Research On Iterative Parameter Estimation Methods For Generalized Time-varying Parameter Systems

In some engineering practices,due to changes in the environment,working conditions,and other factors,system parameters often show time-varying characteristics.An accurate model describing the time-varying input-output behavior of the system is the key to control design and performance optimization.A generalized time-varying parameter system as a special time-varying system is widely used in production engineering.Its parameter identification has always been a difficult problem and a hot topic.In this paper,the unknown parameter estimation problem of generalized timevarying parameter systems is discussed by using gradient iterative algorithms,moving data windows,data filtering,and other methods combined with hierarchical identification theory and auxiliary model momentum theory.In addition,the computational efficiency,estimation accuracy,and convergence rate of the algorithm were studied,and the following research results were obtained:(1)Aiming at the parameter estimation problem of a generalized time-varying parameter system under white noise interference,the general identification model of a generalized time-varying parameter system is derived.Using the gradient descent search method,an iterative algorithm based on gradient is proposed,and a DC motor speed control system model is used for verification.In addition,in order to improve the identification accuracy of the algorithm and realize online identification,a dynamic data window is introduced to realize dynamic data updates.Combined with negative gradient search,the gradient iteration algorithm for moving the data window for a generalized time-varying parameter system is derived.Numerical examples and simulation results of a DC motor speed control system demonstrate that the proposed algorithm can effectively improve the identification accuracy of the algorithm.(2)In the actual industrial system,the system is susceptible to colored noise interference,which affects the performance of the identification algorithm.In order to solve the problem of the large computation amount of the generalized time-varying parameter system identification algorithm under colored noise interference,a generalized augmented gradient iterative algorithm is proposed by using an auxiliary model to estimate unknown variables of the colored noise model and the gradient descent search method.In addition,the identification model of the generalized timevarying parameter system is decomposed into two subsystems by using the model decomposition technique.By coordinating the correlation items in the two submodels,the interactive estimation of the coefficient matrix and parameter vector is realized.The two-stage generalized augmented gradient iterative algorithm of the generalized timevarying parameter system is derived,and the unnecessary iterative calculation in the algorithm is separated out.The computational cost of the proposed algorithm is reduced,and its effectiveness is verified by numerical simulation examples.The calculation amount of the proposed algorithm is analyzed using floating-point operations.The results show that the proposed algorithm is more efficient.(3)Aiming at the problem that the parameter estimation of the generalized timevarying parameter system is biased due to the interference of the moving average noise,the identification model of the system is extended to various types of systems by considering different disturbance vectors in the model.An augmented gradient iteration algorithm is proposed by using the auxiliary model to calculate the estimated residual,which replaces the unmeasurable variable in the noise information vector.Combined with the principle of hierarchical interaction estimation,a hierarchical augmented gradient iterative algorithm is proposed.In order to improve the estimation accuracy of the algorithm,a hierarchical maximum likelihood gradient iterative algorithm for generalized time-varying parameter systems is derived by combining the maximum likelihood principle based on probability statistics theory with the hierarchical identification principle.Numerical simulation results show that the proposed algorithm can effectively improve the accuracy of parameter estimation.(4)For the generalized time-varying parameter system with autoregressive moving average noise interference,the identification accuracy and convergence speed of the algorithm are studied.Through parameter and model decomposition,an independent identification model with time-varying parameters and an independent identification model with colored noise are established,which simplifies the structure of the original identification model.Data filtering technology is introduced to eliminate the influence of colored noise on the estimation of the coefficient matrix to improve the identification accuracy.The concept of momentum is introduced into the modified quantity of the iterative operation of the coefficient matrix,and a filtered-based momentum gradientbased iterative algorithm for the generalized time-varying parameter system is derived.The superiority of the proposed algorithm in identification accuracy and convergence speed is verified by numerical simulation.