Disturbance Rejection for Fractional-Order Time-Delay Systems

Hai-peng, Jiang; Liu, Yongqiang

doi:10.1155/2016/1316046

Cited by 8 publications

(3 citation statements)

References 18 publications

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“…We will show, the new state e n , w ðÞ T is asymptotically stable, and the equilibrium point is e n e, w ðÞ T ¼ 0, 0 ðÞ T ,whenWσ x r t À τ ðÞ ðÞ ¼ 0, as an external disturbance. Let V be, the next candidate Lyapunov function as [8,9]…”

Section: Study Of Trajectory Tracking Errormentioning

confidence: 99%

Trajectory Tracking Using Adaptive Fractional PID Control of Biped Robots with Time-Delay Feedback

Padron¹,

Perez²,

Méndez-Barrios³

et al. 2020

Becoming Human With Humanoid - From Physical Interaction to Social Intelligence

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This paper presents the application of fractional order time-delay adaptive neural networks to the trajectory tracking for chaos synchronization between Fractional Order delayed plant, reference and fractional order time-delay adaptive neural networks. For this purpose, we obtained two control laws and laws of adaptive weights online, obtained using the fractional order Lyapunov-Krasovskii stability analysis methodology. The main methodologies, on which the approach is based, are fractional order PID the fractional order Lyapunov-Krasovskii functions methodology, although the results we obtain are applied to a wide class of non-linear systems, we will apply it in this chapter to a bipedal robot. The structure of the biped robot is designed with two degrees of freedom per leg, corresponding to the knee and hip joints. Since torso and ankle are not considered, it is obtained a 4-DOF system, and each leg, we try to force this biped robot to track a reference signal given by undamped Duffing equation. To verify the analytical results, an example of dynamical network is simulated, and two theorems are proposed to ensure the tracking of the nonlinear system. The tracking error is globally asymptotically stabilized by two control laws derived based on a Lyapunov-Krasovskii functional.

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Section: Study Of Trajectory Tracking Errormentioning

confidence: 99%

Trajectory Tracking Using Adaptive Fractional PID Control of Biped Robots with Time-Delay Feedback

Padron¹,

Perez²,

Méndez-Barrios³

et al. 2020

Becoming Human With Humanoid - From Physical Interaction to Social Intelligence

View full text Add to dashboard Cite

show abstract

“…To establish the convergence of (12) to e = 0, which ensures the desired tracking, .rst, we propose the following Krasovskii [8] and Lur'e functional [9]. This is essential for the design of a globally and asymptotically stabilizing control law.…”

Section: Tracking Error Stabilization and Control Designmentioning

confidence: 99%

Trajectory tracking error using fractional order time-delay recurrent neural networks using Krasovskii-Lur’e functional for Chua’s circuit via inverse optimal control

Padron

Méndez-Barrios²,

González-Galván³

2019

Rev. Mex. Fís.

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This paper presents an application of a Fractional Order Time Delay Neural Networks to chaos synchronization. The two main methodologies, on which the approach is based, are fractional order time-delay recurrent neural networks and the fractional order inverse optimal control for nonlinear systems. The problem of trajectory tracking is studied, based on the fractional order Lyapunov-Krasovskii and Lur’e theory, that achieves the global asymptotic stability of the tracking error between a delayed recurrent neural network and a reference function is obtained. The method is illustrated for the synchronization, the analytic results we present a trajectory tracking simulation of a fractional order time-delay dynamical network and the Fractional Order Chua’s circuits

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“…In this investigation, the Rossler system is forced to follow (synchronize) and antisynchronize with the chaotic Chen system, both systems described, as mentioned above by means of discrete and variable fractional order differential equations with time delay, synchronization and Anti-synchronization are obtained by discrete fractional PID control laws [5] and using the stability theory by Lyapunov Krasovskii [6], as can be seen in the illustrations, the results are satisfactory and the analytical results agree with the results obtained by means of simulation Via Simulink-MatLab.…”

Section: Introductionmentioning

confidence: 99%

Time-Delay Synchronization and anti-Synchronization of Variable-Order Fractional Discrete-Time of Chen-Rossler Chaotics Systems Using Variable-Order Fractional-Discrete Time PID Control

Peréz¹,

Perez²,

Huerta³

2021

Preprint

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In this research article we solve the problem of synchronization and anti-synchronization of chaotic systems described by discrete and time-delayed variable fractional order differential equations. To guarantee the synchronization and anti-synchronization of these systems, we use the well-known PID control theory and the Lyapunov-Krasovskii stability theory for discrete systems of variable fractional order.We illustrate the results obtained through simulation with examples, in which it can be seen that our results are satisfactory, thus achieving synchronization and anti-synchronization of chaotic systems of variable fractional order with discrete time delay.

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Disturbance Rejection for Fractional-Order Time-Delay Systems

Cited by 8 publications

References 18 publications

Trajectory Tracking Using Adaptive Fractional PID Control of Biped Robots with Time-Delay Feedback

Trajectory Tracking Using Adaptive Fractional PID Control of Biped Robots with Time-Delay Feedback

Trajectory tracking error using fractional order time-delay recurrent neural networks using Krasovskii-Lur’e functional for Chua’s circuit via inverse optimal control

Time-Delay Synchronization and anti-Synchronization of Variable-Order Fractional Discrete-Time of Chen-Rossler Chaotics Systems Using Variable-Order Fractional-Discrete Time PID Control

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