related proof of the existence of the designed controller are also given.Thus,the new evidence of the existence of the designed controller and design method of the state feedback matrix are obtained,based on which,the flowchart of the robust model predictive controller is given.Finally,the robust asymptotic stable theory of the closed-loop system is given.Theoretical analysis and simulation demonstrate the feasibility of the controller and the robust asymptotic stability of the system.For a class of uncertain discrete systems with nonlinear disturbance,input time-delay and multiple state time-delay,a robust predictive control algorithm is proposed.First,the min-max optimization problem of the infinite time domain is transformed into a class of convex optimization problem,and the corresponding state feedback controller is designed.The sufficient condition of the existence of the designed controller and the design method of the state feedback gain matrix are given in the form of theory.Based on that,the flowchart of the robust model predictive control algorithm is given.Second,the robust stability theory of the closed-loop system is given and the feasibility of the controller and the robust asymptoticstability of the system are analyzed and simulated.Finally,for some special cases of the uncertain discrete time-delay system,the novel criterion of the existence of the control law is discussed.The stability and feasibility of the closed-loop system is analyzed and simulated to further justify the effectiveness of the controller.For the case where rigorous feedback nonlinear system model is uncertain,the Backstepping is first introduced to design the virtual control law.Then the actual control law and the corresponding adaptive law are derived.The unknown function in the error derivative is approximated using fuzzy logic system and the upper bound of the optimization coefficient norm of the fuzzy system is directly estimated,thus,the obtained controller is simple and of few adaptive parameters.What's more,the computation amount and time are reduced.Based on the Lyapunov stability theory,it is proved that all the signals of the system are bounded and the tracking errors are convergent thus the system is stable.To further improve the dynamic characteristics of the system,the predictive control method is used to adjust controller parameters online.Finally,the effectiveness of the designed control method is proved by simulation.For a class of SISO nonlinear systems with model uncertainty,a fuzzy adaptive predictive controller is designed based on Backstepping method.First,in the controller design,the characteristics of fuzzy basis functions are fully used to avoid the fuzzy basis function terms in the obtained control law and adaptive law.Besides,all the nonlinear parts of the system are treated as an ensemble and the fuzzy logic system is used to approach the so-called ensemble.The square of the optimal weight vector is directly estimated using adaptive parameters thus there is only one adaptive parameter that needs to be adjusted online.In this way,the controller is more simple and requires less computation amount and time,thus is more convenient to use.Besides,the proper Lyapunov candidate functions are constructed and the system stability is analyzed and proved in theory.Finally,the effectiveness of the control method is verified by simulation.The discrete time-varying nonlinear system is considered to study the sliding mode predictive control problem with model uncertainty.For a class of time-variant uncertain nonlinear systems,a sliding mode predictive model is first designed.Then,a sliding mode predictive control algorithm is designed.The feedback correction and rolling optimization technique are utilized in the predictive control to compensate the uncertainty of the system in time and eliminate the chattering effect in the sliding mode control.Finally,the system stability theory is provided.Theoretical analysis demonstrates that the closed-loop system has strong robustness in the cases where the system has uncertainty and unknown upper bound ofoutside disturbance.Numerical simulation and pendulum experiment demonstrate that this scheme is effective.