Disturbance-Observer-Based Robust Synchronization Control for a Class of Fractional-Order Chaotic Systems

Chen, Mou; Shao, Shuyi; Shi, Peng; Shi, Yan

doi:10.1109/tcsii.2016.2563758

Cited by 100 publications

(42 citation statements)

References 15 publications

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“…LEs to obtain the chaotic degradation of the five CSs in their DVs are computed by using the NAs of Euler (6), only the τ max were reported in [29]; in this study, the LEs and D KY are added, and their results are presented in Table 3. In addition, we computed LEs, τ max , and D KY of the five CSs in their DVs by using the NAs of Heun (7) and (8) and RK4 (9)- (13), and their results are presented in Tables 4 and 5, respectively. e results obtained in Tables 3-5 show that MACM CS presents the higher τ max , and Chen and Liu and Chen CSs present the smallest τ max in comparison with Lorenz.…”

Section: Degradation Analysis Of the 3d Css In Eir Dvsmentioning

confidence: 99%

“…We use RMSE to compare the performance and accuracy of the trajectory of state x of the CSs (1)-(5) in their CVs respect to their DVs by using the NAs of Euler (6), Heun (7) and (8), and RK4 (9)- (13). e RMSE is defined as follows:…”

Section: Performance Of Chaotic Behaviormentioning

confidence: 99%

“…Liu and Chen (4) (6), Heun (7) and (8), and RK4 (9)-(13) NA, respectively; we considered n � 30000 samples, a small step size τ � 0.001, and same parameters and initial conditions are shown in Table 1. e error calculation is compared with respect to state variable x (n) of the five 3D CSs in their DVs, and their trajectory errors are referred to as follow: e 1 represents the difference between ODE45 and Euler algorithm (6), e 2 represents the difference between ODE45 and Heun algorithm (7) and (8), and e 3 represents the difference between ODE45 and RK4 algorithm (9)- (13). Figure 2 shows the comparison of the evolution of the state variable x (n) of the Lorenz, Rössler, Chen, Liu and Chen, and MACM CSs in their continuous version using ODE45 and DVs using the NAs of (6)- (13).…”

Section: Control Parametermentioning

confidence: 99%

“…In recent years, scienti c community has become interested in chaotic systems (CSs) due to their potential application in several areas of engineering, where the properties of chaos are desired, such as high sensitivity to initial conditions, high entropy, topology complexity, ergodicity, among others [1][2][3][4][5][6]. Electronic implementations based on chaos have been developed for digital applications, e.g., as pseudorandom sequence generator [7], synchronization of optical networks [8], image encryption [9], chaotic trajectories for autonomous mobile robot [10], chaotic radar [11], among others [12][13][14][15][16][17]. Lorenz is the rst 3D CS reported in the literature [18].…”

Section: Introductionmentioning

confidence: 99%

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Degradation Analysis of Chaotic Systems and their Digital Implementation in Embedded Systems

et al. 2019

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Digital implementation of chaotic systems (CSs) has attracted increasing attention from researchers due to several applications in engineering, e.g., in areas as cryptography and autonomous mobile robots, where the properties of chaotic systems are strongly related. The CSs in the continuous version (CV) need to be discretized where chaotic degradation must be analyzed to guarantee preservation of chaos. In this paper, we present a degradation analysis of five three-dimensional CSs and the necessary conditions to implement the discretized versions (DVs) of Lorenz, Rössler, Chen, Liu and Chen, and Méndez-Arellano-Cruz-Martínez (MACM) CSs. Analytical and numerical analyses of chaos degradation are conducted by using the time series method; the maximum discrete step size and the Lyapunov Exponents (LEs) are computed by using the Euler, Heun, and fourth-order Runge–Kutta (RK4) numerical algorithms (NAs). We conducted comparative studies of performance based on time complexity of the five proposed CSs in their DVs by using four embedded systems (ESs) based on three families of Microchip microcontrollers 8-bit PIC16F, 16-bit dsPIC33FJ, and 32-bit PIC32MZ (of low-cost electronic implementation) and a Field Programmable Gate Array (FPGA). Based on the results, the intervals at control parameters to guarantee chaos are proposed, which improves the performance characteristics of the five proposed CSs in their DVs based on digital applications.

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Section: Degradation Analysis Of the 3d Css In Eir Dvsmentioning

confidence: 99%

Section: Performance Of Chaotic Behaviormentioning

confidence: 99%

Section: Control Parametermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Degradation Analysis of Chaotic Systems and their Digital Implementation in Embedded Systems

et al. 2019

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“…When parameter change, disturbances, or state errors become large, the required input torques will quickly reach saturation due to the needed massive control effort to maintain tracking control performance for robotic manipulators [44][45][46][47][48][49][50][51][52]. Under this case, the unchanged control output will destroy the stability of the closed-loop control systems.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Neural Output Feedback Control for Uncertain Robot Manipulators with Input Saturation

Mei

Cheng-jiang

2017

Complexity

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This paper presents an adaptive neural output feedback control scheme for uncertain robot manipulators with input saturation using the radial basis function neural network (RBFNN) and disturbance observer. First, the RBFNN is used to approximate the system uncertainty, and the unknown approximation error of the RBFNN and the time-varying unknown external disturbance of robot manipulators are integrated as a compounded disturbance. Then, the state observer and the disturbance observer are proposed to estimate the unmeasured system state and the unknown compounded disturbance based on RBFNN. At the same time, the adaptation technique is employed to tackle the control input saturation problem. Utilizing the estimate outputs of the RBFNN, the state observer, and the disturbance observer, the adaptive neural output feedback control scheme is developed for robot manipulators using the backstepping technique. The convergence of all closed-loop signals is rigorously proved via Lyapunov analysis and the asymptotically convergent tracking error is obtained under the integrated effect of the system uncertainty, the unmeasured system state, the unknown external disturbance, and the input saturation. Finally, numerical simulation results are presented to illustrate the effectiveness of the proposed adaptive neural output feedback control scheme for uncertain robot manipulators.

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Adaptive switching control of uncertain fractional systems: Application to Chua's circuit

Aghababa

2018

Adaptive Control & Signal

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SummarySince the introduction of fractional‐order differential equations, there has been much research interest in synthesis and control of oscillatory, periodic, and chaotic fractional‐order dynamical systems. Therefore, in this article, the problem of stabilization and control of nonlinear three‐dimensional perturbed fractional nonlinear systems is considered. The major novelty of this article is handling partially unknown dynamics of nonlinear fractional‐order systems, as well as coping with input saturation along the existence of model variations and high‐frequency sensor noises via just one control input. The method supposes no known knowledge on the upper bounds of the uncertainties and perturbations. It is assumed that the working region of the input saturation function is also unknown. After the introduction of a simple finite‐time stable nonlinear sliding manifold, an adaptive control technique is used to reach the system variables to the sliding surface. Rigorous stability discussions are adopted to prove the convergence of the developed sliding mode controller. The findings of this research are illustrated using providing computer simulations for the control problem of the chaotic unified system and the fractional Chua's circuit model.

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Disturbance-Observer-Based Robust Synchronization Control for a Class of Fractional-Order Chaotic Systems

Cited by 100 publications

References 15 publications

Degradation Analysis of Chaotic Systems and their Digital Implementation in Embedded Systems

Degradation Analysis of Chaotic Systems and their Digital Implementation in Embedded Systems

Adaptive Neural Output Feedback Control for Uncertain Robot Manipulators with Input Saturation

Adaptive switching control of uncertain fractional systems: Application to Chua's circuit

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