Batch scheme recursive parameter estimation of continuous-time systems using the modulating functions method

Hopf and resonant codimension two bifurcation in van der Pol equation with two time delays

In this paper, a new modulating functions method is proposed to non-asymptotically and robustly estimate the state and its fractional derivative for a class of integer order linear systems in noisy environment. For this purpose, the considered system modeled by the state space representation is firstly transformed into the observable canonical form. Secondly, based on that, the new modulating functions method is applied to obtain algebraic integral formulas for the state and its fractional derivative. These integral formulas can give robust estimations in discrete noisy cases. Furthermore, it is shown how to design the required modulating functions. To demonstrate the efficiency and advantages of the proposed method, one numerical example is given by comparing with a Luenberger observer.

Nonlinear systems play a significant role in numerous scientific and engineering disciplines, and comprehending their behavior is crucial for the development of effective control and prediction strategies. This paper introduces a novel data-driven approach for accurately modeling and estimating parameters of nonlinear systems utilizing trust region optimization. The proposed method is applied to three well-known systems: the Van der Pol oscillator, the Damped oscillator, and the Lorenz system, which find broad applications in engineering, physics, and biology. The results demonstrate the efficacy of the approach in accurately identifying the parameters of these nonlinear systems, enabling a reliable characterization of their behavior. Particularly in chaotic systems like the Lorenz system, capturing the dynamics on the attractor proves to be crucial. Overall, this article presents a robust data-driven approach for parameter estimation in nonlinear dynamical systems, holding promising potential for real-world applications.Graphic

A flux-controlled cubic memristor circuit is developed and a van der Pol oscillator is implemented based on the inherent non-linear properties of this memristor. Meanwhile a linear feedback controller is designed to synchronization of two chaotic circuit. The range of the controller gain for synchronizing is derived. Both results of simulations and experiments validate the proposed van der Pol oscillation circuit and the chaos synchronization method.

Parameter Estimation of the Nonlinear Dynamics of a Thyristor Driven DC-Motor Experimental Set-Up Using HMF-Method

Parameter estimation of synchronous generation systems helps system operators develop control schemes to enhance system stability and reliability. However, the input signals used in the online estimation are measured with errors and their direct usage may produce biased parameters. To handle this problem, an online parameter estimation method considering input errors is proposed. A Lagrange multiplier‐based input variable selection method is further proposed to reduce the scales of estimation problem and improve the computational efficiency. In order to avoid ill‐conditioned problem resulted from input error over‐fitting, a Tikhonov regularisation approach is applied and the optimal regularisation parameter is determined via cross‐validation. In the case study, the numerical experiments and real‐world results validate the effectiveness and advantages of the proposed method.

In this paper, an online estimation algorithm of the source term in a first-order hyperbolic partial differential equation (PDE) is proposed. This equation describes heat transport dynamics in concentrated solar collectors where the source term represents the received energy. This energy depends on the solar irradiance intensity and the collector characteristics affected by the environmental changes. Control strategies are usually used to enhance the efficiency of heat production; however, these strategies often depend on the source term which is highly affected by the external working conditions. Hence, efficient source estimation methods are required. The proposed algorithm is based on modulating functions method (MFM) where a moving-horizon strategy is introduced. Numerical results are provided to illustrate the performance of the proposed estimator in open-and closed-loops.

In this paper, independent, symmetric, periodic motions in a van der Pol oscillator are predicted through a semi-analytical method. This semi-analytic method is based on the discretization of the corresponding continuous nonlinear system for an implicit mapping. Through the implicit mapping structures, stable and unstable periodic motions are obtained analytically. A sequence of periodic motions to chaos via 1(S) ◁ 3(S) ◁ ··· ◁ (2m − 1)(S) ◁ ··· is discovered. The stability and bifurcations of periodic motions are determined through eigenvalue analysis. The frequency–amplitude characteristics of periodic motions are discussed. Numerical simulations of the periodic motions are carried out for comparison of numerical and analytical results. Such a periodic motion sequence is for a better understanding of dynamics of the van der Pol oscillator.

This paper does some summarized research on continuous dynamical systems about non-linear electric circuit. Some theoretical analyses and simulations also have been done on the basis of classical chaos models. To the continuous dynamical systems, some basic researches about Chua non-linear electric circuit and Vanderpol equation has been carried out. Finally, considering abundant the chaos phenomenon existing in the power electronic equipment of power system, Buck electric circuit has been discussed, and the chaos phenomenon exists in the circuit indeed.

We present a computationally efficient scheme for parameter estimation of continuous dynamical linear systems given discrete-time noisy observations. The proposed scheme is optimal in the sense that it converges iteratively to the exact Maximum Likelihood estimate, where each iteration increases the likelihood.

This paper presents a hybrid optimization methodology for parameter estimation of reactive transport systems. Using reduced-order advection-diffusion-reaction (ADR) models, the computational requirements of global optimization with dynamic PDE constraints are addressed by combining metaheuristics with gradient-based optimizers. A case study in preparative liquid chromatography shows that the method achieves superior computational efficiency compared to traditional multi-start methods, demonstrating the potential of hybrid strategies to advance parameter estimation in large-scale, dynamic chemical engineering applications.

In this study, an ABC-Local Search (ABC-Ls) method was proposed by including a new local search procedure into the standard artificial bee colony (ABC) algorithm to perform the parameter estimation of photovoltaic systems (PV). The aim of the proposed ABC-Ls method was to improve the exploration capability of the standard ABC with a new local search procedure in addition to the exploitation and exploration balance of the standard ABC algorithm. The proposed ABC-Ls method was first tested on 15 well-known benchmark functions in the literature. In the results of the Friedman Mean Rank test used for statistical analysis, ABC-Ls method successfully ranked first with a value of 1.300 in benchmark functions. After obtaining successful results on the benchmark tests, the proposed ABC-Ls method was applied to the single diode, double diode and Photowatt-PWP-201 PV modules of PV systems for parameter estimations. In addition, the proposed ABC-Ls method has been applied to the KC200GT PV module for parameter estimation under different temperature and irradiance conditions of the PV modules. The success of ABC-Ls method was compared with genetic algorithm (GA), particle swarm optimization (PSO) algorithm, ABC algorithm, tree seed algorithm (TSA), Jaya, Atom search optimization (ASO). The comparison results were presented in tables and graphics in detail. The RMSE values for the parameter estimation of single diode, double diode and Photowatt-PWP-201 PV module of the proposed ABC-LS method were found as 9.8602E−04, 9.8257E−04 and 2.4251E−03, respectively. In this context, the proposed ABC-LS method has been compared with the literature for parameter estimation of single diode, double diode and Photowatt-PWP-201 PV module and it has been found that it provides a parameter estimation similar or better than other studies. The proposed ABC-Ls method for parameter estimation of the KC200GT PV module under different conditions is shown in convergence graphs and box plots, where it achieves more successful, effective and stable results than GA, PSO, ABC, TSA, Jaya and ASO algorithms.

Controlling the chaos using fuzzy estimation of OGY and Pyragas controllers

An accurate dynamic estimation of frequency and magnitude parameters (actual power-line frequency and actual power-line voltages or currents) is very important for different applications in power systems, such as frequency and magnitude relay protection, harmonics and quality of power in transient regimes, especially for local power systems with external UPS (uninterruptible power supply) synchronization (for example, by diesel-generator). Investigated methods and algorithms are modifications of OPD (orthogonal phasor decomposition) and IZC (integrating zero crossing) for frequency estimation and modifications of DFT (discrete Fourier transform) with interpolation in time or frequency domain, or alternatively, with pre-tuned prefilters, for magnitude (harmonics) estimation. Some aspects of choice and optimization of the above DSP (digital signal processing) methods and algorithms were described before in publications, but without comparison of their characteristics, which are the main subject of the proposed publication. Obtained simulation results can be used for improvement of chosen algorithms and their real time applications.

This paper is concerned with the parameter estimation and adaptive control problem for a sort of strict‐feedback nonlinear systems with unknown parameters. In order to deal with the nonlinear functions, we develop a kind of least‐squares estimator in the parameter estimation part. With such an estimator, we design the state‐feedback control law and analyze the properties of the closed‐loop system. To be concrete, the parameter estimator can guarantee the boundedness of parameter estimate error. At the same time, the adaptive control law is proposed to make the system states converge to zero and the equilibrium stable globally under some common assumptions. Finally, simulations are given to demonstrate the theoretical results.