Time-Delay Robust Nonlinear Dynamic Inversion for Chaos Synchronization with Application to Secure Communications

The time-delay robust nonlinear dynamic inversion (TDRNDI) control technique is proposed to synchronize time-delay Chen systems. The time-delay Chen circuit is simple but exhibits complex irregular (chaotic) behavior. For this reason, this circuit can be efficiently used to encrypt messages for secure communication. In this paper, the nonlinear control-based chaos synchronization problem is considered. The proposed TDRNDI controller is a modified version of a robust nonlinear dynamic inversion (RNDI) applicable to chaotic systems, including time-delay systems. The performance and feasibility of the proposed TDRNDI controller are demonstrated by conducting numerical simulations with application to a secure communication network.

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Synchronization of Chaotic Gyros Based on Robust Nonlinear Dynamic Inversion

Journal of Applied Mathematics ◽

10.1155/2013/519796 ◽

2013 ◽

Vol 2013 ◽

pp. 1-8 ◽

Cited By ~ 2

Author(s):

Inseok Yang ◽

Dongik Lee

Keyword(s):

Nonlinear Dynamics ◽

Nonlinear Dynamic ◽

Sliding Mode ◽

Chaotic Behavior ◽

Original System ◽

Control Technique ◽

Dynamic Inversion ◽

Model Uncertainties ◽

Gain Scheduled ◽

Nonlinear Dynamic Inversion

A robust nonlinear dynamic inversion (RNDI) technique is proposed in order to synchronize the behavior of chaotic gyros subjected to uncertainties such as model mismatches and disturbances. Gyro is a crucial device that measures and maintains the orientation of a vehicle. By Leipnik and Newton in 1981, chaotic behavior of a gyro under specific conditions was established. Hence, controlling and synchronizing a gyro that shows irregular (chaotic) motion are very important. The proposed synchronization method is based on nonlinear dynamic inversion (NDI) control. NDI is a nonlinear control technique that removes the original system dynamics into the user-defined desired dynamics. Since NDI removes the original dynamics directly, it does not need linearizing and designing gain-scheduled controllers for each equilibrium point. However, achieving perfect cancellation of the original nonlinear dynamics is impossible in real applications due to model uncertainties and disturbances. This paper proposes the robustness assurance method of NDI based on sliding mode control (SMC). Firstly, similarities of the conventional NDI control and SMC are provided. And then the RNDI control technique is proposed. The feasibility and effectiveness of the proposed method are demonstrated by numerical simulations.

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CHAOS SYNCHRONIZATION OF GENERAL LUR'E SYSTEMS VIA TIME-DELAY FEEDBACK CONTROL

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127403006455 ◽

2003 ◽

Vol 13 (01) ◽

pp. 207-213 ◽

Cited By ~ 119

Author(s):

XIAOXIN LIAO ◽

GUANRONG CHEN

Keyword(s):

Time Delay ◽

Feedback Control ◽

Chaos Synchronization ◽

Control Technique ◽

Lur’E Systems ◽

Synchronization Problem ◽

Delay Feedback Control

This paper studies a master-slave type of chaos synchronization problem for a general form of Lur'e systems by a time-delay feedback control technique, improving some results of Yalçin et al. [2001]. Some fairly simple algebraic conditions are derived for easier verification, facilitating the design and applications of such chaos synchronization systems.

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Designing a Robust Nonlinear Dynamic Inversion Controller for Spacecraft Formation Flying

Mathematical Problems in Engineering ◽

10.1155/2014/471352 ◽

2014 ◽

Vol 2014 ◽

pp. 1-12 ◽

Cited By ~ 4

Author(s):

Inseok Yang ◽

Dongik Lee ◽

Dong Seog Han

Keyword(s):

Nonlinear Dynamic ◽

High Speed ◽

Formation Flying ◽

Control Method ◽

Sliding Mode ◽

Control Technique ◽

Dynamic Inversion ◽

Spacecraft Formation ◽

Spacecraft Formation Flying ◽

Nonlinear Dynamic Inversion

The robust nonlinear dynamic inversion (RNDI) control technique is proposed to keep the relative position of spacecrafts while formation flying. The proposed RNDI control method is based on nonlinear dynamic inversion (NDI). NDI is nonlinear control method that replaces the original dynamics into the user-selected desired dynamics. Because NDI removes nonlinearities in the model by inverting the original dynamics directly, it also eliminates the need of designing suitable controllers for each equilibrium point; that is, NDI works as self-scheduled controller. Removing the original model also provides advantages of ease to satisfy the specific requirements by simply handling desired dynamics. Therefore, NDI is simple and has many similarities to classical control. In real applications, however, it is difficult to achieve perfect cancellation of the original dynamics due to uncertainties that lead to performance degradation and even make the system unstable. This paper proposes robustness assurance method for NDI. The proposed RNDI is designed by combining NDI and sliding mode control (SMC). SMC is inherently robust using high-speed switching inputs. This paper verifies similarities of NDI and SMC, firstly. And then RNDI control method is proposed. The performance of the proposed method is evaluated by simulations applied to spacecraft formation flying problem.

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Time-Delay Margin and Robustness of Incremental Nonlinear Dynamic Inversion Control

Journal of Guidance Control and Dynamics ◽

10.2514/1.g006024 ◽

2021 ◽

pp. 1-11

Author(s):

Yingzhi Huang ◽

Ye Zhang ◽

Daan M. Pool ◽

Olaf Stroosma ◽

Qiping Chu

Keyword(s):

Time Delay ◽

Nonlinear Dynamic ◽

Dynamic Inversion ◽

Delay Margin ◽

Nonlinear Dynamic Inversion

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CHAOS SYNCHRONIZATION OF CHEN SYSTEMS WITH TIME-VARYING DELAYS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127412501830 ◽

2012 ◽

Vol 22 (08) ◽

pp. 1250183 ◽

Cited By ~ 2

Author(s):

JIANENG TANG ◽

CAIRONG ZOU ◽

SHAOPING WANG ◽

LI ZHAO ◽

PINGXIANG LIU

Keyword(s):

Time Delay ◽

Dynamical Systems ◽

Numerical Simulations ◽

Stability Theory ◽

Chaos Synchronization ◽

Delay Systems ◽

Time Varying ◽

Time Delay Systems ◽

Synchronization Problem ◽

The Stability

In this paper, the synchronization problem of Chen systems with time-varying delays is discussed based on the stability theory of time-delay systems. Through the analysis of the error dynamical systems, the time-delay correlative synchronization controller is designed to achieve chaos synchronization. And finally, numerical simulations are provided to verify the effectiveness and feasibility of the developed method.

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