Research On Trajectory Piecewise Linear Method Based On Lattice Model

It is of great importance to construct piecewise linear(PWL)approximation to nonlinear systems.The theories of linear systems are relatively mature.Linearization of nonlinear systems can break nonlinear problems into several linear problems and use linear theories to solve them.This thesis studies the trajectory piecewise linear method based on the lattice PWL model,fitting high-order nonlinear systems and nonlinear motion models to reduce the time complexity in integrated circuit simulation and improve the efficiency of optimal calculation of nonlinear model predictive control law through model order reduction and linear system theory.The main work is as follows.This thesis proposes the equivalent-value selection method to improve the selection method of linearization points.The traditional method that selects linearization points at equal distances does not take into account that the effective radius of different linearization points is different,thus the selected linearization points have redundant information.The equivalent-value selection method selects the linearization point based on the change of function values in different states,which optimize the set of selected linearization points.This thesis constructs single-trajectory,multi-trajectory and Jacobian-free lattice trajectory piecewise linear model(LTPWL)of integrated circuit systems.The singletrajectory and multi-trajectory models of the traditional trajectory piecewise linear(TPWL)method are nonlinear in weight calculation,and the model is not actual linear in subregions,thus the error will be introduced during linear reduction.The LTPWL model can achieve linear fitting of nonlinear systems in subregions to reduce the error introduced during linear reduction.The Jacobian-free LTPWL model does not need to consider the complicated analysis of Jacobian matrix of nonlinear functions,which can be easily applied to different nonlinear systems.Remove the redundant information of LTPWL model.The LTPWL model has redundant terms and literals when first established.The redundant terms and literals do not affect the final calculated value of the model.This thesis optimizes the parameters of the LTPWL model through a irredundant algorithm to improve the computational efficiency of the model.Construct the LTPWL model of the controlled nonlinear system.Due to the nonlinearity of the controlled system,the online optimization of nonlinear model predictive control is a general nonlinear programming problem,for which the effective method is the sequential quadratic programming method.However,this method requires multiple iterations to solve the problem,and the calculation efficiency is low.The LTPWL model breaks the nonlinear system into different linear time-invariant system in the corresponding subregion at different time interval,and transforms the nonlinear programming problem of the nonlinear model predictive control into a quadratic programming problem,which improves the efficiency of the online optimization in model predictive control.