Study On Multilevel Logic Optimization And Model Predictive Control Based On Lattice Piecewise Linear Model

In the field of science and engineering,we often encounter some complex highdimensional nonlinear systems,which have complex state equations and are difficult to model accurately by linear model or existing nonlinear model.The importance of system model is prominent in control field.And the lattice piecewise linear model performs well in function approximation,i.e.,the piecewise linear function can approximate any continuous function in a compact set with arbitrary precision.From a lattice piecewise linear model,the linear structure that constitutes the piecewise linear model is clear.In this dissertation we study the problems of multilevel logic optimization and model predictive control based on lattice piecewise linear model.In order to reduce the repeated calculation in the 2-level lattice piecewise linear model,the current 2-level lattice piecewise linear model is extended to the multi-level case.The process of removing redundant parameters in the 2-level lattice piecewise linear model was discussed and the multilevel optimization of the 2-level lattice piecewise linear model was established based on the Boolean multilevel theory in logic synthesis.The fast factorization method and implication combination method are proposed.The calculation time and storage space are reduced by changing the calculation structure of the 2-level lattice piecewise linear model.The performance of the multi-level model is superior to the 2-level model,which is also shown in the simulation result.In the study of nonlinear model predictive control,a new solving method for optimal control sequence based on lattice piecewise linear model approximation was proposed.It is difficult to ensure the feasibility of the optimization problem at each sampling time by using the former linearization method due to the need to change the linear model from time to time.Besides,the online calculation also took a long time.The method proposed in this dissertation approximates the objective function of the nonlinear model predictive control problem by lattice piecewise linear model,then the nonlinear model predictive control optimization problem becomes a piecewise linear programming problem,in which the subregions as well as local linear functions are clear.Thus the optimal control sequence of the predictive control problem can be obtained by solving a series of convex optimization problems.This method successfully extends the application of lattice piecewise linear model to the control field.Compared with existing method,the lattice piecewise linear model shows advantages interms of calculation efficiency and accuracy.