Cluster synchronization in fractional-order network with nondelay and delay coupling

2021 ◽  
pp. 2250006
Author(s):  
Yi Wang ◽  
Zhaoyan Wu
Keyword(s):  
Adaptive Control ◽  
Fractional Order ◽  
Cluster Synchronization ◽  
Sufficient Condition ◽  
Fractional Order Systems ◽  
Adaptive Controllers ◽  
Control Scheme ◽  
Control Schemes ◽  
The Stability ◽  
Adaptive Control Scheme

In this paper, cluster synchronization for fractional-order complex network with nondelay and delay coupling is investigated. Based on the stability theory of fractional-order systems and the properties of fractional derivative, both static and adaptive control schemes are adopted to design effective controllers. Sufficient condition for achieving cluster synchronization about static controllers is provided. From the condition, the needed feedback gains can be estimated by simple calculations. Further, adaptive control scheme is introduced to design unified controllers. Noticeably, in the adaptive controllers, the feedback gains need not be calculated in advance and can adjust themselves to the needed values according to updating laws. Finally, numerical simulations are given to demonstrate the correctness of the obtained results.

Synchronization of Unknown Uncertain Chaotic Systems Via Adaptive Control Method

2015 ◽  
Vol 10 (5) ◽  
Author(s):  
Mohammad Pourmahmood Aghababa ◽  
Bijan Hashtarkhani
Keyword(s):  
Adaptive Control ◽  
Chaotic Systems ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Adaptive Controllers ◽  
Control Scheme ◽  
Uncertain Chaotic Systems ◽  
The Stability ◽  
Feedback Control Strategy ◽  
Adaptive Control Scheme

In this paper, an adaptive control scheme is offered to synchronize two different uncertain chaotic systems. It is assumed that the whole dynamics of both master and slave chaotic systems and their bounds are unknown and different. The error system stabilization is achieved in two cases: with input nonlinearities and without input nonlinearities. We design an adaptive control scheme based on the state boundedness property of the chaotic systems. The proposed method does not need any information about nonlinear/linear terms of the chaotic systems. It only uses an adaptive feedback control strategy. The stability of the proposed controllers is proved by using the Lyapunov stability theory. Finally, the designed adaptive controllers are applied to synchronize two different pairs of the chaotic systems (Lorenz–Chen and electromechanical device–electrostatic transducer).

A computationally efficient adaptive robust control scheme for a quad-rotor transporting cable-suspended payloads

2021 ◽  
pp. 095441002110136
Author(s):  
Nasim Ullah ◽  
Irfan Sami ◽  
Wang Shaoping ◽  
Hamid Mukhtar ◽  
Xingjian Wang ◽  
...  
Keyword(s):  
Robust Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Adaptive Robust Control ◽  
Computationally Efficient ◽  
Control Scheme ◽  
Control Schemes ◽  
Adaptive Laws ◽  
Unknown Disturbances ◽  
The Stability

This article proposes a computationally efficient adaptive robust control scheme for a quad-rotor with cable-suspended payloads. Motion of payload introduces unknown disturbances that affect the performance of the quad-rotor controlled with conventional schemes, thus novel adaptive robust controllers with both integer- and fractional-order dynamics are proposed for the trajectory tracking of quad-rotor with cable-suspended payload. The disturbances acting on quad-rotor due to the payload motion are estimated by utilizing adaptive laws derived from integer- and fractional-order Lyapunov functions. The stability of the proposed control systems is guaranteed using integer- and fractional-order Lyapunov theorems. Overall, three variants of the control schemes, namely adaptive fractional-order sliding mode (AFSMC), adaptive sliding mode (ASMC), and classical Sliding mode controllers (SMC)s) are tested using processor in the loop experiments, and based on the two performance indicators, namely robustness and computational resource utilization, the best control scheme is evaluated. From the results presented, it is verified that ASMC scheme exhibits comparable robustness as of SMC and AFSMC, while it utilizes less sources as compared to AFSMC.

Stability of Nonlinear Fractional-Order Time Varying Systems

2015 ◽  
Vol 11 (3) ◽  
Author(s):  
Sunhua Huang ◽  
Runfan Zhang ◽  
Diyi Chen
Keyword(s):  
Laplace Transform ◽  
Fractional Order ◽  
Caputo Derivative ◽  
Local Stability ◽  
State Feedback ◽  
Sufficient Condition ◽  
Time Varying ◽  
Fractional Order Systems ◽  
Time Varying Systems ◽  
The Stability

This paper is concerned with the stability of nonlinear fractional-order time varying systems with Caputo derivative. By using Laplace transform, Mittag-Leffler function, and the Gronwall inequality, the sufficient condition that ensures local stability of fractional-order systems with fractional order α : 0<α≤1 and 1<α<2 is proposed, respectively. Moreover, the condition of the stability of fractional-order systems with a state-feedback controller is been put forward. Finally, a numerical example is presented to show the validity and feasibility of the proposed method.

scholarly journals Adaptive - Synchronization of Fractional-Order Chaotic Systems with Nonidentical Structures

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Li-xin Yang ◽  
Wan-sheng He
Keyword(s):  
Adaptive Control ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Control Technique ◽  
Adaptive Synchronization ◽  
Fractional Order Systems ◽  
The Stability ◽  
Different Chaotic Systems ◽  
Theoretical Results

This paper investigates the adaptive - synchronization of the fractional-order chaotic systems with nonidentical structures. Based on the stability of fractional-order systems and adaptive control technique, a general formula for designing the controller and parameters update law is proposed to achieve adaptive - synchronization between two different chaotic systems with different structures. The effective scheme parameters identification and - synchronization of chaotic systems can be realized simultaneously. Furthermore, two typical illustrative numerical simulations are given to demonstrate the effectiveness of the proposed scheme, for each case, we design the controller and parameter update laws in detail. The numerical simulations are performed to verify the effectiveness of the theoretical results.

scholarly journals Hybrid Stability Checking Method for Synchronization of Chaotic Fractional-Order Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Seng-Kin Lao ◽  
Lap-Mou Tam ◽  
Hsien-Keng Chen ◽  
Long-Jye Sheu
Keyword(s):  
Fractional Order ◽  
Design Stage ◽  
Fractional Order Systems ◽  
State Variables ◽  
Driving System ◽  
Control Scheme ◽  
The Stability ◽  
Synchronization Scheme ◽  
Hyperchaotic Systems ◽  
Stability Checking

A hybrid stability checking method is proposed to verify the establishment of synchronization between two hyperchaotic systems. During the design stage of a synchronization scheme for chaotic fractional-order systems, a problem is sometimes encountered. In order to ensure the stability of the error signal between two fractional-order systems, the arguments of all eigenvalues of the Jacobian matrix of the erroneous system should be within a region defined in Matignon’s theorem. Sometimes, the arguments depend on the state variables of the driving system, which makes it difficult to prove the stability. We propose a new and efficient hybrid method to verify the stability in this situation. The passivity-based control scheme for synchronization of two hyperchaotic fractional-order Chen-Lee systems is provided as an example. Theoretical analysis of the proposed method is validated by numerical simulation in time domain and examined in frequency domain via electronic circuits.

scholarly journals Robust Fractional Adaptive Control Based on the Strictly Positive Realness Condition

2009 ◽  
Vol 19 (1) ◽  
pp. 69-76 ◽  
Author(s):  
Samir Ladaci ◽  
Abdelfatah Charef ◽  
Jean Loiseau
Keyword(s):  
Adaptive Control ◽  
Fractional Order ◽  
Robust Adaptive Control ◽  
Adaptive Controllers ◽  
Actuator Dynamics ◽  
Control Scheme ◽  
Positive Realness ◽  
Robust Adaptive ◽  
Model Reference Adaptive ◽  
Strictly Positive Realness

Robust Fractional Adaptive Control Based on the Strictly Positive Realness ConditionThis paper presents a new approach to robust adaptive control, using fractional order systems as parallel feedforward in the adaptation loop. The problem is that adaptive control systems may diverge when confronted with finite sensor and actuator dynamics, or with parasitic disturbances. One of the classical robust adaptive control solutions to these problems makes use of parallel feedforward and simplified adaptive controllers based on the concept of positive realness. The proposed control scheme is based on the Almost Strictly Positive Realness (ASPR) property of the plant. We show that this condition implies also robust stability in the case of fractional order controllers. An application to Model Reference Adaptive Control (MRAC) with a fractional order adaptation rule is provided with an implementable algorithm. A simulation example of a SISO robust adaptive control system illustrates the advantages of the proposed method in the presence of disturbances and noise.

Neural Approximation-Based Adaptive Control for Pure-Feedback Fractional-Order Systems With Output Constraints and Actuator Nonlinearities

2018 ◽  
pp. 468-495 ◽  
Author(s):  
Farouk Zouari ◽  
Amina Boubellouta
Keyword(s):  
Adaptive Control ◽  
Fractional Order ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Fractional Order Systems ◽  
Control Approach ◽  
Output Constraints ◽  
Actuator Nonlinearities ◽  
Unknown Control ◽  
The Stability

In this chapter, an adaptive control approach-based neural approximation is developed for a category of uncertain fractional-order systems with actuator nonlinearities and output constraints. First, to overcome the difficulties arising from the actuator nonlinearities and nonaffine structures, the mean value theorem is introduced. Second, to deal with the uncertain nonlinear dynamics, the unknown control directions and the output constraints, neural networks, smooth Nussbaum-type functions, and asymmetric barrier Lyapunov functions are employed, respectively. Moreover, for satisfactorily designing the control updating laws and to carry out the stability analysis of the overall closed-loop system, the Backstepping technique is used. The main advantage about this research is that (1) the number of parameters to be adapted is much reduced, (2) the tracking errors converge to zero, and (3) the output constraints are not transgressed. At last, simulation results demonstrate the feasibility of the newly presented design techniques.

Adaptive Control of Robot Manipulators Including Motor Dynamics

1995 ◽  
Vol 209 (3) ◽  
pp. 207-217
Author(s):  
H Yu ◽  
S Lloyd
Keyword(s):  
Adaptive Control ◽  
Control Structure ◽  
Robot Manipulators ◽  
Control Law ◽  
Task Space ◽  
Control Scheme ◽  
Control Schemes ◽  
The Stability ◽  
Adaptive Control Law ◽  
Motor Dynamics

An adaptive control scheme for robot manipulators including motor dynamics is proposed in this paper. The proposed scheme avoids the assumption that the values of motor parameters are known which is required in reference (13). An exponential control law is first developed under the assumption of no uncertainty. This forms a controller structure for the adaptive control. Using this control structure, a full-order adaptive control law is proposed to overcome parameter uncertainty for both robot link and motor. The stability analysis is in the Lyapunov stability sense. The method is further extended to the task space. Extensive simulations are performed to compare the different control schemes.

scholarly journals Composite adaptive control of a robotic joint for passive deployment applications

2002 ◽  
Vol 216 (3) ◽  
pp. 275-289
Author(s):  
A V C Reedman ◽  
K Bouazza-Marouf
Keyword(s):  
Adaptive Control ◽  
Control Strategies ◽  
Adaptive Controllers ◽  
Control Scheme ◽  
And Control ◽  
The Mathematical Model ◽  
Composite Adaptive Control ◽  
Single Worm ◽  
Adaptive Control Scheme ◽  
Computed Torque

A composite adaptive control scheme for the control of an actively constrained revolute joint with backlash cancellation is presented in this paper. The drive mechanism consists of two motor-driven worms coupled to a single worm wheel. The mathematical model and control strategies are reviewed. This is followed by the derivation of the composite adaptive controllers. Simulation and experimental results show that the composite adaptive control scheme gives an equivalent performance to a computed-torque algorithm without compromising the mechanism's ability to cancel backlash.

Control Fractional-Order Continuous Chaotic System via a Simple Fractional-Order Controller

2013 ◽  
Vol 336-338 ◽  
pp. 770-773
Author(s):  
Dong Zhang ◽  
Shou Liang Yang
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Equilibrium Points ◽  
Stability Theorem ◽  
Asymptotically Stable ◽  
Fractional Order Systems ◽  
Control Scheme ◽  
The Stability ◽  
Fractional Order Controller ◽  
Order Continuous

A universal fractional-order controller is proposed to asymptotically stable the unstable equilibrium points and the nonequilibrium points of continuous fractional-order chaos systems. The simple fractional-order controller is obtained based on the stability theorem of nonlinear fractional-order systems. The control scheme is simple and theoretically rigorous. The numerical simulations demonstrate the validity and feasibility of the proposed fractional-order controller.

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