Hybrid Impulsive Control Research Articles

Finite-time passivity of multi-weighted coupled neural networks with directed topologies and time-varying delay

In this paper, the finite-time passivity (FTP) problem for multi-weighted coupled neural networks (MWCNNs) with directed topologies and time-varying delay is discussed. Firstly, by designing a new state feedback controller, several FTP criteria are given for the considered network. Then, some finite-time synchronization (FTS) criteria are established by employing the FTP results. Secondly, a hybrid impulsive and state feedback controller is first designed, under which different FTP and FTS criteria are presented and the synchronization time is successfully shortened compared to the non-hybrid controller without impulses. Finally, numerical simulations are given to show the effectiveness and superiority of the obtained results.

Delay-compensatory synchronization on uncertain chaotic neural networks via average delayed impulsive gains

This paper mainly studies the exponential synchronization issue of chaotic neural networks with parametric uncertainties and time-varying delays via hybrid impulsive control and delay compensatory strategy. Considering the hybrid impulses and flexible delays in the controller, the idea of average delayed impulsive gain (ADIG) is introduced to quantify the effects of hybrid impulses from a comprehensive viewpoint, i.e., not only the desynchronizing/synchronizing delay-free impulses but also the desynchronizing/synchronizing delayed impulses are discussed. Meanwhile, the impulsive delays are fetched and integrated to compensate the desynchronizing impulses dynamically, which removes certain strict restrictions on the impulsive gains and impulsive delays compared with existed works. Correspondingly, some relaxed sufficient criteria for exponential synchronization are derived by jointly utilizing the concept of average delayed impulsive gain, the delay compensatory scheme and the mathematical induction methodology. Ultimately, two examples with some comparisons are given to verify the applicability and superior performance of the obtained results.

Quasi-Synchronization of Discrete-Time-Delayed Heterogeneous-Coupled Neural Networks via Hybrid Impulsive Control.

This article explores the quasi-synchronization of discrete-time-delayed heterogeneous-coupled neural networks (CNNs) via hybrid impulsive control. By introducing an exponential decay function, two non-negative regions are introduced that are named time-triggering and event-triggering regions, respectively. The hybrid impulsive control is modeled by the dynamical location of Lyapunov functional in two regions. When the Lyapunov functional locates in the time-triggering region, the isolated neuron node releases impulses to corresponding nodes in a periodical manner. Whereas, when the trajectory locates in the event-triggering region, the event-triggered mechanism (ETM) is activated, and there are no impulses. Under the proposed hybrid impulsive control algorithm, sufficient conditions are derived for quasi-synchronization with a definite error convergence level. Compared with pure time-triggered impulsive control (TTIC), the proposed hybrid impulsive control method can effectively reduce the times of impulses and save communication resources on the premise of ensuring performance. Finally, an illustrative example is given to verify the validity of the proposed method.

Synchronization of Fractional Delayed Memristive Neural Networks with Jump Mismatches via Event-Based Hybrid Impulsive Controller

This study investigates the asymptotic synchronization in fractional memristive neural networks of the Riemann–Liouville type, considering mixed time delays and jump mismatches. Addressing the challenges associated with discrepancies in the circuit switching speed and the accuracy of the memristor, this paper introduces an enhanced model that effectively navigates these complexities. We propose two novel event-based hybrid impulsive controllers, each characterized by unique triggering conditions. Utilizing advanced techniques in inequality and hybrid impulsive control, we establish the conditions necessary for achieving synchronization through innovative Lyapunov functions. Importantly, the developed controllers are theoretically optimized to minimize control costs, an essential consideration for their practical deployment. Finally, the effectiveness of our proposed approach is demonstrated through two illustrative simulation examples.

Stability of Fractional Reaction-Diffusion Memristive Neural Networks Via Event-Based Hybrid Impulsive Controller

This article explores the asymptotic stability of fractional delayed memristive neural networks with reaction-diffusion terms. A novel hybrid impulsive controller triggered by a specific event is proposed to stabilize the network, thereby replacing the conventional approach of modifying network parameters. The proposed controller is proven to prevent Zeno behavior. Sufficient conditions for the asymptotic stability of fractional delayed memristive neural networks with reaction-diffusion terms are established through Lyapunov direct method, inequality techniques, Green’s theorem and impulse analysis. Furthermore, the proposed controller is theoretically shown to be more resource-efficient than the conventional one, and our work extends existing research to make it more suitable for practical application such as pattern recognition, image processing and so on. Finally, an example is provided to illustrate the validity of the findings.

Exponential Synchronization of Delayed Stochastic Complex Dynamical Networks via Hybrid Impulsive Control

Exponential Synchronization of Delayed Stochastic Complex Dynamical Networks via Hybrid Impulsive Control

Event-triggered hybrid impulsive control for synchronization of fractional-order multilayer signed networks under cyber attacks

In this paper, we consider the exponential bipartite synchronization (EBS) problem of fractional-order multilayer signed networks with time-varying delays (FO-MSNT) under random cyber attacks. In contrast to the existing literature, the proposed hybrid event-triggered controller combines the advantages of feedback controller and impulsive controller, and the event-triggered condition is constructed by applying the network topology and the Lyapunov function of the subsystem, rather than the state function of the subsystem. Based on the Lyapunov–Razumikhin method and the graph theory, some sufficient conditions for achieving EBS of FO-MSNT under cyber attacks which are related to the topology of networks, the event-triggered parameters, the order of fractional derivative and the signal sent by the enemy are obtained. Furthermore, fractional-order coupled Chua’s circuits model and fractional-order power systems built on MSNT are established and the EBS issues under cyber attacks are analyzed. Numerical examples and simulations are provided to show the validity of our theories.

Synchronization of Multi-Term Fractional-Order Neural Networks with Switching Parameters via Hybrid Impulsive Control

This paper investigates the hybrid impulsive control synchronization problem of multi-term fractional-order neural networks (MFNNs) with switching parameters. Firstly, a novel MFNN with switching parameters model is introduced by incorporating multi-term Caputo fractional-order derivative to extend the existing framework for fractional-order cases. Then, the relationship between multi-term fractional-order derivative and distributed-order derivative is analyzed, and a synchronization criterion for a class of multi-term fractional-order impulsive switched systems is derived by utilizing the properties of the distributed-order derivative weight function. Furthermore, a hybrid impulsive controller is designed to obtain sufficient conditions for synchronization of MFNNs with switching parameters. To validate the effectiveness of the obtained conclusions, a numerical example is presented to demonstrate the validity of the proposed MFNN model and synchronization criterion.

Communication Limited Hybrid Impulsive Control of Fuzzy Time-Delay Multiagent Network

Communication Limited Hybrid Impulsive Control of Fuzzy Time-Delay Multiagent Network

Robust H∞$$ {H}_{\infty } $$ continuous‐discrete hybrid impulsive dynamic output feedback control for delays descriptor Markovian jump systems with multidimensional impulsive operator

AbstractThis study focuses on the robust continuous‐discrete hybrid impulsive dynamic output feedback (DOF) control issue for time delays descriptor Markovian jump systems (TDDMJSs) with multidimensional impulsive operator. By applying an improved impulse‐time‐dependent Lyapunov–Krasovskii (L‐K) functional, the novel stochastic admissibilization conditions are formulated as linear matrix inequalities. A desired hybrid impulsive DOF controller is achieved, which includes a continuous DOF controller and a discrete impulsive DOF controller. The stochastic admissibilization of the closed‐loop TDDMJSs can be satisfied by virtue of the desired hybrid impulsive DOF controller. In the end, the validity of the proposed hybrid impulsive DOF controller design method is demonstrated by two examples, including an oil catalytic cracking process.

Hybrid Impulsive Control Based Synchronization of Leakage and Multiple Delayed Fractional-Order Neural Networks with Parameter Mismatch

Hybrid Impulsive Control Based Synchronization of Leakage and Multiple Delayed Fractional-Order Neural Networks with Parameter Mismatch

Global Synchronization of Fractional-Order Multi-Delay Coupled Neural Networks with Multi-Link Complicated Structures via Hybrid Impulsive Control

This study discusses the global asymptotical synchronization of fractional-order multi-delay coupled neural networks (FMCNNs) via hybrid control schemes. In addition to internal delays and different coupling delays, more importantly, multi-link complicated structures are introduced into our model. Unlike most existing works, the synchronization target is not the special solution of an isolated node, and a more universally accepted synchronization goal involving the average neuron states is introduced. A generalized multi-delay impulsive comparison principle with fractional order is given to solve the difficulties resulting from different delays and multi-link structures. To reduce control costs, a pinned node strategy based on the principle of statistical sorting is provided, and then a new hybrid impulsive pinning control method is established. Based on fractional-order impulsive inequalities, Laplace transforms, and fractional order stability theory, novel synchronization criteria are derived to guarantee the asymptotical synchronization of the considered FMCNN. The derived theoretical results can effectively extend the existing achievements for fractional-order neural networks with a multi-link nature.

Hybrid Impulsive Feedback Control for Drive–Response Synchronization of Fractional-Order Multi-Link Memristive Neural Networks with Multi-Delays

This article addresses the issue of drive–response synchronization in fractional-order multi-link memristive neural networks (FMMNN) with multiple delays, under hybrid impulsive feedback control. To address the impact of multiple delays on system synchronization, an extended fractional-order delayed comparison principle incorporating impulses is established. By leveraging Laplace transform, Mittag–Leffler functions, the generalized comparison principle, and hybrid impulsive feedback control schemes, several new sufficient conditions are derived to ensure synchronization in the addressed FMMNN. Unlike existing studies on fractional-order single-link memristor-based systems, our response network is a multi-link model that considers impulsive effects. Notably, the impulsive gains αi are not limited to a small interval, thus expanding the application range of our approach (αi∈(−2,0)∪(−∞,−2)∪(0,+∞)). This feature allows one to choose impulsive gains and corresponding impulsive intervals that are appropriate for the system environment and control requirements. The theoretical results obtained in this study contribute to expanding the relevant theoretical achievements of fractional-order neural networks incorporating memristive characteristics.

Exponential Bipartite Synchronization of Fractional-Order Multilayer Signed Networks via Hybrid Impulsive Control.

This article investigates the problem of exponential bipartite synchronization of fractional-order multilayer signed networks via hybrid impulsive control. First, the mathematical model of the networks is established by integrating the fractional dynamics of nodes, the multilayer network edges, and the positive and negative weights (antagonistic relationship), which is more pluralistic and practical. Second, a hybrid impulsive controller is designed, which is composed of the feedback control part and the impulsive control part to realize the exponential bipartite synchronization objective. Both positive and negative impulsive effects are considered and the ranges of the impulsive control gain related to the order of Caputo fractional derivative are discussed. In addition, some sufficient conditions for exponential bipartite synchronization of fractional-order multilayer signed networks are obtained by using the signed graph theory, Lyapunov method, and average impulsive interval method. Furthermore, in order to illustrate the practicability of the theoretical results, fractional-order coupled Chua's circuits model and fractional-order power systems built on multilayer signed networks are established and the exponential bipartite synchronization issues are analyzed. Numerical examples and simulations are provided to show the effectiveness of the obtained results.

Stability of stochastic state-dependent delayed complex networks under stochastic hybrid impulsive control

Stability of stochastic state-dependent delayed complex networks under stochastic hybrid impulsive control

Synchronization analysis of fractional delayed memristive neural networks via event-based hybrid impulsive controllers

In this paper, the asymptotic synchronization of Riemann–Liouville fractional delayed memristive neural networks is explored. Firstly, in order to achieve the control target more effectively and economically, a new type of event-based hybrid impulsive controller is designed. In addition, through inequality techniques and impulse analysis methods, some sufficient criteria for asymptotic synchronization are obtained by constructing new Lyapunov–Krasovskii functionals. At the same time, it is verified that Zeno behavior could be eliminated under the given trigger conditions in the error system. It should be noted that some results based on algebraic inequalities fill in the gaps of existing ones and our controller is more practical and energy-saving. Lastly, a simulation instance is depicted to verify the validity and correctness of the submitted conclusions.

Multi-group hybrid impulsive flocking control of heterogenous multi-agent systems

This paper studies the flocking control problem of heterogenous multi-agent systems with multi-group tracking various virtual leaders. In particular, hybrid impulsive control protocol is designed based on the partially discrete agents’ information transmission, where full information exchange only occurs at each impulsive time instant. Meanwhile, braking and gyroscopic forces are implemented for the collision avoidance purpose. Conditions for multi-group formation are established in terms of coupling strength and the length of impulse period. The designed control protocols guarantee that the multi-agent systems are able to achieve asymptotic stability as well as collision-free motions. Numerical examples and computer simulations are provided to validate the theoretical results.

Event-triggered stabilisation of sampled-data singular systems: a hybrid control approach

This paper provides a design of event-triggered feedback stabilisation scheme for a class of sampled-data singular systems, in which the input matrix corresponding to the algebraic equation is not full column rank. First, unlike the conventional piecewise-constant sampled-data feedback controller, a novel hybrid impulsive and sampled-data state feedback controller is designed, which can effectively match with the algebraic equation at sampling instants. An improved discrete event-triggering mechanism with checking period is proposed to achieve exponential stabilisation. Based on these, by applying the input delay approach and defining a new input-delay dependent Lyapunov functional, a sufficient stability condition is presented which ensures that the solution of the event-triggered control system exists and is unique, and the system is exponentially stable with definite decay rate. The estimate of decay coefficient is also given explicitly. Then, an optimisation-based method is developed to jointly design the hybrid controller gains and the event parameters. Finally, two simulation examples including a linearised 2-generator and 6-bus power network system are given to illustrate the validity of the new approach.

Event-triggered hybrid impulsive control on lag synchronization of delayed memristor-based bidirectional associative memory neural networks for image hiding

Memristor-based bidirectional associative memory neural networks (MBAMNNs) analysis can help to reveal the dynamic basis of secure communication. Effectively representing the synchronization of MBAMNNs is the principal task of applying brain-inspired neural networks to image hiding. Previous research has typically utilized continuous control methods to represent the synchronization of MBAMNNs, but these are not well coordinated under limited network bandwidth. Besides, the special communication features and uncertainties of MBAMNNs will affect the image encryption/decryption by introducing the concept of chaos synchronization for image hiding, but few studies have explored such elements. To address these two issues, we propose an event-triggered hybrid impulsive scheme on lag synchronization for image hiding. Specifically, we incorporate both time-varying uncertainties and the multi-layer topology structure of MBAMNNs into a designed event-triggered scheme. The frequency of the controller can be automatically updated from two novel triggered conditions, and Zeno-behavior can be avoided effectively. Experimental results demonstrate that our scheme not only outperforms several exciting approaches in synchronization but also can effectively realize the image hiding under low energy consumption.

A hybrid impulsive and sampled-data control for fractional-order delayed reaction–diffusion system of mRNA and protein in regulatory mechanisms

In genetic regulatory networks, the diffusion effects of mRNA and protein play a key role in regulatory mechanisms of gene expression, especially in translation and transcription. Hybrid impulsive and sampled-data controller are proposed in this paper. By constructing a suitable Lyapunov functional, and utilizing average impulsive interval approach, finite-time stabilization criteria are derived for fractional-order delayed reaction–diffusion genetic regulatory networks (FDRDGRNs). Meanwhile, impulsive control gains and sampled-data control gains are obtained by solving a set of linear matrix inequalities (LMIs). Finally, a numerical example is presented to show the applicability of the proposed scheme.