Impulsive Control Strategy Research Articles

Stabilization and Synchronization of Neural Networks via Impulsive Adaptive Control.

This article addresses the stabilization and synchronization problems of coupled neural networks (NNs) via an impulsive adaptive control (IAC) strategy. Unlike the traditional fixed-gain-based impulsive methods, a novel discrete-time-based adaptive updating law for the impulsive gain is designed to maintain the stabilization and synchronization performance of the coupled NNs, where the adaptive generator only intermittently updates its data at the impulsive instants. Several stabilization and synchronization criteria for the coupled NNs are established based on the impulsive adaptive feedback protocols. Additionally, the corresponding convergence analysis are also provided. Finally, the effectiveness of the obtained theoretical results is illustrated using two comparison simulation examples.

Dynamics and event-triggered control of rumor propagation model with saturated incidence and time delay on heterogeneous networks

Considering the impact of user’s cognitive ability in rumor propagation, this paper proposes a new susceptible infection recovery (2SIR) rumor propagation model with saturation incidence and time delay on heterogeneous networks. First, the existence of the equilibria is discussed by using mean field theory and basic reproduction number. Second, the dynamic behaviors of the rumor-free and persistent equilibria are analyzed via the local linearization method, Lyapunov stability theory and irreducible matrix properties. Furthermore, an event-triggered impulsive control strategy is proposed to control the rumor spreaders and some corresponding control conditions are given. Finally, some numerical simulation results and a practical example are presented to verify the correctness of the theoretical results and reflect the impact of cognitive ability and time delay on rumor propagation.

Dynamics of a stochastic impulsive vegetation system with regime switching

This paper describes an analytical and numerical investigation of a novel stochastic impulsive vegetation system with regime switching. Impulsive control, white noise, regime switching, and rainfall are modeled as crucial factors to simulate natural ecological phenomena, with the aim to explore the effects of those factors on the dynamics of vegetation system. Dynamics of the system, including the existence and uniqueness of global positive solutions, extinction, non-persistence in the mean, weak persistence and stochastic persistence, are investigated firstly under the effects of impulsive control and regime switching. For system without impulsive perturbations, we investigate the existence and uniqueness of the stationary distribution for the system, demonstrating that the vegetation can survive forever. Using a sophisticated sensitivity analysis technique, it is found that the vegetation biomass is highly sensitive to the rainfall but least sensitive to the saturation constant of the vegetation consumption. Our numerical results reveal that either the reduced rainfall or increased environmental disturbance can tip the balance of vegetation system, but this relationship can be effectively regulated by implementing impulsive control schemes. Additionally, it is observed that system at high-level rainfall may be detrimental to maintain the balance of vegetation, but regime switching in rainfall patterns can balance different states of vegetation and provide higher survival chance for vegetation. Significantly, it emphasizes that the persistence-extinction behaviors of the vegetation are more sensitive to the change of regime switching, indicating that the proper and general environmental disturbances is beneficial to maintain dynamic balance of vegetation system. These findings may provide new insights into the complex vegetation system dynamics.

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.

Synchronization of Kuramoto-oscillator networks under event-triggered impulsive control with noise perturbation

This paper studies the stochastic average synchronization of Kuramoto-oscillator networks under event-triggered impulsive control (ETIC) strategies, in which the event-triggered mechanism (ETM) determines the impulsive control time sequence. The continuous ETM is designed to avoid the Zeno behavior by continuous measuring, and the periodic ETM is proposed by periodic sampling. Based on the proposed ETIC methods, several sufficient conditions for the stochastic average synchronization of Kuramoto-oscillator networks are established. Unlike time-triggered impulsive control, where the triggered instants are pre-designed, ETIC is activated only upon the occurrence of an event, so synchronization conditions are heavily dependent on the ETM. Furthermore, there is no control input between two successive triggering instants, and the control input is required only at the trigger instants. Finally, numerical simulations are shown to illustrate the effectiveness of the theoretical results. Besides, it is found that the presence of noise may favor the synchronization of Kuramoto-oscillator networks.

Event-triggered impulsive tracking control for uncertain strict-feedback nonlinear systems via the neural-network-based backstepping technique

This paper studies the problem of event-triggered impulsive tracking control (ETITC) for uncertain strict-feedback nonlinear systems (USFNSs). In contrast to existing impulsive control schemes, this paper incorporates the neural-network (NN)-based backstepping technique into impulsive control design, such that stronger nonlinearities and uncertainties are allowed to be included in the concerned systems. The proposed state-feedback ETITC scheme guarantees that all the signals of the closed-loop system are bounded and the tracking error ultimately converges to an adjustable bounded region, while also avoiding the Zeno behavior. In addition, by constructing a NN-based observer, this paper further develops an output-feedback ETITC scheme to extend its investigation to the scenario where full states are not available for impulsive control design. Finally, an illustrative example involving a chemical reactor system is presented to demonstrate the effectiveness of our control schemes.

DoS attacks resilience of heterogeneous complex networks via dynamic event-triggered impulsive scheme for secure quasi-synchronization

This paper addresses the secure quasi-synchronization issue of heterogeneous complex networks (HCNs) under aperiodic denial-of-service (DoS) attacks with dynamic event-triggered impulsive scheme (ETIS). The heterogeneity of networks and the aperiodic DoS attacks, which hinder communication channels and synchronization goals, present challenges to the analysis of secure quasi-synchronization. The ETIS leverages impulsive control and dynamic event-triggered scheme (ETS) to handle the network heterogeneity and the DoS attacks. We give specific bounds on the attack duration and frequency that the network can endure, and obtain synchronization criteria that relate to event parameters, attack duration, attack frequency, and impulsive gain by the variation of parameter formula and recursive methods. Moreover, we prove that the dynamic ETS significantly reduces the controller updates, saves energy without sacrificing the system decay rate, and prevents the Zeno phenomenon. Finally, we validate our control scheme with a numerical example.

Global regulation for uncertain feedforward nonlinear systems based on event-triggered impulsive control: a time-varying gain scaling approach

This paper addresses the problem of global regulation for uncertain feedforward nonlinear systems using event-triggered impulsive control. By constructing a state transformation with a time-varying scaling gain, both the state-feedback and output-feedback event-triggered impulsive control strategies are established. It is proven that the proposed impulsive controllers ensure the global regulation of the concerned systems while avoiding the Zeno behaviour. Furthermore, the derived results of this work are generalised to a broader class of uncertain feedforward nonlinear systems incorporating time-varying nonlinearities, as well as to a class of uncertain strict-feedback nonlinear systems. It is noteworthy that this paper is the first attempt to design an impulsive regulating controller for feedforward nonlinear systems. Finally, a simulation example is presented to verify the effectiveness of our theoretical results.

Secure impulsive cluster synchronization control of complex dynamical networks with parameter mismatches under deception attacks

The issue of secure cluster synchronization (SCS) of complex dynamical networks (CDNs) with parameter mismatches under deception attacks is investigated in this article. Firstly, the deception attacks are supposed to inject false information into controller-to-actuator channels, while the occurrences of deception attack are always subject to Bernoulli distribution. Secondly, an improved pinning impulsive control strategy is designed. The impulsive gain in the control strategy is take from a new range. Moreover, we obtain the estimation of synchronization error upper bound and boundaries of secure synchronization region. The synchronization error will converge to a bounded ball that depends on attack energy at a exponential rate. The CDNs without deception attacks under pinning impulsive control can achieve complete cluster synchronization. Finally, two numerical examples with 20 nodes based on MATLAB software are presented to demonstrate the effectiveness of the theoretical results.

Secure intermittent impulsive consensus control for fractional-order multiagent systems under denial-of-service and deception attacks

This article addresses the secure consensus problem of fractional-order multiagent systems (FOMASs) under denial-of-service (DoS) and deception attacks in the intermittent impulsive control framework. Unlike previous cyber attack models, the multiple attacks are considered, which the agent-to-agent communication channels and the controller-to-actuator channels are randomly subjected to deception and DoS attacks, respectively. Some random variables that follow the Bernoulli distribution are proposed, which are related to the communication channels between adjacent agents to describe deceptive attack behavior. To reduce control costs and resist cyber attacks, a novel intermittent impulsive control strategy is designed to make the FOMASs achieve consensus faster, when DoS attacks are sleeping. The designed intermittent impulsive control includes the advantages of discrete sampling control and intermittent control, which means that it can reduce the injection of erroneous data by constraining the frequency of information transmission. Furthermore, some sufficient criteria including the parameters of multiple attacks are yielded to ensure mean-square quasi-consensus of FOMASs. Finally, two examples are provided to validate the rationality for the presented security control method in this study from the perspective of numerical simulation experiments.

Hyper-Exponential Stabilization of Neural Networks by Event-Triggered Impulsive Control With Actuation Delay.

This brief studies the hyper-exponential stabilization of neural networks (NNs) by event-triggered impulsive control, where the impulse instants are determined by the event-triggered conditions. In the presence of actuation delay, an event-triggered impulsive control scheme is devised. For reducing the sampling task of continuous detection, a periodic-detection scheme is also introduced. Within these frameworks, the occurrence of Zeno behavior is rigorously precluded, and some criteria are formulated to achieve the stabilization of the system with a hyper-exponential convergence rate. Moreover, a numerical simulation is provided to elucidate the validity of the theoretical findings.

Bipartite finite-time consensus of multi-agent systems with intermittent communication via event-triggered impulsive control

This paper concentrates on the bipartite finite-time consensus (BFTC) problem of nonlinear multi-agent systems (MASs) under intermittent communication via event-triggered impulsive control. First, a finite-time consensus (FTC) protocol with an event-triggered mechanism is developed for the MASs with nonlinear dynamics to save limited resources. Then, an impulsive control scheme is introduced to the designed algorithm to further improve the control performance. Based on the structurally balanced graph theory, both antagonistic and cooperative interactions are discussed in this article. Regarding whether the MASs have encountered intermittent communication, sufficient conditions are provided for achieving consensus of the MASs by using the Lyapunov theory and inductive methods. Moreover, the Zeno behavior is excluded. Finally, numerical simulations are given to validate the effectiveness of the algorithm. The result shows that the designed event-triggered BFTC control protocol with an impulsive strategy has a faster convergence rate than that without an impulsive strategy.

Scaled consensus of heterogeneous multi-agent systems under asynchronous DoS attacks

This paper addresses the issue of scaled consensus in heterogeneous multi-agent systems (HMASs) under asynchronous Denial-of-Service (DoS) attacks. In the system structure, our exploration centers on the challenge of achieving scaled consensus in HMASs. The aim is to guarantee that the states of both first-order and second-order agents within the system reach predetermined scalar values, aligning with diverse real-world scenarios. Subsequently, the security of the system in directed communication topology under asynchronous DoS attack is also taken into account. To achieve above research objectives, an impulsive control scheme based on topology switching is proposed and a corresponding algorithm for determining the pulse moments based on the Floyd algorithm is devised. This scheme utilizes the topology switching caused by asynchronous DoS attacks as the driving force for impulsive control. Furthermore, leveraging the correlation property of random matrices, we derive the sufficient conditions for the system to achieve secure control. Finally, a numerical simulation is provided to validate the effectiveness of the protocol and the accuracy of conclusions.

Time-Varying Function Matrix Projection Synchronization of Caputo Fractional-Order Uncertain Memristive Neural Networks with Multiple Delays via Mixed Open Loop Feedback Control and Impulsive Control

This paper shows solicitude for the generalized projective synchronization of Caputo fractional-order uncertain memristive neural networks (FOUMNNs) with multiple delays. By extending the constant scale factor to the time-varying function matrix, we establish an extraordinary synchronization mode called time-varying function matrix projection synchronization (TFMPS), which is a generalized version of traditional matrix projection synchronization, modified projection synchronization, complete synchronization, and anti-synchronization. To achieve the goal of TFMPS, we design a novel mixed controller including the open loop feedback control and impulsive control, which employs the state information in the time-delayed interval and the sampling information at the impulse instants. It has a prominent advantage that impulse intervals are not restricted by time delays. To establish the connection between the error system and the auxiliary system, a generalized fractional-order comparison theorem with time-varying coefficients and impulses is established. Applying the stability theory, the comparison theorem, and the Laplace transform, new synchronization criteria of FOUMNNs are acquired under the mixed impulsive control schemes, and the derived synchronization theorem and corollary can effectively expand the correlative synchronization achievements of fractional-order systems.

Prediction and control of cholera outbreak: Study case of Cameroon

This paper deals with the problem of the prediction and control of cholera outbreak using real data of Cameroon. We first develop and analyze a deterministic model with seasonality for the cholera, the novelty of which lies in the incorporation of undetected cases. We present the basic properties of the model and compute two explicit threshold parameters R¯0 and R̲0 that bound the effective reproduction number R0, from below and above, that is R̲0≤R0≤R¯0. We prove that cholera tends to disappear when R¯0≤1, while when R̲0>1, cholera persists uniformly within the population. After, assuming that the cholera transmission rates and the proportions of newly symptomatic are unknown, we develop the EnKf approach to estimate unmeasurable state variables and these unknown parameters using real data of cholera from 2014 to 2022 in Cameroon. We use this result to estimate the upper and lower bound of the effective reproduction number and reconstructed active asymptomatic and symptomatic cholera cases in Cameroon, and give a short-term forecasts of cholera in Cameroon until 2024. Numerical simulations show that (i) the transmission rate from free Vibrio cholerae in the environment is more important than the human transmission and begin to be high few week after May and in October, (ii) 90% of newly cholera infected cases that present the symptoms of cholera are not diagnosed and (iii) 60.36% of asymptomatic are detected at 14% and 86% of them recover naturally. The future trends reveals that an outbreak appeared from July to November 2023 with the number of cases reported monthly peaked in October 2023. An impulsive control strategy is incorporated in the model with the aim to avoid or prevent the cholera outbreak. In the first year of monitoring, we observed a reduction of more than 75% of incidences and the disappearance of the peaks when no control are available in Cameroon. A second monitoring of control led to a further reduction of around 60% of incidences the following year, showing how impulse control could be an effective means of eradicating cholera.

Parameter variational based adaptive bipartite formation control of second-order multi-agent systems with antagonistic interactions

This article mainly concentrates on researching the leader-following bipartite formation of second-order nonlinear multi-agent systems (MASs) with antagonistic interactions and time-varying delay. A novel distributed feedback control and impulsive control strategy is proposed for realizing the bipartite formation. By establishing an error system, the bipartite formation issue of the MASs is transformed into the stability issue of the error systems. Sufficient conditions for achieving the bipartite formation of second-order nonlinear MASs are obtained by jointly employing the extended parameters variation formula, the comparison principle and the definition of average impulsive interval. In addition, in order to obtain the optimal control gains and control effects, an adaptive control strategy is taken into account by designing the adaptive updating laws. Ultimately, the effectiveness of the theoretical results is demonstrated by two numerical simulations.

A rumor propagation model in multilingual environment with time and state dependent impulsive control

In this paper we are interested in the problem of modeling, analysis and control of rumor spreading on online social networks. As the diversity of languages and the difference of user nodes in the network, a heterogeneous rumor spreading model with two language spreaders is proposed, and the impulsive isolation control strategy is considered. Firstly, the model with periodic impulsive isolation control and time-delay recovery rate is discussed. Based on the stability theory of impulsive differential equations, some conditions regarding the impulsive period and control gains are given for the rumor asymptotically disappearance and persistent existence. Secondly, a new type of event-triggered impulsive isolation control method is developed to address the tradeoff between restraining rumor and minimizing the cost of control, and some conditions are given to make the rumor disappear asymptotically. Furthermore, an improved event-triggered mechanism is established based on the fixed-time stability theory, which provides the conditions for the rumor to disappear within a fixed-time. Finally, some numerical simulations and an actual example are given to verify the rationality of the model and the effectiveness of the control methods.

Reinforcement learning for optimal control of linear impulsive systems with periodic impulses

This paper focuses on the finite- and infinite-horizon optimal control problems of linear impulsive systems with periodic impulses under the quadratic performance index. Necessary and sufficient conditions for the optimal impulsive system are derived in terms of hybrid Riccati equations by utilizing the variational method and the collocation method combined with a time-varying Lyapunov function. Different from the existing model-based impulsive control schemes, three reinforcement learning (RL)-based algorithms are proposed to solve the optimal impulsive controller and hybrid controller for the impulsive system without the exact knowledge of the system dynamics. The asymptotical stability of the impulsive control system and the convergence of the RL-based algorithms are proved rigorously. Finally, a numerical simulation illustrates the effectiveness of the proposed control methods.

Sliding-mode-based impulsive control for a class of time-delay systems with input disturbance

This paper addresses the impulsive stabilization problem for a class of time-delay systems in the presence of input disturbances. A novel impulsive control law is constructed, which is based on the discrete-time equivalent control design technique. The sliding-mode-based impulsive control law allows counteracting the disturbance effect using its previous step value. To adapt in real time to the variation in sampling periods, the sliding function is designed as a function of impulse interval. Piecewise Lyapunov functions based on the partition on the maximum impulse interval are introduced to deal with the time-varying structure of the sliding function. Sufficient conditions for exponential input-to-state stability (EISS) of the impulsively controlled systems are derived, in which the EISS gain characterizes the attenuation ability of the proposed impulsive control law on the disturbance estimation error. The disturbance attenuation performance of the proposed impulsive control strategy is demonstrated through the time-delay Chua’s circuit.

Periodic Self-Triggered Impulsive Synchronization of Hybrid Stochastic Complex-Valued Delayed Networks

This paper studies the synchronization problem for hybrid stochastic delay complex-valued networks with time-varying multi-links (HSDCNT) via periodic self-triggered impulsive control (PSIC). Therein, PSIC combines with the benefits of impulsive control and periodic self-triggered strategy. Moreover, time delays, stochastic disturbances, and time-varying multi-links are considered simultaneously. Particularly, the synchronization for HSDCNT is studied on the complex space and no split real and imaginary parts. Actually, different from the previous PSIC-based results, this paper extends the real-valued neural networks to HSSs, delayed systems, and complex-valued networks, which is significant and challenging. Then, as a practical application, we consider the synchronization of a kind of Cohen-Grossberg neural network in the complex space. Finally, a numerical example is utilized for demonstration.