Finite-time and fixed-time anti-synchronization of Markovian neural networks with stochastic disturbances via switching control

Convergence-Rate-Based Event-Triggered Mechanisms for Quasi-Synchronization of Delayed Nonlinear Systems on Time Scales

Most of the existing event-triggered mechanisms (ETMs) were designed according to the difference between the quadratic form of measurement errors and the quadratic form of sampling states (or real-time states). In order to reduce the amount of data transmission and develop ETMs for continuous-time and discrete-time delayed nonlinear systems (NSs) simultaneously, this article investigates quasi-synchronization (QS) of NSs on time scales based on a novel ETM, which is designed according to the convergence rate instead of measurement errors of the addressed systems. First, a novel ETM is designed under known nonlinear dynamics, and it is demonstrated that QS with given convergence rate and error level can be achieved under matrix inequality criteria. Second, if the nonlinear functions are unknown, we adapt our ETM to handle this special case. Not only QS but also complete synchronization with given convergence rate can be achieved under the ETMs. If the constructed Lyapunov functions passes through 0, the designed ETM will keep it at the origin. In this case, finite-time synchronization is achieved. Third, under the designed ETMs, it is proved that Zeno behavior can be excluded. At last, four numerical simulations are presented to demonstrate the feasibility and the advantage of the designed ETMs in this article.

Novel adaptive synchronization in finite-time and fixed-time for impulsive complex networks with semi-Markovian switching

This paper intensively studied the finite-time (FNT) and fixed-time (FXT) synchronization issues for complex networks (CNs) with semi-Markovian switching and impulsive effect. The impulses are assumed to be independent of the semi-Markovian switching. Firstly, a unified FNT and FXT stability criterion of impulsive dynamical system with time-varying delays is extended by comparison principle. Secondly, two novel hybrid control schemes, which are composed of adaptive gain and switching state-feedback are proposed. Thirdly, by employing Kronecker product, Lyapunov-Krasovskii functional and inequality technique, FNT and FXT synchronization criteria for impulsive CNs with semi-Markovian switching are presented in a set of low-dimensional linear matrix inequalities, and the settling times are computed respectively. Finally, simulations are given to verify the proposed adaptive FNT and FXT synchronization criteria.

Fixed-time projective synchronization of delayed memristive neural networks via aperiodically semi-intermittent switching control

This paper studies the fixed-time projective synchronization problem for a class of delayed memristive neural networks via aperiodically semi-intermittent switching control. Instead of using the common traditional controller containing two power exponent terms, a novel aperiodically semi-intermittent switching controller is designed, containing only one power exponent term which serves as a function of the state of the error system. With the aid of the extended differential inclusion framework, the analysis method, and the inequality technique, some new sufficient conditions are derived to guarantee fixed-time projective synchronization for the considered systems. Compared with periodically semi-intermittent control methods, the control time width of each section in aperiodically semi-intermittent control can be adjusted. Especially, the settling time is directly reckoned, which is closely related to the number of neurons and the maximum ratio of the second subinterval span in each non-periodic span to all non-periodic time spans rather than the initial value. Additionally, the projection synchronization has a strong practicality, as the projection coefficient can be adjusted for different needs instead of being fixed. Meanwhile, the study improves some previous related works. Ultimately, a numerical example is given to substantiate the correctness of the obtained results.

Finite-/fixed-time synchronization for Cohen-Grossberg neural networks with discontinuous or continuous activations via periodically switching control

This paper is concerned with finite-/fixed-time synchronization for a class of Cohen-Grossberg neural networks with discontinuous or continuous activations and mixed time delays. Based on the finite-time stability theory, Lyapunov stability theory, the concept of Filippov solution and the differential inclusion theory, some useful finite-/fixed-time synchronization sufficient conditions for the considered Cohen-Grossberg neural networks are established by designing two kinds of novel periodically switching controllers. Instead of using uninterrupted high control strength, the periodically switching controller in each period is used with high strength control in one stage and weak strength in the other. It can overcome the effects caused by the uncertainties of Filippov solution induced by discontinuous neuron activation functions and reduce the control cost. Besides, the period switching control rate is closely related to the settling time T. Finally, two numerical examples are given to demonstrate the effectiveness and feasibility of the obtained results.

Fixed-Time Synchronization Control of Delayed Dynamical Complex Networks

Fixed-time synchronization problem for delayed dynamical complex networks is explored in this paper. Compared with some correspondingly existed results, a few new results are obtained to guarantee fixed-time synchronization of delayed dynamical networks model. Moreover, by designing adaptive controller and discontinuous feedback controller, fixed-time synchronization can be realized through regulating the main control parameter. Additionally, a new theorem for fixed-time synchronization is used to reduce the conservatism of the existing work in terms of conditions and the estimate of synchronization time. In particular, we obtain some fixed-time synchronization criteria for a type of coupled delayed neural networks. Finally, the analysis and comparison of the proposed controllers are given to demonstrate the validness of the derived results from one numerical example.

Synchronization for stochastic coupled networks with Lévy noise via event-triggered control

This paper addresses the realization of almost sure synchronization problem for a new array of stochastic networks associated with delay and Lévy noise via event-triggered control. The coupling structure of the network is governed by a continuous-time homogeneous Markov chain. The nodes in the networks communicate with each other and update their information only at discrete-time instants so that the network workload can be minimized. Under the framework of stochastic process including Markov chain and Lévy process, and the convergence theorem of non-negative semi-martingales, we show that the Markovian coupled networks can achieve the almost sure synchronization by event-triggered control methodology. The results are further extended to the directed topology, where the coupling structure can be asymmetric. Furthermore, we also proved that the Zeno behavior can be excluded under our proposed approach, indicating that our framework is practically feasible. Numerical simulations are provided to demonstrate the effectiveness of the obtained theoretical results.