Finite-time Synchronization Control Research Articles

Finite-time funnel synchronization control based on distributed observer for multi-motor driving systems with input saturation

In this article, the finite-time synchronization control problem is developed for multi-motor driving systems with input saturation. A radial basis function (RBF) neural network is utilized to estimate the unknown uncertainties and the disturbances. In contrast to current control strategies, this study proposes a new approach that utilizes a finite-time distributed observer to estimate the reference signal and then uses the estimated signal to design a synchronization controller, which effectively separates the tracking problem from the synchronous controller design. Furthermore, a funnel function is constructed to actualize the state constraints and confine the synchronization error within a specified boundary. Then, a finite-time funnel control protocol is proposed to ensure that each motor follows the estimated reference signal. Eventually, we illustrate the effectiveness of the proposed method through a numerical example.

Synchronous oscillation characteristic and finite-time function projection synchronization control method for microgrids

Due to the nonsynchronization of each microsource node in a microgrid, the physical parameters of each node are not uniform. Therefore, unstable oscillation will occur for the whole microgrid system. To solve the oscillation problem caused by the nonsynchronization of each microsource node in the microgrid, a hierarchical control structure microgrid model is researched in this paper. Based on the theory of chaotic synchronization and finite time, a new microgrid synchronous oscillation characteristic and finite-time function projection synchronization control method is proposed. First, combining complex networks and microgrids, a nonlinear dynamic model of microgrid hierarchical control is established, and the abilities of the small-world network model and the formal network model to adjust for asynchronous oscillations are verified by comparing the two models. Then, aiming at the unsynchronized oscillations caused by external system noise, a new finite-time function projection synchronization control method is proposed. According to the verification results, the method can control external disturbances, avoiding system oscillation.

Finite-time synchronization control scheme for underactuated satellite formation reconfiguration

A synchronization control scheme for underactuated satellite formation reconfiguration in circular orbits is proposed in this paper. The main idea of the synchronization scheme is to control the satellite without radial or along-track thrust to track its desired configuration while synchronizing its motion with that of other underactuated satellites to maintain the predefined or time-varying formation. Firstly, a new underactuated control approach is presented for either underactuated case. Based on the inherent coupling of the system states, the finite-time convergence of the system trajectory could be guaranteed by the sliding mode-based underactuated controller. Secondly, to synchronize the reconfiguration motion between followers, the sum of the sliding mode errors of every two neighbor followers is defined as the synchronization control. The Lyapunov-based method proves the finite-time convergence of synchronization control. More importantly, the minimum nonzero eigenvalue of the Laplace matrix can reduce the system state convergence region. Numerical simulations also verify the performance of the proposed underactuated synchronization controller.

New Results on Finite-Time Synchronization Control of Chaotic Memristor-Based Inertial Neural Networks with Time-Varying Delays

In this work, we are concerned with the finite-time synchronization (FTS) control issue of the drive and response delayed memristor-based inertial neural networks (MINNs). Firstly, a novel finite-time stability lemma is developed, which is different from the existing finite-time stability criteria and extends the previous results. Secondly, by constructing an appropriate Lyapunov function, designing effective delay-dependent feedback controllers and combining the finite-time control theory with a new non-reduced order method (NROD), several novel theoretical criteria to ensure the FTS for the studied MINNs are provided. In addition, the obtained theoretical results are established in a more general framework than the previous works and widen the application scope. Lastly, we illustrate the practicality and validity of the theoretical results via some numerical examples.

Event-Triggered Finite-Time Synchronization Control for Quaternion-Valued Memristive Neural Networks by an Non-Decomposition Method

Applying the event-triggered control, this paper discusses the finite-time synchronization issue of quaternion-valued memristive neural networks (QVMNNs) with time-varying delays. By employing the improved one norm and sign function of quaternion, the QVMNNs can be analyzed as an entirety without any decomposition. To relieve the communication pressure, a proper event-triggered controller is designed, then the event-triggered conditions and some criteria are also established to guarantee finite-time synchronization. Moreover, the synchronization time is estimated by direct analysis, and the positive lower bound of the inter-event time is obtained to get rid of the Zeno behavior. In addition, according to the acquired event-triggered scheme, a self-triggered scheme is further provided to refrain from continuous detection. Ultimately, the validity of the obtained theoretical results is demonstrated by a numerical simulation.

Finite-time adaptive dynamic surface synchronization control for dual-motor servo systems with backlash and time-varying uncertainties

The dual-motor driving servo system is continuously developed to satisfy strict safety and reliability requirements. However, several factors may degrade the system’s performance, such as transmission backlash, parameter drift, and motor dynamic characteristic differences. To overcome these factors, this study proposes a finite-time tracking and synchronization control method for dual-motor servo systems that suffer from backlash and time-varying uncertainties. Our solution utilizes an adaptive dynamic surface and cross-coupling control scheme to deal with tracking and synchronization control issues and compensate for the unknown time-varying uncertainties. Through synchronizing the speed and acceleration states, the proposed controller guarantees high control performance and eliminates the force fighting caused by the motor’s dynamic characteristic differences. In addition, finite-time control ensures the tracking error converges to an arbitrarily small neighborhood of zero in finite time. Moreover, the singularity problem in the derivative of the virtual control signal is avoided by introducing a new compensation term. Several simulations prove the proposed controller’s stability and effectiveness.

Finite-Time Synchronization Control of Networked Chaotic Complex-Valued Systems With Adaptive Coupling

In the present paper, the finite-time synchronization control problem is addressed for the networked complex-valued dynamical systems with directed and undirected topologies. By combining the two-phase method with delayed impulsive control and designing adaptive coupling weights, several finite-time synchronization results and the corresponding settling times are obtained by using the complex-valued states directly. In particular, the delayed impulsive control is introduced in the first phase to guarantee that the controlled system can globally exponentially converge to the inner of the unit ball, while the finite-time control term is used only in the second phase to ensure the finite-time stability. Finally, two numerical examples are used to show the validity of our control strategy.

A Novel Delay-Dependent Finite-Time Control of Telerobotics System With Asymmetric Time-Varying Delays

Finite-time stability (FTS) is desirable in teleoperation control as it provides fast transient, high-precision, and better disturbance rejection properties. In most cases, a stringent condition on communication time delays or an additional time-delay estimation method is necessary to guarantee finite-time synchronization with the existing finite-time control schemes for the teleoperation system. This article proposes the first result of global finite-time synchronization control algorithm for the teleoperation system without any approximation function. Specifically, a novel proportional plus damping (P + d) like control algorithm is designed by employing a continuous nonsmooth function on the position synchronization errors and the velocity signals, dexterously. Furthermore, global FTS is proved with the Lyapunov stability theory based on linear-matrix-inequality (LMI) and geometric homogeneous techniques. The delay-dependent FTS criteria are also derived, which can be used to compute the allowable maximal transmission delay with the given control parameters. Finally, simulation results demonstrate the effectiveness of the proposed approach, and experiments on a teleoperated pair of three-degree-of-freedom (DOF) PHANToM robots are also presented to show the superior performances of the control strategy.

Finite-time synchronization control for a class of perturbed nonlinear systems with fixed convergence time and hysteresis quantizer: applied to Genesio–Tesi chaotic system

Finite-time synchronization control for a class of perturbed nonlinear systems with fixed convergence time and hysteresis quantizer: applied to Genesio–Tesi chaotic system

Adaptive neural-based finite-time attitude synchronization and tracking control of multiple rigid bodies under actuator faults and saturation

PurposeThe purpose of this paper, is to solve the problem of finite-time fault-tolerant attitude synchronization and tracking control of multiple rigid bodies in presence of model uncertainty, external disturbances, actuator faults and saturation. It is assumed that the rigid bodies in the formation may encounter loss of effectiveness and/or bias actuator faults.Design/methodology/approachFor the purpose, adaptive terminal sliding mode control and neural network structure are used, and a new sliding surface is proposed to guarantee known finite-time convergence not only at the reaching phase but also on the sliding surface. The sliding surface is then modified using a proposed auxiliary system to maintain stability under actuator saturation.FindingsAssuming that the communication topology between the rigid bodies is governed by an undirected connected graph and the upper bounds on the actuators’ faults, estimation error of model uncertainty and external disturbance are unknown, not only the attitudes of the rigid bodies in the formation are synchronized but also they track the time-varying attitude of a virtual leader. Using Lyapunov stability approach, finite-time stability of the proposed control algorithms demonstrated on the sliding phase as well as the reaching phase. The effectiveness of the proposed algorithm is also validated by simulation.Originality/valueThe proposed controller has the advantage that the need for any fault detection and diagnosis mechanism and the upper bounds information on estimation error and external disturbance is eliminated.

Finite-Time Synchronization Control for Bilateral Teleoperation Systems With Asymmetric Time-Varying Delay and Input Dead Zone

In this article, the synchronization control problem of bilateral teleoperation systems with time-varying delays and input dead zones is addressed. A novel radial basis function network (RBFN)-based adaptive finite-time synchronization control scheme is proposed, where system uncertainties, asymmetric time-varying delays, and dead-zone phenomena are considered simultaneously. Specifically, an RBFN is designed to approximate system uncertainties and unknown nonlinearities. The approximation error as well as the time-associated uncertainty and the nonlinear margin of the dead zone is compensated by an adaptive compensator. Using a Lyapunov-Krasovskii function and the finite-time stability criteria, the system is proved to be semiglobally practically finite-time stable. The theoretical analysis is given to prove the stability of the closed-loop system. The tracking performance of the designed controller is demonstrated by comparative simulation studies and experiment results.

Dynamic modeling and aperiodically intermittent strategy for adaptive finite-time synchronization control of the multi-weighted complex transportation networks with multiple delays* *Project supported by the National Natural Science Foundation of China (Grant No. 61803275), Liaoning Provincial Department of Education Scientific Research Fund Project, China (Grant Nos. lnjc202018 and lnzd202007), Liaoning BaiQianWan Talents Program (Grant No. 2017076), and Liaoning Province Doctor Starting

The idea of network splitting according to time delay and weight is introduced. Based on the cyber physical systems (CPS), a class of multi-weighted complex transportation networks with multiple delays is modeled. The finite-time synchronization of the proposed complex transportation networks model is studied systematically. On the basis of the theory of stability, the technique of adaptive control, aperiodically intermittent control and finite-time control, the aperiodically intermittent adaptive finite-time synchronization controller is designed. The controller designed in this paper is beneficial for understanding the synchronization in multi-weighted complex transportation networks with multiple delays. In addition, the conditions for the existence of finite time synchronization have been discussed in detail. And the specific value of the settling finite time for synchronization is obtained. Moreover, the outer coupling configuration matrices are not required to be irreducible or symmetric. Finally, simulation results of the finite-time synchronization problem are given to illustrate the correctness of the results obtained.

Event-triggered adaptive fault-tolerant attitude synchronization and tracking control of multiple rigid bodies with finite-time convergence

This study investigates finite-time attitude synchronization and tracking control of multiple rigid bodies under event-triggered control strategy in presence of actuator faults and an external disturbance. The event-triggered implementation technique aims to reduce resource utilization in regard to control effort and communication burden. To achieve this aim, the adaptive sliding mode structure is used, and a novel triggering condition is proposed. In presence of unknown actuator faults and external disturbance, it is shown that the multiple rigid bodies track a time-varying attitude of a virtual leader synchronously in finite time under limited data communication. Moreover, a lower bound on the inter-event times has been derived to ensure that the Zeno behavior is avoided. The effectiveness of the proposed method is validated by numerical simulation along with comparison with another relevant research.

Fractional-Order Hidden Attractor Based on the Extended Liu System

In this paper, a new commensurate fractional-order chaotic oscillator is presented. The mathematical model with a weak feedback term, which is named hypogenetic flow, is proposed based on the Liu system. And with changing the parameters of the system, the hidden attractor can have no equilibrium points or line equilibrium. What is more interesting is that under the occasion that no equilibrium point can be obtained, the phase trajectory can converge to a minimal field under the lead of some initial conditions, similar to the fixed point. We call it the virtual equilibrium point. On the other hand, when the value of parameters can produce an infinite number of equilibrium points, the line equilibrium points are nonhyperbolic. Moreover than that, there are coexistence attractors, which can present hyperchaos, chaos, period, and virtual equilibrium point. The dynamic characteristics of the system are analyzed, and the parameter estimation is also studied. Then, an electronic circuit implementation of the system is built, which shows the feasibility of the system. At last, for the fractional system with hidden attractors, the finite-time synchronization control of the system is carried out based on the finite-time stability theory of the fractional system. And the effectiveness of the controller is verified by numerical simulation.

Finite-time and fixed-time synchronization control of discontinuous fuzzy Cohen-Grossberg neural networks with uncertain external perturbations and mixed time delays

This paper aims to investigate the synchronization control of a class of discontinuous fuzzy Cohen-Grossberg neural networks (DFCGNNs) with uncertain external perturbations and mixed time delays (discrete and distributed time-delays). By using functional differential inclusions theory, inequality technique and the non-smooth analysis of Lyapunov-Krasovskii functional, a simple switching adaptive control is designed and some new criteria are obtained to achieve the finite-time synchronization of the proposed drive-response systems. Besides, the upper bound of the settling time is estimated. Based on the finite-time synchronization, we further present a novel discontinuous state-feedback controller to the response neural system in order to derive the fixed-time synchronization criteria and estimate the settling time. Compared with the previous results which can only fixed-timely synchronize or finite-timely synchronize some simple delayed fuzzy neural network systems with continuous activation functions and without uncertain external perturbations, the DFCGNNs with uncertain external perturbations and mixed time delays addressed and the theoretical results of this paper are more generalized and inclusive. Finally, several simulation examples and remarks are provided to verify the correctness and advantages of the main results.

Finite-Time Synchronization for a Class of Multiweighted Complex Networks with Markovian Switching and Time-Varying Delay

In this paper, we investigate the finite-time synchronization control for a class of nonlinear coupled multiweighted complex networks (NCMWCNs) with Markovian switching and time-varying delay analytically and quantitatively. The value of this study lies in four aspects: First, it designs the finite-time synchronization controller to make the NCMWCNs with Markovian switching and time-varying delay achieve global synchronization in finite time. Second, it derives two kinds of finite-time estimation approaches by analyzing the impact of the nonlinearity of nonlinear coupled function on synchronization dynamics and synchronization convergence time. Third, it presents the relationship between Markovian switching parameters and synchronization problems of subsystems and the overall system. Fourth, it provides some numerical examples to demonstrate the effectiveness of the theoretical results.

Further results on finite-time synchronization of delayed inertial memristive neural networks via a novel analysis method

In this paper, we propose a novel analysis method to investigate the finite-time synchronization (FTS) control problem of the drive–response inertial memristive neural networks (IMNNs) with mixed time-varying delays (MTVDs). Firstly, an improved control scheme is proposed under the delay-independent conditions, which can work even when the past state cannot be measured or the specific time delay function is unknown. Secondly, based on the assumption of bounded activation functions, we establish a new Lemma, which can effectively deal with the difficulties caused by memristive connection weights and MTVDs. Thirdly, by constructing a suitable Lyapunov functions and using a new inequality method, novel sufficient conditions to ensure the FTS for the discussed IMNNs are obtained. Compared with the existing results, our results obtained in a more general framework are more practical. Finally, some numerical simulations are given to substantiate the effectiveness of the theoretical results.

Adaptive finite-time synchronization control for fractional-order complex-valued dynamical networks with multiple weights

In this paper, finite-time synchronization issue of fractional-order complex-valued dynamical networks with multiple weights is addressed. Multiple weights are pulled into consideration, which makes our model more practical and general than single-weight one. Combining Lyapunov method with graph-theoretic method and making use of the theory of complex functions, finite-time synchronization criteria for fractional-order complex-valued dynamical networks with multiple weights are established by using feedback control and adaptive control, respectively. Furthermore, the settling time of synchronization is effectively estimated, which is connected with the order of fractional derivative, the parameters of control and topological structure of networks. Eventually, numerical simulations are exhibited to demonstrate the validity of theoretical results and analyse the relationship between the settling time of synchronization and the order of fractional derivative with the parameters of control.

Finite-time synchronization of fractional-order complex-valued coupled systems

In this paper, instead of separating the complex-valued system into two real-valued systems, the finite-time synchronization of fractional-order complex-valued coupled systems is investigated for the first time. Compared with other finite-time synchronization control, it should be stressed that an effective and novel controller is firstly designed without the help of sign functions. Moreover, some sufficient conditions are derived on the basis of the graph-theoretic approach and the theory of complex functions. Besides, the settling time of synchronization is estimated which is related to the order of fractional derivative, control parameters and the topological structure of the networks. Finally, two numerical examples are provided to show the feasibility and effectiveness of theoretical results.

Finite-time and fixed-time synchronization control of fuzzy Cohen-Grossberg neural networks

This paper aims to investigate the finite-time and fixed-time robust synchronization of fuzzy Cohen-Grossberg neural networks with discontinuous activations. To deal with the discontinuous property, the framework of Filippov solution is invoked to solve the inexistence of the classical solutions. For the purpose of achieving fixed-time synchronization, we turn to investigating the fixed-time stability problem of the error system between the drive-response systems. By the functional differential inclusions theory, inequality technique and the non-smooth Lyapunov-Krasovskii functional and designing a simple discontinuous state-feedback control law for the response neural system, some sufficient algebraic criteria are derived to achieve synchronization within a fixed time, and the settling time is given. Moreover, based on the fixed-time robust synchronization and under the same basic assumptions, we further complete the finite-time synchronization of the addressed drive-response systems by designing a simple switching adaptive controller, and the upper bound of the settling time is also estimated. It should be regarded as the first time to study the finite-time synchronization of fuzzy Cohen-Grossberg neural networks with discontinuous activations based on the adaptive control. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed synchronization strategies.