scholarly journals Pinning Control Strategy of Multicommunity Structure Networks

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Chao Ding ◽  
Hong Yao ◽  
Jun Du ◽  
Xing-zhao Peng ◽  
Zhe Wang
Keyword(s):  
Community Structure ◽  
Control Strategy ◽  
Coupling Strength ◽  
Lyapunov Stability Theory ◽  
Pinning Control ◽  
Control Law ◽  
Structure Information ◽  
The Stability ◽  
Intensive Control ◽  
Better Than

In order to investigate the effects of community structure on synchronization, a pinning control strategy is researched in a class of complex networks with community structure in this paper. A feedback control law is designed based on the network community structure information. The stability condition is given and proved by using Lyapunov stability theory. Our research shows that as to community structure networks, there being a threshold hT≈5, when coupling strength bellows this threshold, the stronger coupling strength corresponds to higher synchronizability; vice versa, the stronger coupling strength brings lower synchronizability. In addition the synchronizability of overlapping and nonoverlapping community structure networks was simulated and analyzed; while the nodes were controlled randomly and intensively, the results show that intensive control strategy is better than the random one. The network will reach synchronization easily when the node with largest betweenness was controlled. Furthermore, four difference networks’ synchronizability, such as Barabási-Albert network, Watts-Strogatz network, Erdös-Rényi network, and community structure network, are simulated; the research shows that the community structure network is more easily synchronized under the same control strength.

The Control of a Neural Complex Network

2014 ◽  
Vol 687-691 ◽  
pp. 444-446
Author(s):  
Fan Di Zhang
Keyword(s):  
Neural Network ◽  
Community Structure ◽  
Lyapunov Stability ◽  
Control Strategy ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Pinning Control ◽  
Projective Synchronization ◽  
Cluster Synchronization ◽  
Special Cases

In this paper, the synchronization of a neural network with community structure is investigated. Cluster projective generalizes previously existing synchronization schemes. The cluster projective synchronization is more general that includes projective synchronization and cluster synchronization, as its special cases. The cluster projective synchronization of these networks is discussed via some pinning control strategy. Several sufficient conditions for the network to achieve cluster projective synchronization are derived based on Lyapunov stability theory. Numerical simulations are used to demonstrate the effectiveness and feasibility of the proposed scheme.

scholarly journals Hybrid Passivity Based and Fuzzy Type-2 Controller for Chaotic and Hyper-Chaotic Systems

2017 ◽  
Vol 11 (2) ◽  
pp. 96-103 ◽  
Author(s):  
Fernando Serrano ◽  
Josep M. Rossell
Keyword(s):  
Lyapunov Exponents ◽  
Chaotic System ◽  
Control Strategy ◽  
Chaotic Systems ◽  
Control Law ◽  
Four Dimensions ◽  
Design Requirements ◽  
The Stability ◽  
Theoretical Results

AbstractIn this paper a hybrid passivity based and fuzzy type-2 controller for chaotic and hyper-chaotic systems is presented. The proposed control strategy is an appropriate choice to be implemented for the stabilization of chaotic and hyper-chaotic systems due to the energy considerations of the passivity based controller and the flexibility and capability of the fuzzy type-2 controller to deal with uncertainties. As it is known, chaotic systems are those kinds of systems in which one of their Lyapunov exponents is real positive, and hyper-chaotic systems are those kinds of systems in which more than one Lyapunov exponents are real positive. In this article one chaotic Lorentz attractor and one four dimensions hyper-chaotic system are considered to be stabilized with the proposed control strategy. It is proved that both systems are stabilized by the passivity based and fuzzy type-2 controller, in which a control law is designed according to the energy considerations selecting an appropriate storage function to meet the passivity conditions. The fuzzy type-2 controller part is designed in order to behave as a state feedback controller, exploiting the flexibility and the capability to deal with uncertainties. This work begins with the stability analysis of the chaotic Lorentz attractor and a four dimensions hyper-chaotic system. The rest of the paper deals with the design of the proposed control strategy for both systems in order to design an appropriate controller that meets the design requirements. Finally, numerical simulations are done to corroborate the obtained theoretical results.

Impact Control in Hydraulic Actuators

2004 ◽  
Vol 127 (2) ◽  
pp. 197-205 ◽  
Author(s):  
P. Sekhavat ◽  
Q. Wu ◽  
N. Sepehri
Keyword(s):  
Lyapunov Stability Theory ◽  
Control Law ◽  
Asymptotic Convergence ◽  
Hydraulic Parameters ◽  
Hydraulic Actuators ◽  
Task Control ◽  
Nonsmooth Systems ◽  
Type Contact ◽  
The Stability ◽  
Short Transition

Every manipulator contact task that begins with a transition from free motion to constraint motion may exhibit impacts that could drive the system unstable. Stabilization of manipulators during this transition is, therefore, an important issue in contact task control design. This paper presents a discontinuous controller to regulate the transition mode in hydraulic actuators. The controller, upon sensing a nonzero force, positions the actuator at the location where the force was sensed, thus, exerting minimal force on a nonmoving environment. The scheme does not require force or velocity feedback as they are difficult to measure throughout the short transition phase. Also, no knowledge about the environment or hydraulic parameters is required for control action. Due to the discontinuity of the control law, the control system is nonsmooth. First, the existence, continuation and uniqueness of Filippov’s solution to the system are proven. Next, the extension of Lyapunov stability theory to nonsmooth systems is employed to guarantee the global asymptotic convergence of the entire system’s state towards the equilibrium point. Complete dynamic characteristics of hydraulic functions and Hertz-type contact model are included in the stability analysis. Experiments are conducted to verify the practicality and effectiveness of the proposed controller. They include actuator collisions with hard and soft environments and with various approach velocities.

Synchronization control of complex dynamical networks with piecewise constant arguments

2018 ◽  
Vol 41 (2) ◽  
pp. 540-551 ◽  
Author(s):  
Tianhu Yu ◽  
Menglong Su
Keyword(s):  
Impulsive Control ◽  
Lyapunov Stability Theory ◽  
Pinning Control ◽  
Complex Dynamical Networks ◽  
Control Law ◽  
Dynamical Networks ◽  
Piecewise Constant Arguments ◽  
Piecewise Constant ◽  
Synchronization Problem ◽  
Theoretical Results

The pinning synchronization problem is investigated for complex dynamical networks with hybrid coupling via impulsive control. Based on the Lyapunov stability theory, some novel synchronization criteria are derived and an impulsive pinning control law is proposed. By introducing a differential inequality for systems with piecewise constant arguments, it is not necessary to establish any relationship between the norms of the error states with or without piecewise constant arguments. Typical numerical examples are utilized to illustrate the validity and improvements as regards conservativeness of the theoretical results.

scholarly journals Design controler of the quasi-time optimization approach for stabilizing and trajectory tracking of inverted pendulum

2018 ◽  
Vol 226 ◽  
pp. 02007 ◽  
Author(s):  
Nguyen Xuan Chiem ◽  
Hai Nguyen Phan
Keyword(s):  
Inverted Pendulum ◽  
External Disturbance ◽  
Reference Signal ◽  
Lyapunov Stability Theory ◽  
Vertical Position ◽  
Control Law ◽  
Optimization Approach ◽  
Time Control ◽  
Time Optimization ◽  
Better Than

This article describes the method of stabilizing and tracking the trajectory of the inverted pendulum with the quasi-time optimization approach. The controller proposed in this paper is not only to stabilize the inverted pendulum in a vertical position but also to cause the inverted pendulum to follow a predetermined reference signal even when there is an interference effect. The focus of this project is the design of a quasi-time control law based on the quasi-time optimization approach and Lyapunov stability theory. The simulation and experimental results suggest that the proposed controller controls the inverted pendulum balance and cart position stability which are better than the LQR method even when there is an external disturbance effect.

Backstepping Control for a Five-Phase Permanent Magnet Synchronous Motor Drive

2015 ◽  
Vol 6 (4) ◽  
pp. 842 ◽  
Author(s):  
Anissa Hosseynia ◽  
Ramzi Trabelsi ◽  
Atif Iqbal ◽  
Med Faouzi Mimounia
Keyword(s):  
Permanent Magnet ◽  
Control Strategy ◽  
Permanent Magnet Synchronous Motor ◽  
Synchronous Motor ◽  
Backstepping Control ◽  
Lyapunov Theory ◽  
Motor Drive ◽  
Control Law ◽  
Backstepping Controller ◽  
The Stability

This paper deals with the synthesis of a speed control strategy for a five-phase permanent magnet synchronous motor (PMSM) drive based on backstepping controller. The proposed control strategy considers the nonlinearities of the system in the control law. The stability of the backstepping control strategy is proved by the Lyapunov theory. Simulated results are provided to verify the feasibility of the backstepping control strategy.

Response control of a floating airport in heading waves with output saturation

2018 ◽  
Vol 25 (3) ◽  
pp. 571-580
Author(s):  
Shuyan Xia ◽  
Daolin Xu ◽  
Haicheng Zhang ◽  
Yousheng Wu
Keyword(s):  
Control Strategy ◽  
Control Method ◽  
Stability Control ◽  
Control Law ◽  
Backstepping Method ◽  
Floating Platform ◽  
Nonlinear Dynamic Model ◽  
Floating Structure ◽  
The Stability ◽  
Floating Airport

This paper presents a nonlinear control strategy to stabilize the response of a floating platform in waves. The floating platform consists of multiple floating modules connected in sequence with flexible connectors. A nonlinear dynamic model with a number of controllers is developed for the stability control of the chain-shape floating structure. The backstepping method in conjunction with the Lyapunov stability criteria is proposed to derive the control law for each of the control actuators where the actuator forces are limited with output saturation. The numerical experiments illustrate the feasibility and effectiveness of the control strategy in various conditions of heading waves. The performance of the control method is discussed, especially associated with the saturated output.

Control of an Underactuated Three-Link Passive–Active–Active Manipulator Based on Three Stages and Stability Analysis

2014 ◽  
Vol 137 (2) ◽  
Author(s):  
Xu-Zhi Lai ◽  
Chang-Zhong Pan ◽  
Min Wu ◽  
Simon X. Yang ◽  
Wei-Hua Cao
Keyword(s):  
Nonlinear Control ◽  
Control Strategy ◽  
Lyapunov Theory ◽  
Control Law ◽  
Integrated Method ◽  
The Third ◽  
Preparatory Stage ◽  
The Stability ◽  
And Control ◽  
Nonlinear Control Law

This paper presents a novel three-stage control strategy for the motion control of an underactuated three-link passive–active–active (PAA) manipulator. First, a nonlinear control law is designed to make the angle and angular velocity of the third link convergent to zero. Then, a swing-up control law is designed to increase the system energy and control the posture of the second link. Finally, an integrated method with linear control and nonlinear control is introduced to stabilize the manipulator at the straight-up position. The stability of the control system is guaranteed by Lyapunov theory and LaSalle’s invariance principle. Compared to other approaches, the proposed strategy innovatively introduces a preparatory stage to drive the third link to stretch-out toward the second link in a natural way, which makes the swing-up control easy and quick. Besides, the intergraded method ensures the manipulator moving into the balancing stage smoothly and easily. The effectiveness and efficiency of the control strategy are demonstrated by numerical simulations.

scholarly journals Synchronization and Control of Linearly Coupled Singular Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Fang Qingxiang ◽  
Peng Jigen ◽  
Cao Feilong
Keyword(s):  
Singular Systems ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Pinning Control ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Coupling Matrix ◽  
The Stability ◽  
And Control

The synchronization and control problem of linearly coupled singular systems is investigated. The uncoupled dynamical behavior at each node is general and can be chaotic or, otherwise the coupling matrix is not assumed to be symmetrical. Some sufficient conditions for globally exponential synchronization are derived based on Lyapunov stability theory. These criteria, which are in terms of linear matrix inequality (LMI), indicate that the left and right eigenvectors corresponding to eigenvalue zero of the coupling matrix play key roles in the stability analysis of the synchronization manifold. The controllers are designed for state feedback control and pinning control, respectively. Finally, a numerical example is provided to illustrate the effectiveness of the proposed conditions.

scholarly journals Direct Self-Repairing Control for Quadrotor Helicopter Attitude Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Huiliao Yang ◽  
Bin Jiang ◽  
Ke Zhang
Keyword(s):  
Sliding Mode ◽  
Tracking Error ◽  
Lyapunov Stability Theory ◽  
Actuator Faults ◽  
Quadrotor Helicopter ◽  
Adaptive Fuzzy Sliding Mode ◽  
Fuzzy Sliding Mode ◽  
The Stability ◽  
Lock In ◽  
Better Than

A quadrotor helicopter with uncertain actuator faults, such as loss of effectiveness and lock-in-place, is studied in this paper. An adaptive fuzzy sliding mode controller based on direct self-repairing control is designed for such nonlinear system to track the desired output signal, when any actuator of this quadrotor helicopter is loss of effectiveness or stuck at some place. Moreover, using the Lyapunov stability theory, the stability of the whole system and the convergence of the tracking error can be guaranteed. Finally, the availability of the proposed method is verified by simulation on 3-DOF hover to ensure that the system performance under faulty conditions can be quickly recovered to its normal level. And this proposed method is also proved to be better than that of LQR through simulation.

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