Model Predictive Control For Two Classes Of Nonlinear Discrete Systems

With the development of modern industry and progress of science technology,the process industry is changed to more complex and with strong nonlinearcharacteristics so that linear model predictive control(LMPC)may not always obtainsatisfactory control results. Predictive control based nonlinear model (NMPC) hasbecome an important research issue in the control engineering fieds. Modelpredictive control methods for two classes of nonlinear systems, namely, nonlineardiscrete stochastic systems with actuator saturation and nonlinear quadratic systemsare studies in this paper. Stability analysis of the proposed predictive controlmethods is given, while the validity of the proposed control methods is verified viasimulation experiments. The main contents are outlined as follows:1. The model predictive control is investigated for nonlinear discretestochastic systems with actuator saturation. The actuator saturation, randomnonlinearity and external disturbances simultaneously are included in this controlledsystems. The saturation function is decomposed into a linear and a nonlinear part byusing the sector conditions, and the stochastic nonlinearity is described by statisticalmeans. Based on the Lyapunov stability theorem and linear matrix inequality (LMI)technique, sufficient conditions are given to guarantee the performance and thestochastic stability of closed-loop system. Finally, a simulation example is employedto show the feasibility and effectiveness of the model predictive control method.2. The model predictive control is investigated for nonlinear discrete quadraticsystems. For a given polytopic initial feasible set, a state feedback model predictivecontroller is designed, sufficient conditions for the closed-loop systems to be stableand cost function to be minimum are derived by using linear matrix inequalities.Based on Lyapunov theorem, the feasibility of the proposed model predictive controlalgorithm and the stability of the closed-loop systems are proved. Finally, asimulation example is employed to show the feasibility and effectiveness of themodel predictive control method.