Parameters estimation of systems with delayed and structured entries

Belkoura, Lotfi; Richard, Jean‐Pierre; Fliess, Michel

doi:10.1016/j.automatica.2008.12.026

Cited by 91 publications

(69 citation statements)

References 13 publications

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“…On the other hand, timedelay estimation of systems with unknown time delay is a challenging problem that has attracted continuous attention during the last four decades (Ren, 2005). Even though considerable efforts have been made on parameter estimation, there are still many open problems in time-delay identification due to difficulty in formulation (Richard, 2003;Belkoura et al, 2009;Khan, 2011;El-Fallah and El-Sallam, 2011;Khan and Khan, 2010). Obviously, one can expect that the more accurate the knowledge on the delay is, the higher the achievable control performances will be (Richard, 2003).…”

Section: Introductionmentioning

confidence: 99%

Time-Delay Estimation using the Characteristic Roots of Delay Differential Equations

Yi¹

2012

American Journal of Applied Sciences

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Problem statement: For ordinary dynamic systems (i.e., non-delayed), various methods such as linear least-squares, gradient-weighted least-squares, Kalman filtering and other robust techniques have been widely used in signal processing, robotics, civil engineering. On the other hand, time-delay estimation of systems with unknown time-delay is still a challenging problem due to difficulty in formulation caused. Approach: The presented method makes use of the Lambert W function and analytical solutions of scalar first-order Delay Differential Equations (DDEs). The Lambert W function has been known to be useful in solving delay differential equations. From the solutions in terms of the Lambert W function, the dominant characteristic roots can be obtained and used to estimate time-delays. The function is already embedded in various software packages (e.g., MATLAB) and thus, the presented method can be readily used for time-delay systems. Results: The presented method and the provided examples show ease of formulation and accuracy of time-delay estimation. Conclusion: Estimation of time-delays can be conducted in an analytical way. The presented method will be extended to general systems of DDEs and application to physical systems.

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Section: Introductionmentioning

confidence: 99%

Time-Delay Estimation using the Characteristic Roots of Delay Differential Equations

Yi¹

2012

American Journal of Applied Sciences

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“…On the other hand, although gradientbased optimization techniques have excellent local searching capabilities, they have yet to be fully exploited to solve the parameter identification problem for time-delay chaotic systems. In addition, the existing identification methods for nonlinear time-delay systems (see [12][13][14][15][16][17]) are not suitable for chaotic systems, as such systems typically contain nonlinear terms with more than one unknown delay/parameter.…”

Section: Introductionmentioning

confidence: 99%

A gradient-based parameter identification method for time-delay chaotic systems

Chai

Loxton

2014

Proceedings of the 33rd Chinese Control Conference

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In this paper, the parameter identification problem for a general class of time-delay chaotic systems is considered. The objective of the problem is to determine optimal values for an unknown time-delay and unknown system parameters such that the dynamic model of the system best fits given experimental data. We propose a gradient-based optimization algorithm to solve this problem, where accurate values for the partial derivatives of the error function are obtained by solving a set of auxiliary time-delay systems. Simulation results for two example problems show that the proposed algorithm is robust and efficient.

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“…Therefore, estimating the delay is an essential challenge. First works about delay estimation in the control field often consider the delay as a parameter and apply identification techniques [2], [23]. A larger description of delay estimation techniques is provided in [14].…”

Section: Introductionmentioning

confidence: 99%

Interconnected delay and state observer for nonlinear systems with time-varying input delay

Léchappé

Moulay

Plestan

et al. 2016

2016 American Control Conference (ACC)

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Abstract-This work presents a general framework to estimate both state and delay thanks to two interconnected observers. This scheme can be applied to a large class of nonlinear systems with time-varying input delay. In order to illustrate this approach, a new delay observer based on an optimization technique is proposed. Theoretical results are illustrated and compared with existing works in simulation.

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Parameters estimation of systems with delayed and structured entries

Cited by 91 publications

References 13 publications

Time-Delay Estimation using the Characteristic Roots of Delay Differential Equations

Time-Delay Estimation using the Characteristic Roots of Delay Differential Equations

A gradient-based parameter identification method for time-delay chaotic systems

Interconnected delay and state observer for nonlinear systems with time-varying input delay

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