Least Squares Based and Two-Stage Least Squares Based Iterative Estimation Algorithms for H-FIR-MA Systems

This paper studies the identification of Hammerstein finite impulse response moving average (H-FIR-MA for short) systems. A new two-stage least squares iterative algorithm is developed to identify the parameters of the H-FIR-MA systems. The simulation cases indicate the efficiency of the proposed algorithms

Parameter and State Estimator for State Space Models

This paper proposes a parameter and state estimator for canonical state space systems from measured input-output data. The key is to solve the system state from the state equation and to substitute it into the output equation, eliminating the state variables, and the resulting equation contains only the system inputs and outputs, and to derive a least squares parameter identification algorithm. Furthermore, the system states are computed from the estimated parameters and the input-output data. Convergence analysis using the martingale convergence theorem indicates that the parameter estimates converge to their true values. Finally, an illustrative example is provided to show that the proposed algorithm is effective

Partially coupled gradient estimation algorithm for multivariable equation-error autoregressive moving average systems using the data filtering technique

System identification provides many convenient and useful methods for engineering modelling. This study targets the parameter identification problems for multivariable equation-error autoregressive moving average systems. To reduce the influence of the coloured noises on the parameter estimation, the data filtering technique is adopted to filter the input and output data, and to transform the original system into a filtered system with white noises. Then the filtered system is decomposed into several subsystems and a filtering-based partially-coupled generalised extended stochastic gradient algorithm is developed via the coupling concept. In contrast to the multivariable generalised extended stochastic gradient algorithm, the proposed algorithm can give more accurate parameter estimates. Finally, the effectiveness of the proposed algorithm is well demonstrated by simulation examples

Recursive search-based identification algorithms for the exponential autoregressive time series model with coloured noise

This study focuses on the recursive parameter estimation problems for the non-linear exponential autoregressive model with moving average noise (the ExpARMA model for short). By means of the gradient search, an extended stochastic gradient (ESG) algorithm is derived. Considering the difficulty of determining the step-size in the ESG algorithm, a numerical approach is proposed to obtain the optimal step-size. In order to improve the parameter estimation accuracy, the authors employ the multi-innovation identification theory to develop a multi-innovation ESG (MI-ESG) algorithm for the ExpARMA model. Introducing a forgetting factor into the MI-ESG algorithm, the parameter estimation accuracy can be further improved. With an appropriate innovation length and forgetting factor, the variant of the MI-ESG algorithm is effective to identify all the unknown parameters of the ExpARMA model. A simulation example is provided to test the proposed algorithms

Two Identification Methods for Dual-Rate Sampled-Data Nonlinear Output-Error Systems

This paper presents two methods for dual-rate sampled-data nonlinear output-error systems. One method is the missing output estimation based stochastic gradient identification algorithm and the other method is the auxiliary model based stochastic gradient identification algorithm. Different from the polynomial transformation based identification methods, the two methods in this paper can estimate the unknown parameters directly. A numerical example is provided to confirm the effectiveness of the proposed methods

Hierarchical gradient- and least squares-based iterative algorithms for input nonlinear output-error systems using the key term separation

This paper considers the parameter identification problems of the input nonlinear output-error (IN-OE) systems, that is the Hammerstein output-error systems. In order to overcome the excessive calculation amount of the over-parameterization method of the IN-OE systems. Through applying the hierarchial identification principle and decomposing the IN-OE system into three subsystems with a smaller number of parameters, we present the key term separation auxiliary model hierarchical gradient-based iterative algorithm and the key term separation auxiliary model hierarchical least squares-based iterative algorithm, which are called the key term separation auxiliary model three-stage gradient-based iterative algorithm and the key term separation auxiliary model three-stage least squares-based iterative algorithm. The comparison of the calculation amount and the simulation analysis indicate that the proposed algorithms are effective. (c) 2021 The Franklin Institute. Published by Elsevier Ltd. All rights reserved

Filtering Based Recursive Least Squares Algorithm for Multi-Input Multioutput Hammerstein Models

This paper considers the parameter estimation problem for Hammerstein multi-input multioutput finite impulse response (FIR-MA) systems. Filtered by the noise transfer function, the FIR-MA model is transformed into a controlled autoregressive model. The key-term variable separation principle is used to derive a data filtering based recursive least squares algorithm. The numerical examples confirm that the proposed algorithm can estimate parameters more accurately and has a higher computational efficiency compared with the recursive least squares algorithm

A Real-time Nonlinear Model Predictive Controller for Yaw Motion Optimization of Distributed Drive Electric Vehicles

This paper proposes a real-time nonlinear model predictive control (NMPC) strategy for direct yaw moment control (DYC) of distributed drive electric vehicles (DDEVs). The NMPC strategy is based on a control-oriented model built by integrating a single track vehicle model with the Magic Formula (MF) tire model. To mitigate the NMPC computational cost, the continuation/generalized minimal residual (C/GMRES) algorithm is employed and modified for real-time optimization. Since the traditional C/GMRES algorithm cannot directly solve the inequality constraint problem, the external penalty method is introduced to transform inequality constraints into an equivalently unconstrained optimization problem. Based on the Pontryagin’s minimum principle (PMP), the existence and uniqueness for solution of the proposed C/GMRES algorithm are proven. Additionally, to achieve fast initialization in C/GMRES algorithm, the varying predictive duration is adopted so that the analytic expressions of optimally initial solutions in C/GMRES algorithm can be derived and gained. A Karush-Kuhn-Tucker (KKT) condition based control allocation method distributes the desired traction and yaw moment among four independent motors. Numerical simulations are carried out by combining CarSim and Matlab/Simulink to evaluate the effectiveness of the proposed strategy. Results demonstrate that the real-time NMPC strategy can achieve superior vehicle stability performance, guarantee the given safety constraints, and significantly reduce the computational efforts

Least-Squares Based and Gradient Based Iterative Parameter Estimation Algorithms for a Class of Linear-in-Parameters Multiple-Input Single-Output Output Error Systems

The identification of a class of linear-in-parameters multiple-input single-output systems is considered. By using the iterative search, a least-squares based iterative algorithm and a gradient based iterative algorithm are proposed. A nonlinear example is used to verify the effectiveness of the algorithms, and the simulation results show that the least-squares based iterative algorithm can produce more accurate parameter estimates than the gradient based iterative algorithm