This paper studies the problem of parameter estimation for frequency response signals For a linear system, the frequency response is a sine signal with the same frequency as the input sine signal When a multi-frequency sine signal is applied to a system, the system response also is a multi-frequency sine signal The signal modeling for multi-frequency sine signals is very difficult due to the highly nonlinear relations between the characteristic parameters and the model output In order to obtain the parameter estimates of the multi-frequency sine signal, the signal modeling methods based on statistical identification are proposed by means of the dynamical window discrete measured data By constructing a criterion function with respect to the model parameters to be estimated, a hierarchical multi-innovation stochastic gradient estimation method is derived through parameter decomposition Moreover, the forgetting factor and the convergence factor are introduced to improve the performance of the algorithm The simulation results show the effectiveness of the proposed methods

Hierarchical Parameter Estimation for the Frequency Response Based on the Dynamical Window Data

Mathematical models are basic for designing controller and system identification is the theory and methods for establishing the mathematical models of practical systems. This paper considers the parameter identification for Hammerstein controlled autoregressive systems. Using the key term separation technique to express the system output as a linear combination of the system parameters, the system is decomposed into several subsystems with fewer variables, and then a hierarchical least squares (HLS) algorithm is developed for estimating all parameters involving in the subsystems. The HLS algorithm requires less computation than the recursive least squares algorithm. The computational efficiency comparison and simulation results both confirm the effectiveness of the proposed algorithms.

A hierarchical least squares identification algorithm for Hammerstein nonlinear systems using the key term separation

The filtering‐based maximum likelihood iterative estimation algorithms for a special class of nonlinear systems with autoregressive moving average noise using the hierarchical identification principle

This study presents a combined parameter and state estimation algorithm for a bilinear system described by its observer canonical state-space model based on the hierarchical identification principle. The Kalman filter is known as the best state filter for linear systems, but not applicable for bilinear systems. Thus, a bilinear state observer (BSO) is designed to give the state estimates using the extremum principle. Then a BSO-based recursive least squares (BSO-RLS) algorithm is developed. For comparison with the BSO-RLS algorithm, by dividing the system into three fictitious subsystems on the basis of the decomposition–coordination principle, a BSO-based hierarchical least squares algorithm is proposed to reduce the computation burden. Moreover, a BSO-based forgetting factor recursive least squares algorithm is presented to improve the parameter tracking capability. Finally, a numerical example illustrates the effectiveness of the proposed algorithms.

/pdf/state-filtering-based-least-squares-parameter-estimation-for-oghrk3a23t.pdf

State filtering-based least squares parameter estimation for bilinear systems using the hierarchical identification principle

By combining the coupling identification concept with the gradient search, this study develops a partially coupled generalised extended projection algorithm and a partially coupled generalised extended stochastic gradient algorithm to estimate the parameters of a multivariable output-error-like system with autoregressive moving average noise from input–output data The key is to divide the identification model into several submodels based on the hierarchical identification principle and to establish the parameter estimation algorithm by using the coupled relationship between these submodels The simulation test results indicate that the proposed algorithms are effective

https://ietresearch.onlinelibrary.wiley.com/doi/pdf/10.1049/iet-spr.2019.0481

Recursive coupled projection algorithms for multivariable output-error-like systems with coloured noises

This paper considers the parameter estimation of a multiple-input–output-error system with autoregressive noise. In order to solve the problem of the information vector containing unknown inner variables, an auxiliary model-based recursive generalized least squares algorithm and a least squares-based iterative algorithm are proposed according to the auxiliary model identification idea and the iterative search principle. The simulation results indicate that the least squares-based iterative algorithm can generate more accurate parameter estimates than the auxiliary model-based recursive generalized least squares algorithm. Two examples are given to test the proposed algorithms.

Recursive and Iterative Least Squares Parameter Estimation Algorithms for Multiple-Input–Output-Error Systems with Autoregressive Noise

A kernel-based identification approach for a class of nonlinear systems with quantized output data

This paper investigates the tracking control problem of uncertain p-normal nonlinear systems with full-state constraints via event-triggered mechanism. By skillful constructing an adaptive dynamic gain and a time-varying event-triggered strategy, a state-feedback controller is proposed to achieve practical tracking. The adaptive dynamic gain is incorporated to deal with the system uncertainties and eliminate the bad effect of the sampling error. A rigorous Lyapunov stability analysis method is put forward to verify that all the closed-loop signals are uniformly bounded and the tracking error converges into a prescribed arbitrary accuracy, and full-state constraints are not violated. Compared with the existing event-triggered strategies, the proposed time-varying event-triggered strategy is low-complexity without designing the hyperbolic tangent function. 

Event-triggered tracking control of uncertain p-normal nonlinear systems with full-state constraints.


 The two-input one-output Hammerstein model consists of two parallel nonlinear static blocks followed by a linear dynamic part. By using Hammerstein structure to map the relationship between a battery state of charge (SOC) and its terminal voltage/current, a hierarchical stochastic gradient algorithm is studied to estimate parameters of Hammerstein SOC model, so as to predict battery SOC. First, the Hammerstein model is transformed into a bilinear parameter system with the least number of required parameters. Then, a hierarchical stochastic gradient algorithm with a forgetting factor is used to update the two sets of model parameters of the bilinear parameter system, so as to realize SOC estimation. Furthermore, the experiment platform of lithium-ion battery was built and the data of the urban dynamometer driving schedule profile and the Los Angeles 92 profile were collected. Finally, the MATLAB simulation results show that the proposed parameter optimized method based Hammerstein model has the advantages of fast convergence speed and high SOC estimation accuracy.

A Hierarchical Identification Method for Lithium-Ion Battery SOC Based on the Hammerstein Model

This paper investigates the global fixed-time tracking control problem of nonlinear cascade systems with unknown high powers. In the process of control design, a upper bound and a lower bound of high powers are introduced to compensate the unknown system powers, and a state feedback controller is designed under any initial system conditions. Based on the Lyapunov stability analysis method and the fixed-time stability theory, it is verified that the proposed method can regulate the output tracking error to a disc region of the origin within a fixed-time and all the closed-loop signals are bounded. At last, the effectiveness of the proposed scheme is verified by some simulation results.

/pdf/fixed-time-tracking-control-for-nonlinear-cascade-systems-1r3qyxvj.pdf

Jiling Ding

Papers

Recursive and Iterative Least Squares Parameter Estimation Algorithms for Multiple-Input–Output-Error Systems with Autoregressive Noise

A kernel-based identification approach for a class of nonlinear systems with quantized output data

Event-triggered tracking control of uncertain p-normal nonlinear systems with full-state constraints.

A Hierarchical Identification Method for Lithium-Ion Battery SOC Based on the Hammerstein Model

Fixed-Time Tracking Control for Nonlinear Cascade Systems with Unknown High Powers