Parameter Estimation Of Nonlinear System Based On Regularized Least Squares Algorithm

With the rapid development of industry,the linear system can not accurately describe the dynamic characteristics of the controlled object,it is necessary to establish a nonlinear model to describe the dynamics of systems.Regularization theory was first proposed to solve the ill-posed problem.Because it can solve the problem of information matrix pathology,it is widely used in the field of system identification.In this paper,the regularized least squares algorithm is improved by using redundant rule,self-organizing mapping,and kernel functions for nonlinear models with unknown structure and known structure,respectively.It can simultaneously obtain parameter estimates and time-delay of nonlinear systems.In addition,the proposed algorithms are applied to the state of charge estimation of lithium batteries.The specific research contents are as follows:1.For the time-delayed rational model,a redundant rule method is used to transform the it into a redundant model,and the unknown parameters of the redundant model are estimated by combining the Ridge regression and least squares algorithms.In order to select the redundant parameters,a least squares algorithm based on Lasso regression is proposed to avoid the setting of threshold values.In addition,a three-stage identification framework is proposed to improve the estimation accuracy of the unknown parameters and time-delay.The simulation results illustrate the effectiveness of the proposed algorithms.2.A kernel regularized least squares algorithm is proposed for nonlinear time-delayed systems with unknown structure.Since the structure and time-delay of the model are unknown,a model pool consisting of multiple Volterra systems is constructed by using a self-organizing mapping method with the aim of approximating the nonlinear model with different time-delay.For the problem of dimensional catastrophe of Volterra systems,a kernel method is used to map the data from high-dimensional space to low-dimensional space and combine the regularized least squares method to estimate the unknown parameters interactively.Compared with traditional algorithms,the proposed algorithm does not require priori knowledge of the model structure.Finally,the effectiveness of the algorithm is verified by simulation examples.3.To estimate the state of charge(SOC)of the lithium battery,a second-order resistivecapacitive(RC)equivalent circuit model is constructed to simulate the dynamic performance of the battery,and a regularized least squares algorithm is combined with Kalman filter to estimate the battery model parameters and SOC.When the state vector contains outliers,a strong tracking filter(STF)theory is introduced to adaptively adjust the gain matrix to further improve the robustness of the algorithm.When some of the measurable output data are missing,the algorithm is improved based on the auxiliary model approach to achieve the estimation of the lost output data and SOC.Finally,the simulation results illustrate the effectiveness of the proposed algorithms.In summary,for the nonlinear time-delayed system with unknown structure and known structure,the regularized least squares algorithm is improved to achieve the simultaneous estimation of unknown parameters and time-delay,and the algorithm is applied to the SOC estimation of the lithium battery.The numerical simulation shows that the proposed algorithms are effective.