Convergence analysis of a synchronous gradient estimation scheme for time-varying parameter systems

SummaryIn practical applications, many processes have nonlinear characteristics that require nonlinear models for accurate description. However, constructing such models and determining their parameters are a challenging task. This article explores filtered identification methods for estimating the parameters of a particular type of nonlinear Hammerstein systems with ARMA noise. An auxiliary model‐based least squares algorithm is developed for such systems based on the auxiliary model identification idea. A hierarchical least squares algorithm that utilizes the hierarchical identification principle is proposed to enhance computational efficiency. Additionally, a key term separation technique is employed to express the system output as a linear combination of parameters, allowing the system to be decomposed into smaller subsystems for more efficient estimation of parameters. Simulation results demonstrate the effectiveness of these proposed algorithms.

Iterative parameter identification for Hammerstein systems with ARMA noises by using the filtering identification idea

Bedoui,

Abderrahim,

Ding

2024

Parameter estimation methods for time‐invariant continuous‐time systems from dynamical discrete output responses based on the Laplace transforms

Ibrahim,

Ding

2024

SummaryIn industrial process control systems, parameter estimation is crucial for controller design and model analysis. This article examines the issue of identifying parameters in continuous‐time models. This article presents a stochastic gradient estimation algorithm and a recursive least squares estimation algorithm for identifying the parameters of continuous systems. It derives the parameter identification model of linear continuous‐time systems based on the Laplace transforms of the input and output of the systems. To prove that the techniques given here work, we have included a simulated example.

Auxiliary model‐based recursive least squares and stochastic gradient algorithms and convergence analysis for feedback nonlinear output‐error systems

Miao,

Yang,

Ding

2024

SummaryThis paper deals with the problem of the parameter estimation for feedback nonlinear output‐error systems. The auxiliary model‐based recursive least squares algorithm and the auxiliary model‐based stochastic gradient algorithm are derived for parameter estimation. Based on the stochastic process theory, the convergence of the proposed algorithms are proved. The simulation results indicate that the proposed algorithms can estimate the parameters of feedback nonlinear output‐error systems effectively.