Pinning Control Strategy Research Articles

Control of chaos in Frenkel–Kontorova model using reinforcement learning* *Project supported by the National Natural Science Foundation of China (Grant Nos. 12072262 and 11672231).

It is shown that we can control spatiotemporal chaos in the Frenkel–Kontorova (FK) model by a model-free control method based on reinforcement learning. The method uses Q-learning to find optimal control strategies based on the reward feedback from the environment that maximizes its performance. The optimal control strategies are recorded in a Q-table and then employed to implement controllers. The advantage of the method is that it does not require an explicit knowledge of the system, target states, and unstable periodic orbits. All that we need is the parameters that we are trying to control and an unknown simulation model that represents the interactive environment. To control the FK model, we employ the perturbation policy on two different kinds of parameters, i.e., the pendulum lengths and the phase angles. We show that both of the two perturbation techniques, i.e., changing the lengths and changing their phase angles, can suppress chaos in the system and make it create the periodic patterns. The form of patterns depends on the initial values of the angular displacements and velocities. In particular, we show that the pinning control strategy, which only changes a small number of lengths or phase angles, can be put into effect.

Adaptive and Exponential Synchronization of Uncertain Fractional-Order T-S Fuzzy Complex Networks With Coupling Time-Varying Delays via Pinning Control Strategy

This article investigates the adaptive and exponential synchronization problems of fractional-order Takagi-Sugeno (T-S) fuzzy complex networks (FOTSFCN) with coupling time-varying delays and uncertainty. Firstly, the FOTSFCN model is established by embedding T-S fuzzy logic to reduce the complexity and robustness of the FOTSFCN. Secondly, based on the adaptive pinning control strategy, we obtain the asymptotic synchronization and exponential synchronization criteria to achieve synchronous control of FOTSFCN. Furthermore, according to the Lyapunov stability theory, we prove that the FOTSFCN controlled by the proposed controller is robust stable and the effect of coupling time-varying delays and uncertain disturbances on the tracking error can be subsided in view of the linear matrix inequalities (LMIs). Finally, the effectiveness and applicability of the theoretical results are presented through two illustrative examples.

Pinning Stabilization of Boolean Control Networks via a Minimum Number of Controllers.

The stabilization problem of Boolean control networks (BCNs) under pinning control is investigated in this article, and the set of pinned nodes is minimized. A BCN is a Boolean network with Boolean control inputs in it. When the given BCNs cannot realize stabilization under existing Boolean control inputs, pinning control strategy is introduced to make the BCNs achieve stabilization. The Warshall algorithm is introduced to verify the stabilizability of BCNs, then novel computational feasible algorithms are developed to design the minimum number pinning controller for the system. By using our method, the minimum set of pinned nodes can be found with relatively low computational complexity. Finally, the theoretical result is validated using a biological example.

Impulsive Effects Based Distributed Synchronization of Heterogeneous Coupled Neural Networks

This paper is devoted to investigating the exponential synchronization problem on a class of coupled heterogeneous neural networks with hybrid time-varying delays. Since the heterogeneity of neural networks, the quasi-synchronization rather than complete synchronization is studied. Consider that the controller would suffer from impulsive disturbances, the distributed pinning control strategy is introduced. By jointly applying the concept of average impulsive intervals, the extended comparison principle of impulsive systems, and the vector norm techniques, sufficient conditions for the achievement of exponential quasi-synchronization on coupled heterogeneous neural networks are eventually obtained. In view that different impulsive effects play different roles in network synchronizing, two different situations of exponential synchronization are considered, respectively, by separately discussing the impulsive-effects-related parameter. Additionally, on account of the extended parameter variation formula for impulsive systems with hybrid time-varying delays, the exponential convergence velocities and the quasi-synchronization errors are estimated, separately, with respect to different ranges of impulsive effects. At last, three numerical examples with distinct impulsive effect values are given to illustrate the effectiveness of the theoretical analysis and the control schemes.

Pinning exponential cluster synchronization for fractional-order complex dynamical networks with switching topology and mode-dependent impulses

In this paper, we focus on the global exponential cluster synchronization of switched fractional-order complex dynamical networks (FCDNs) with switching topology and impulses, where the impulse effects are independent or dependent of switched modal. Compared with the literature, impulsive effects can occur not at the mode switched moment, but also at the instants without me AII) with the average dwell time (ADT) and the mode-dependent average impulsive interval (MDAII) with the mode-dependent average dwell time, by adopting multiple Lyapunov functional approach, the inequality analysis technique and pinning control strategy, the global exponential cluster synchronization conditions are achieved. Finally, the validity of theoretical results is verified by two simulation examples.

Parameters Variation-Based Synchronization on Derivative Coupled Lur’e Networks

This paper investigates the exponential synchronization of coupled Lur’e dynamical networks with multiple time-varying delays and derivative coupling. In order to synchronize the Lur’e dynamical networks to the corresponding Lur’e systems, we propose a kind of impulsive pinning control strategy, where different functions of impulsive effects are taken into account. Sufficient conditions are derived for the exponential synchronization of the derivative coupled Lur’e dynamical networks by jointly applying the contradiction proof method, the concept of an average impulsive interval, comparison principle, and the extended parameters variation formula. Simultaneously, the convergence rates of exponential synchronization are obtained according to the definition of the impulsive solution equation on different functions of impulsive effects. Furthermore, three numerical examples are presented to demonstrate the validity of the theoretical analysis and the control protocol.

Fuzzy-Model-Based $\mathcal {H}_{\infty }$ Pinning Synchronization for Coupled Neural Networks Subject to Reaction–Diffusion

This article investigates the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> synchronization problem for fuzzy coupled neural networks subject to reaction–diffusion. An available control method, namely, the adaptive pinning control strategy, is employed. In view of such a method, one may accomplish control objectives by controlling a small number of nodes instead of all nodes, and in this regard, it is possible to reduce the control cost to some extent, and the method can adaptively adjust the coupling strength as well. Furthermore, a novel inequality is introduced, which can ensure that the developed results are less conservative compared with some existing ones of dealing with the reaction–diffusion terms. Then, through the utilization of fuzzy set theory together with Lyapunov stability theory, some sufficient conditions with the ability to ensure the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> performance level of the resulting synchronization error system are deduced. Finally, an illustrative example is presented to show the advantages and effectiveness of the proposed methods.

Pinning Synchronization of Complex Dynamical Networks on Time Scales

The purpose of this paper is to investigate the synchronization problem of complex dynamical networks on time scales, which includes the synchronization problem of continuous-time and discrete-time complex dynamical networks as special cases. A pinning control strategy is designed to achieve synchronization of complex dynamical networks on time scales. Based on the theory of calculus on time scales and the Lyapunov method, pinning synchronization criteria for complex dynamical networks on time scales are established. Moreover, a numerical example is given to verify the effectiveness of theoretical results.

Couple-Group Consensus of Cooperative-Competitive Heterogeneous Multiagent Systems: A Fully Distributed Event-Triggered and Pinning Control Method.

This article discusses the couple-group consensus for heterogeneous multiagent systems via event-triggered and pinning control methods. Considering cooperative-competitive interaction among the agents, a novel group consensus protocol is designed. As inducing the time-correlation threshold function, a class of fully distributed event-triggered conditions without depending on any global information is proposed. Utilizing the Lyapunov stability theory, some sufficient conditions are obtained. Under hybrid event triggered and pinning control, pinning control strategies are first introduced. It is shown that under the proposed strategies, all agents can asymptotically achieve pinning couple-group consensus with discontinuous communication in a fully distributed way. Furthermore, the Zeno behavior for each agent is overcome. Finally, the reduction of the systems' controller update frequency and the correctness of our conclusions are illustrated by some simulations.

Finite- and Fixed-Time Cluster Synchronization of Nonlinearly Coupled Delayed Neural Networks via Pinning Control

In this article, the cluster synchronization problem for a class of the nonlinearly coupled delayed neural networks (NNs) in both finite- and fixed-time cases are investigated. Based on the Lyapunov stability theory and pinning control strategy, some criteria are provided to ensure the cluster synchronization of the nonlinearly coupled delayed NNs in both finite-and fixed-time aspects. Then, the settling time for stabilization that is dependent on the initial value and independent of the initial value is estimated, respectively. Finally, we illustrate the feasibility and practicality of the results via a numerical example.

H∞ Pinning Control of Complex Dynamical Networks Under Dynamic Quantization Effects: A Coupled Backward Riccati Equation Approach.

In this article, a pinning control strategy is developed for the finite-horizon H∞ synchronization problem for a kind of discrete time-varying nonlinear complex dynamical network in a digital communication circumstance. For the sake of complying with the digitized data exchange, a feedback-type dynamic quantizer is introduced to reflect the transformation from the raw signals into the discrete-valued ones. Then, a quantized pinning control scheme takes place on a small fraction of the network nodes with the hope of cutting down the control expenses while achieving the expected global synchronization objective. Subsequently, by resorting to the completing-the-square technique, a sufficient condition is established to ensure the finite-horizon H∞ index of the synchronization error dynamics against both quantization errors and external noises. Moreover, a controller design algorithm is put forward via an auxiliary H2 -type criterion, and the desired controller gains are acquired in terms of two coupled backward Riccati equations. Finally, the validity of the presented results is verified via a simulation example.

Leader-following consensus of nonlinear singular multi-agent systems under signed digraph

This paper investigates the leader-following consensus problem for a singular multi-agent system with nonlinear dynamics and signed digraph topology. Firstly, an algorithm is proposed to address the structural balance problem of the signed network, which is suitable for all types of signed graphs. Secondly, by using M-matrix theory, the bipartite consensus conditions for the singular nonlinear multi-agent system are established when the topology digraph is structurally balanced. Thirdly, the global asymptotic stability conditions are presented when the signed network is structurally unbalanced. Both the controllers are designed by using pinning control strategies. Finally, numerical examples are given to illustrate the correctness and effectiveness of the proposed methods.

Distributed Tie-Line Power Flow Control of Autonomous DC Microgrid Clusters

For microgrids (MGs) owned by different utilities, it is always desirable that the steady state impact of load or generation changes in one MG, does not affect the generation cost in another MG. To ensure this, the power flow through the tie-line is typically regulated at a pre-scheduled value thereby enforcing the individual MGs to manage their respective load at steady state. To this end, this article presents a distributed control scheme to regulate tie-line power flow between two autonomous dc MG clusters. In this article, a unifying hierarchical control scheme based on distributed communication is proposed where the tie-line power flow control based on a pinning control strategy is unified with the distributed optimization and average voltage regulation control loops. The distributed optimization utilizes economic dispatch to minimize the operating costs of the DG, while the average voltage control regulates the MGs average voltage at its nominal value. With the application of this approach, the responsibility of tie-line regulation is distributed in an economic manner without degrading the voltage quality in the system. Time-domain simulations, real-time simulation using Ethernet-based transmission control protocol/internet protocol (TCP/IP) communication, and experimental results are presented to validate the performance of proposed distributed control under normal and faulty system conditions.

Cluster Synchronization of Two-Layer Networks via Aperiodically Intermittent Pinning Control

As is well known, complex networks in reality are usually interconnected. To describe the interconnected networks, multiplex networks were presented recently. In this brief, an aperiodically intermittent pinning control scheme is put forward to realize cluster exponential synchronization in a two-layer (leader-follower) network with multi-links and time-varying delays. Based on the principle of intermittent control and Lasalle invariant principle, some criteria for cluster synchronization are deduced by theoretical analysis. Numerical simulations are provided to verify the effectiveness of the proposed scheme. In comparison with the previous methods, our model better describes the real-world networks and our control effectively reduces the control cost.

Bipartite synchronization of coupled Lurie networks with signed graph and time-varying delay

This paper addresses the bipartite leader-following and leaderless synchronization in a signed network composed by an array of coupled Lurie systems with time-varying delay, where the signed network contains both the non-delay coupling term and the delay coupling term. By using the pinning control strategy and a gauge transformation to transform the problem of bipartite synchronization for signed network into that of synchronization of unsigned network, choosing an appropriate Lyapunov–Krasovskii functional (LKF), applying Jensen inequality and reciprocally convex inequality to estimate the derivative of the LKF, several sufficient conditions, which guarantee the bipartite leader-following and leaderless synchronization for the coupled Lurie networks with time-varying delay, are newly obtained in terms of linear matrix inequalities (LMIs). When the delay coupling term is not considered, some criteria in terms of low-dimensional LMIs are established by using M-matrix theory. A numerical example is provided to illustrate the effectiveness of the proposed results.

Pinning Synchronization of Nonlinearly Coupled Complex Dynamical Networks on Time Scales

In this paper, we study the synchronization problem for nonlinearly coupled complex dynamical networks on time scales. To achieve synchronization for nonlinearly coupled complex dynamical networks on time scales, a pinning control strategy is designed. Some pinning synchronization criteria are established for nonlinearly coupled complex dynamical networks on time scales, which guarantee the whole network can be pinned to some desired state. The model investigated in this paper generalizes the continuous-time and discrete-time nonlinearly coupled complex dynamical networks to a unique and general framework. Moreover, two numerical examples are given for illustration and verification of the obtained results.

Impulsive Synchronization of Derivative Coupled Neural Networks With Cluster-Tree Topology

This article is devoted to discussing the exponential synchronization for a kind of delay derivative coupled neural networks with stochastic disturbance and multiple time-varying delays. To simulate more practical situations and widen the synchronization application fields in network science, the coupled neural networks with cluster-tree topology structure is studied by applying a novel impulsive pinning control strategy, which skillfully considered the neural networks in current cluster that directly linked to the neural networks in other clusters. Since the existence of delayed impulses, the general comparison principle for normal impulsive differential equations is efficiently extended. In view of the concept of average impulsive interval, the parameters classification discussion method and the mathematical induction method, some judgement conditions for achievement of the cluster synchronization on derivative coupled neural networks are derived. Additionally, the exponential convergence velocity of the derivative coupled neural networks is accurately estimated. Finally, numerical examples are presented to demonstrate the effectiveness of the control strategy and the theoretical results.

Synchronisation for multi‐network with two types of inter‐network coupling faults: pinning control effects

Investigation of simultaneous occurrence of permanent and/or recoverable faults of coupled nodes within different networks in a larger network structure is an appealing timely research topic. For the modelling of such a multi-network structure, the coupling terms in the same network and the coupling terms among different networks are described separately in order to explain clearly the multi-network feature here. The dimension-transformation matrix is used to deal with the mismatched dimensions of nodes in the different networks. Then a synchronisation controller is designed from the underlying theory of pinning control schemes. Furthermore, following the ideas of Lyapunov stability theory, a sufficient stability condition under the pinning control is derived which guarantees nodes in the same network synchronisation. Computer simulation results for a numerical case study of three coupled networks with nodes that possess rather complex non-linear dynamics demonstrate that the proposed controllers can enforce synchronisation despite different types of faults being occurred in the multi-network. It is also shown that the specific pinning control scheme is more effective than the random pinning.

LMI-based criterion for global Mittag-Leffler lag quasi-synchronization of fractional-order memristor-based neural networks via linear feedback pinning control

This paper addresses global Mittag-Leffler lag quasi-synchronization (GMLQS) of fractional-order memristor-based neural networks (FMNNs). Firstly, for a general class of fractional-order nonlinear systems with interval uncertainties, a kind of linear feedback pinning controller, which works by feeding back partial state errors to the partial controlled variables, is designed to achieve global Mittag-Leffler ultimate boundedness (GMUB). Correspondingly, a GMUB criterion in the form of linear matrix inequality (LMI) is derived with the aid of a Lyapunov function and a newly established fractional-order differential inequality. Then, the linear feedback pinning controller is employed for GMUB of the synchronization error system, which is equivalent to GMLQS of FMNNs. Since there exists the propagation delay between drive-response FMNNs and the synchronization error system can not be obtained straightforwardly, an identical equation about Caputo’s fractional derivatives is established to overcome this difficulty. Moreover, the detailed pinning control scheme design procedures for a prescribed GMLQS performance are presented, where the performance involves both ultimate error bound and transient behavior. In the control scheme, an auxiliary LMI and an optimization objective function are introduced, which can significantly reduce control cost. Finally, a numerical example is presented to show the feasibility of the control scheme. The results obtained in this paper have improved the existing criterion on quasi-synchronization of FMNNs, and will also provide a novel insight into pinning control of fractional-order nonlinear systems.

Synchronization of Singular Markovian Jumping Neutral Complex Dynamical Networks with Time-Varying Delays via Pinning Control

This article discusses the synchronization problem of singular neutral complex dynamical networks (SNCDN) with distributed delay and Markovian jump parameters via pinning control. Pinning control strategies are designed to make the singular neutral complex networks synchronized. Some delay-dependent synchronization criteria are derived in the form of linear matrix inequalities based on a modified Lyapunov-Krasovskii functional approach. By applying the Lyapunov stability theory, Jensen’s inequality, Schur complement, and linear matrix inequality technique, some new delay-dependent conditions are derived to guarantee the stability of the system. Finally, numerical examples are presented to illustrate the effectiveness of the obtained results.