Switched Complex Networks Research Articles

Effects of impulse on prescribed-time synchronization of switching complex networks

The specified convergence time, designated by the user, is highly attractive for many high-demand applications such as industrial robot control, missile guidance, and autonomous vehicles. For the application of neural networks in the field of secure communication and power systems, the importance of prescribed-time synchronization(PTs) and stable performance of the system is more prominent. This paper introduces a prescribed-time controller without the fractional power function and sign function, which can reach synchronization at a prescribed time and greatly reduce the chattering phenomenon of neural networks. Additionally, by constructing synchronizing/desynchronizing impulse sequences, the PTs of switching complex networks(SCN) is achieved with impulse effects, where the time sequences of switching and impulse occurrences in the networks are constrained by the average dwell time. This approach effectively reduces the impact of frequent mode switching on network synchronization, and the synchronization time can be flexibly adjusted within any physically allowable range to accommodate different application requirements. Finally, the effectiveness of the proposed control strategy is demonstrated by two examples.

Low Energy Cost Synchronization Strategy for Markovian Switching Complex Systems/Networks: Multiple Perspectives Comparative Analysis

In this paper, the low energy cost synchronization control strategy of Markovian switching complex systems/networks is mainly studied and analyzed through multiple perspectives. Firstly, in order to achieve synchronization of Markovian switching complex networks with low energy cost, a control scheme based on the optimal node selection strategy that does not depend on the network coupling strength is improved, and a finite-time controller with a simpler structure is constructed. Secondly, based on the event-triggered control strategy an effective trigger event is designed to achieve the low energy cost synchronization of Markovian switching complex networks on the basis of reducing the information transmission and interaction between networks. Finally, the two control strategies mentioned in this paper are compared and analyzed from multiple perspectives through numerical simulations to better guide practical engineering.

Synchronization of stochastic switching complex networks with a target of nonzero inputs

SummaryIn this article, we study the mean square synchronization problems for complex networks with a target of nonzero inputs under stochastic switching topology that is driven by an ergodic continuous‐time Markov process. First, we design an adaptive continuous controller based on relative full states that is consist of a synchronization term and an uncertainty elimination term, where the latter term can completely eliminate the effects of target's nonzero inputs and is continuous by adding an exponential decay function with positive initial values into the denominator. By developing a stochastic Lyapunov function, we show that zero error synchronization in the mean square sense can be achieved if the union of switching graphs contains a directed spanning tree with the target being the root. Second, we design an adaptive continuous controller based on relative outputs. Finally, we give two simulation examples to validate the theoretical results.

Event‐based reduced‐order H∞$H_{\infty }$ estimation for switched complex networks based on T‐S fuzzy model

AbstractThis paper investigates the design of a reduced‐order filter for a specific class of switched complex network systems with time‐varying delays. To handle the nonlinear components of the complex network, a T‐S fuzzy model is employed to convert them into a set of linear components. To tackle the issue of heavy network load, a memory‐based adaptive trigger mechanism is proposed. In this study, a reduced‐order state estimator is designed using the T‐S fuzzy model. To demonstrate the exponential stability of the error system, a suitable Lyapunov function is constructed based on the Lyapunov stability principle. The parameter matrix of the reduced‐order estimator is determined using the linear matrix inequality and convex linearization method. Additionally, a sufficient condition for the exponential stability of the error system at the suppression level is provided. Finally, the feasibility of the proposed scheme is validated through a simulation experiment.

Switching clusters’ synchronization for discrete space-time complex dynamical networks via boundary feedback controls

Unlike the existing literatures that consider only discrete-time networks, this paper explores the double effects of both discrete time and discrete spatial diffusions in a switching complex dynamical networks. By means of the knowledge of clusters controls, a clusters synchronous frame of space-time discrete switching complex networks with boundary feedback controller is newly proposed and established. With the helps of some indispensable vector-valued sequence inequalities and Lyapunov function with switching signals and clusters’ information, the boundary feedback controllers are designed to synchronize space-time discrete switching complex networks coupled with nodes’ states or spatial diffusions in the form of clusters. Additionally, a realizable computer algorithm is given to make the derived results of this paper easier to enforce. The current work is pioneering in consideration of discrete spatial diffusions and provides a theoretical and practical basis for future research in this regard.

Finite/Prescribed-Time Cluster Synchronization of Complex Dynamical Networks With Multiproportional Delays and Asynchronous Switching

This article focuses on the finite-time and prescribed-time cluster synchronization problems of switched complex networks with proportional delays. Considering that the matched controller often switches behind the switched systems, asynchronous switching law and switching parameters have been introduced to the complex dynamical networks. By applying the stability theory of dynamical systems and the average dwell time approach, some sufficient criteria in form of linear matrix inequalities have been developed to guarantee such networks finite/prescribed-time cluster synchronization under the pinning control scheme. Finally, one numerical example is presented to show the effectiveness of the theoretical results.

Synchronization of time scales switched complex networks via impulsive couplings

We investigate the asymptotic synchronization problem of switched complex networks (SCNs) on time scales. Switches are made by a following time sequence with a dwell time constraint. By designing a Lyapunov function and a matrix inequality, self‐synchronizing criteria for SCNs are derived based on time scales theory. An impulsive coupling approach is designed to control links between nodes at the impulsive time. It is shown that the non‐synchronized SCNs can be synchronized by impulsive coupling with interval constraint. Three simulations on different time scales verify the effectiveness of our conclusions.

Impulsive stabilization of complex-valued stochastic complex networks via periodic self-triggered intermittent control

The aim of this article is to research the stabilization issue of complex-valued stochastic Markovian switching complex networks with time delays and time-varying multi-links (CSMCTM) via periodic self-triggered intermittent impulsive control (PSIIC). Thereinto, PSIIC is designed for the first time by combining intermittent impulsive control with periodic self-triggered control for intermittent control. It is worth emphasizing that the triggered protocol is designed to be more flexible, and easier to implement than previously reported triggered protocol. Then, by means of impulsive control, intermittent control, event-driven control theory and stability analysis, a stabilization criterion of CSMCTM in the sense of exponential stability in mean square is obtained. Whereafter, the stability of a class of complex-valued inertial neural networks is researched as a practical application of our theoretical results. Ultimately, a numerical example gives a corresponding verification.

Formula omitted] event-triggered synchronization control of singular semi-Markov switched complex networks with transmitted delays

This paper deals with the H∞ exponential synchronization problem of singular semi-Markov switched complex dynamical networks (CDNs) subject to transmitted delays. Firstly, an event-triggered communication mechanism (ETCM) is developed to save singular semi-Markov switched CDNs bandwidth. A positive constant sampled-data interval is applied to avoid the Zeno behavior in an ETCM. Secondly, by discussing the data transmission of sensors and controllers, the novel delays singular semi-Markov switched CDNs are modeled to investigate the H∞ exponential synchronization problem of singular semi-Markov switched CDNs with transmitted delays via the based-on ETCM output control protocol. Moreover, some new sufficient conditions are established such that H∞ exponential synchronization of singular semi-Markov switched CDNs can be achieved. Finally, the simulation result of the presented method is shown via two cases, which demonstrates the effectiveness of the main results.

Synchronization of semi-Markovian switching complex networks with partial unknown transition rates via event-triggered control

This article investigates the synchronization of semi-Markovian switching complex networks with partial unknown transition rates. Different from Markovian switching system, semi-Markov process is characterized by a fixed transition probability matrix and a probability density function of the sojoturn time, and the sojourn time obeys an expanded exponential distribution, which relaxes the restriction that the sojoturn time obeys memoryless exponential distribution. To realize synchronization, event-triggered control is applied which effectively reduced the control cost. It is demonstrated that the semi-Markovian switching complex networks can realize synchronization under appropriate control gain, event-triggered parameter and average sojourn time. Besides, to cope with the uncertainties that may occur during the switching process, the synchronization of the semi-Markovian switching complex networks with parameter uncertainties and external disturbances is also discussed. In the end, two simulation examples are provided to verify the feasibility of our results.

Observer-based synchronisation control for discrete-time delayed switched complex networks with coding–decoding approach

ABSTRACT In this paper, we investigate the synchronisation control problem for a class of discrete-time switched complex networks with time-varying delays via a coding–decoding-based approach. An observer-based control scheme is proposed for each node by utilising the outputs of complex networks. The data are transmitted in a digital manner and only the sequence of finite coded signals is sent from the observer to the controller. We design a proper coding–decoding procedure for each node to ensure that the closed-loop networks achieve the expected synchronisation performance. By applying the average dwell-time switching strategy and a uniform quantisation approach, some criteria are firstly presented to ensure the detectability of the complex networks. Then sufficient conditions are provided for the existence of desired observer-based controller, guaranteeing the synchronisation of complex networks. Finally, a numerical example is given to illustrate the effectiveness of the obtained theoretical results.

Dynamic event-triggered resilient state estimation for time-varying complex networks with Markovian switching topologies

This paper addresses a resilient state estimation problem for an array of nonlinear complex networks with switching topologies under the dynamic event-triggered mechanism (ETM). To reduce the unnecessary data delivery, the dynamic ETM is introduced to schedule the data delivery from sensors to estimators. The model of the switched complex networks is established by adopting a Markov chain which is better to reflect the characteristics of practical complex networks. A set of novel estimators is obtained by using the properties of Kronecker product combining with the Lyapunov–Krasovskii method, and some easy-to-check conditions are derived such that the dynamics of state estimation error satisfies the prescribed H∞ performance index. In addition, the parameters of the designed resilient state estimators can be acquired by solving a series of convex optimization problems. In the end, a simulation example is given to demonstrate the validity of the proposed theoretical results in this paper.

Event‐based finite‐time H∞ synchronization control for switched complex networks with average dwell time

AbstractThis paper investigates the problem of the event‐triggered finite‐time nonfragile synchronization control for a class of discrete time‐delayed complex networks with switched topology. To decrease the unnecessary signal transmission and save control cost, the dynamic event‐triggering scheme is employed in the controller‐to‐actuator channel where the varying triggering threshold is governed by a dynamical equation. The main purpose of this paper is to design a nonfragile synchronization controller such that the synchronization error dynamics satisfies both the finite‐time boundedness and the disturbance rejection level. By constructing appropriate Lyapunov–Krasovskii functional and using the average‐dwell‐time technique, the desired controller gains are acquired in terms of the solution to a set of linear matrix inequalities. Finally, a numerical simulation example is provided to demonstrate the effectiveness of the proposed synchronization controller design scheme.

Finite-Time Antisynchronization and Parameters Identification of Nonlinear Coupled Multiple-Weight Markovian Switching Complex Networks with Stochastic Perturbations

The paper mainly focuses on the synchronization of multiple-weight Markovian switching complex networks under nonlinear coupling mode. Based on the finite-time stability theory, Itô’s lemma, and some inequality technologies, the synchronization criterion of network models in the nonlinear coupling mode is obtained; at the same time, unknown parameters of networks are also identified by an effective controller. In addition, several corollaries are given to illustrate the general applicability of the control rules in the paper. Finally, two typical numerical simulations are given to prove the rationality and feasibility of theoretical analysis of network models.

Time‐varying parameters identification and synchronization of switching complex networks using the adaptive fuzzy‐impulsive control with an application to secure communication

AbstractIn this paper, secure communication using the synchronization of complex networks has been studied. The method of secure communication is based on chaotic parameter modulation. The adaptive update rules are obtained for the identification of parameters and messages in the receiver. Considered networks have time‐varying parameters. Also, the switching topology has been considered for the networks. Different topologies are selected for the transmitter and receiver networks. Using a fuzzy inference engine, an impulsive controller is designed for synchronization. Finally, the simulation results show the effectiveness of the proposed method.

Event-Driven Synchronization of Switched Complex Networks: A Reachable-Set-Based Design

This study is concerned with the event-driven synchronization for discrete-time switched complex networks. To mitigate the transmission frequency, the dynamic event-triggered mechanism is introduced to orchestrate information transmission. In addition, the investigated complex networks are subject to the unknown nonrandom perturbation with bounded peak, and thus, conventional approaches do not apply, and new approaches are required. For handling this situation, a novel reachable-set-based synchronization technique is then established. With the dwell time switching strategy, sufficient conditions with less conservativeness are formulated, under which the synchronization error is attracted exponentially to a bounded closed region for any initial conditions. Alternatively, for some specified initial sets, the synchronization error is constrained permanently in a bounded closed set. Finally, numerical simulations substantiate the effectiveness and applicability of the theoretical results.

Full state constraints control of switched complex networks based on time‐varying barrier Lyapunov functions

This manuscript proposes an adaptive backstepping synchronous control method with full state constraints by drawing into the time-varying barrier Lyapunov functions (T-BLFs) for a kind of uncertain switched complex networks. Generally, a complex dynamic network in practical terms either possesses a switched topology or its nodes are with switched parameters. In this context, the synchronisation problem of the switched complex network is tackled by utilising adaptive backstepping method after converting switched complex network into the non-autonomous strict feedback form. Meanwhile, most of the system states are supposed to be constrained during the switch over the procedure. Thus, the constraint-handling method based on T-BLFs is developed in the backstepping process to guarantee the full state restriction boundaries are not violated, and then to realise the asymptotic stability of the nodes states of the switched complex networks. Four simulation examples are presented to verify the feasibility and effectiveness of the proposed control approach.

Event-triggering [formula omitted] synchronization for discrete time switched complex networks via the quasi-time asynchronous controller

This paper is concerned with the problem of event triggering H∞ synchronization control for discrete-time switched complex networks via quasi-time asynchronous controllers. One event triggering mechanism is introduced with the triggering parameters depending on triggering states. Applying quasi-time dependent multiple Lyapunov functions and the mode-dependent average dwell time technique, quasi-time dependent synchronization conditions are obtained with a lower weighted performance index. And then, a quasi-time dependent asynchronous controller is designed with quasi-time dependent control gains in each triggering interval. In addition, not only no more than one switching, but also multiple switchings are taken into account in each triggering interval, by which the assumption in some existing results is relaxed. Finally, the proposed result is applied to the PWM-driven boost converter.

More general results of aperiodically intermittent synchronization for stochastic Markovian switching complex networks with multi-links and time-varying coupling structure

The paper is concerned with the pth moment exponential synchronization for stochastic Markovian switching complex networks with multi-links via aperiodically intermittent control. Different from the current literature on multi-links systems, the networks we consider have time-varying topology structure. New differential inequalities are established in which the Markovian switching and multiple time-varying delays are taken into account and the constraint on parameter that determines exponential convergence rate is reduced. Based on Lyapunov method, graph theory and differential inequality techniques, some sufficient conditions are obtained to achieve exponential synchronization. As a result, the developed synchronization criteria have more accurate exponential convergence rate than that in most existing literature which focuses on delayed systems with intermittent control. Finally, an application to modified Chua’s circuits and corresponding numerical simulations are presented to demonstrate the effectiveness of the proposed theoretical results.

Mixed H2/H∞ State Estimation for Discrete-Time Switched Complex Networks With Random Coupling Strengths Through Redundant Channels.

This article investigates the mixed H2/H∞ state estimation problem for a class of discrete-time switched complex networks with random coupling strengths through redundant communication channels. A sequence of random variables satisfying certain probability distributions is employed to describe the stochasticity of the coupling strengths. A redundant-channel-based data transmission mechanism is adopted to enhance the reliability of the transmission channel from the sensor to the estimator. The purpose of the addressed problem is to design a state estimator for each node, such that the error dynamics achieves both the stochastic stability (with probability 1) and the prespecified mixed H2/H∞ performance requirement. By using the switched system theory, an extensive stochastic analysis is carried out to derive the sufficient conditions ensuring the stochastic stability as well as the mixed H2/H∞ performance index. The desired state estimator is also parameterized by resorting to the solutions to certain convex optimization problems. A numerical example is provided to illustrate the validity of the proposed estimation scheme.