Event-triggered Impulsive Control Research Articles

Quasi-synchronization of drive–response systems with parameter mismatch via event-triggered impulsive control

In this paper, an event-triggered impulsive control method is proposed to investigate the quasi-synchronization of drive–response systems with parameter mismatch, which integrates the event-triggered control and impulsive control together. The impulsive instants are event-triggered and determined by a certain state-dependent triggering law. Sufficient conditions for achieving quasi-synchronization are achieved. The synchronization error is shown to be no more than a nonzero bound. Furthermore, Zeno-behavior of impulsive instants is excluded. Finally, a numerical example is presented to verify the validity of the theoretical results.

Stability of impulsive dynamical networks with different impulse time sequences and application to event-triggered impulsive control

This paper studies the stability for impulsive dynamical networks (IDN) where different nodes may have different impulse time sequences. By deriving the conditions of global uniform exponential stability for zero-order delayed systems, the criteria of stability for IDN are established. The stability results for IDN are then used to design event-triggered impulsive control (ETIC) for stabilization of continuous-time dynamical networks (CDN). In every node of CDN, three levels of event-triggering conditions are set for ETIC. The exponential stabilization of CDN is shown to be achieved by the designed ETIC and it also shows that the ETIC is robust w.r.t. time-delays. Moreover, a non-instantaneous ETIC (NI-ETIC) is proposed for the stabilization of CDN. Three examples with numerical simulations are given to show that the designed ETIC has lower impulse frequency and cost of control than the classic time-triggered impulsive control. It is also shown that the discontinuity and the instantanity of ETIC are improved by the NI-ETIC.

Event-Triggered Impulsive Control for Nonlinear Systems With Actuation Delays

This article studies impulsive stabilization of nonlinear systems. We propose two types of event-triggering algorithms to update the impulsive control signals with actuation delays. The first algorithm is based on continuous event detection, while the second type makes decision about updating the impulsive control inputs according to periodic event detection. Sufficient conditions are derived to ensure asymptotic stability of the impulsive control systems with the designed event-triggering algorithms. Lower bounds of the time period between two consecutive events are also obtained, so that the closed-loop impulsive systems are free of Zeno behavior. That is to say that the pulse phenomena are excluded from the event-triggered impulsive control systems, in the community of impulsive differential equations. An illustrative example demonstrates effectiveness of the proposed algorithms and our theoretical results.

Pinning synchronization of dynamical neural networks with hybrid delays via event-triggered impulsive control

<abstract><p>In this study, a new event-triggered impulsive control strategy is used to solve the problem of pinning synchronization in coupled impulsive dynamical neural networks with hybrid delays. In view of discontinuous coupling terms and system dynamics, the inner delay and the impulsive delay are both investigated. Compared with the traditional pinning impulsive control, event-triggered pinning impulsive control (EPIC) generates impulse instants only when an event occurs, and is therefore more in line with practical applications. In order to deal with the complexities of mixed delays, some generalized inequalities related to hybrid delays based on Lyapunov functions are proposed, which are subject to the designed event-triggered rule. Then, in order to ensure network synchronization, linear matrix inequalities (LMIs) can provide some sufficient conditions with less conservatism while a proposed event-triggered function could successfully eliminate Zeno behavior. In addition, numerical examples are presented to prove the feasibility of the presented EPIC method.</p></abstract>

Event-Based Impulsive Control for Heterogeneous Neural Networks with Communication Delays

The quasi-synchronization for a class of general heterogeneous neural networks is explored by event-based impulsive control strategy. Compared with the traditional average impulsive interval (AII) method, instead, an event-triggered mechanism (ETM) is employed to determine the impulsive instants, in which case the subjectivity of selecting the controlling sequence can be eliminated. In addition, considering the fact that communication delay is inevitable between the allocation and execution of instructions in practice, we further nominate an ETM centered on communication delays and aperiodic sampling, which is more accessible and affordable, yet can straightforwardly avoid Zeno behavior. Hence, on the basis of the novel event-triggered impulsive control strategy, quasi-synchronization of heterogeneous neural network model is investigated and some general conditions are also achieved. Finally, two numerical simulations are afforded to validate the efficacy of theoretical results.

Event-triggered and self-triggered impulsive control for two-time-scale systems

This paper studies the stability problem of two-time-scale system via event-triggered impulsive control and self-triggered impulsive control. The overall system is modeled with the hybrid formalism. Two Chang transformations are introduced to completely decouple the hybrid system states into flow set and jump set. A composite impulsive controller based on slow and fast system states is proposed, under which the slow and fast subsystems are simultaneously triggered by event-triggered and self-triggered mechanism, respectively. As a result, the stability conditions are derived for the system under event-triggered and self-triggered impulsive control, respectively. Furthermore, the theoretical result of self-triggered impulsive control is applied to the consensus of the interconnected two-time-scale systems. Finally, simulation examples and comparison study show the effectiveness of the proposed control strategies.

Event-triggered fault-tolerant secure containment control of multi-agent systems through impulsive scheme

This paper studies a containment control problem of multi-agent systems. A two-layer distributed control framework is proposed to handle the external network attack and internal actuator failure. In the network layer, an event-triggered impulsive control protocol is designed to handle the deception attack, which can deal with stochastic attacks injected into the controller under limited energy bound. Compared with the traditional event-triggered-based continuous control method, the impulsive control mechanism can further reduce energy consumption with better robustness. In the physical layer, a fault-tolerant controller, which considers multiplicative failure, is investigated to maintain the system’s stability. Rigorous proofs for controller stability are given through Lyapunov theory, and Zeno behavior is also avoided within the designed control mechanism. Finally, a numerical simulation is demonstrated to test and verify the proposed control scheme.

Quasiconsensus of fractional-order heterogeneous multiagent systems under event-triggered impulsive control method

This paper investigates the quasiconsensus problem of fractional-order heterogeneous multiagent systems, the distributed impulsive control protocol is designed for the multiagent system. In contrast to some existing results, the impulsive moments are determined by preset events, i.e., the event-triggered mechanism is used. Based on the fractional-order Lyapunov stability theory and fractional-order differential inequality, the quasiconsensus criteria are derived; furthermore, the prescribed error bound is given. Then, Zeno behavior for the considered event-triggered control method is excluded. Finally, numerical examples are given to shown the effectiveness of the proposed method.

Finite-time impulsive control for stochastic T-S fuzzy systems: A waiting-time-based event-triggered method

The finite-time impulsive control problem is studied for stochastic T-S fuzzy systems with parameter uncertainties. In order to reduce numbers of impulsive control and information transmission, we proposed event-triggered impulsive control (ETIC) scheme involving the co-design of event-triggered mechanisms and impulsive gains to ensure stochastic finite-time stability (SFTS) of considered systems. For ETIC scheme, impulsive inputs are adopted to systems only at event-triggering instants. The waiting-time is introduced into ETIC scheme to avoid Zeno behavior and save communication resources further. Compared with the time-triggered impulsive control, a theoretical analysis indicates that ETIC not only removes the restriction of upper bound for impulsive intervals, but also significantly reduce the number of impulsive control while ensuring the same control performance. Two examples illustrated the advantage and validity of ETIC scheme.

Stabilization via Event-Triggered Impulsive Control With Constraints for Switched Stochastic Systems.

This article studies the event-triggered impulsive control (ETIC) with constraints for the stabilization of switched stochastic systems (SSSs). An ETIC scheme with constraints is proposed for SSS by designing two levels of events via three indices: 1) a threshold value; 2) a control-free index; and 3) a check period. It is also constrained via a constraint index. Based on the activation probabilities and transition probabilities of subsystems, the stabilizations in terms of the p th moment exponential stability and almost exponential stability are achieved, respectively, by the ETIC with constraints. Moreover, based on the scheme of ETIC with constraints, sampling-based ETIC and random ETIC are proposed, respectively. The stabilization conditions via sampling-based ETIC and random ETIC are also derived. It is shown that the ETIC with constraints is non-Zeno and robust with respect to time delays and can achieve lower impulse frequency than the classic time-based impulsive control and recent ETIC schemes. Finally, two examples are presented to demonstrate the effectiveness of the ETIC with constraints.

Event-Triggered Impulsive Controller Design for Synchronization of Delayed Chaotic Neural Networks and Its Fractal Reconstruction: An Application to Image Encryption

This paper examines synchronization of delayed chaotic neural networks with impulsive control, event-triggered impulsive control, and event-triggered delayed impulsive control. Lyapunov-based event-triggered mechanism is constructed to derive few sufficient conditions in terms of Linear Matrix Inequalities (LMIs). The feedback and event-triggered gain matrices are evaluated with the help of numerical packages. The fractal interpolation functions are employed to reconstruct the chaotic sequence of the neural networks since the chaotic attractor has self-similar properties and coincides with the fractal functions. In this study, a linear fractal interpolation is used to reconstruct both the master-slave chaotic attractor and the encrypted chaotic attractor, with optimized scaling factors.Finally, an application of the image encryption algorithm is given in terms of RSA public-key cryptosystems, permutation, and finite field diffusion for the chaotic sequence generated by fractal interpolation functions.

Hybrid event-triggered impulsive flocking control for multi-agent systems via pinning mechanism

This paper studies the leader-following flocking control problem of unmanned aerial vehicle (UAV) systems by integrating a hybrid impulsive framework, where the full exchange of information only occurs at each impulsive time instant. It is also shown that the overall stability can be achieved via impulses while the continuous dynamics remains destabilizing. Meanwhile, the even-triggered and pinning mechanisms are considered to further reduce control resource usage and transmission redundancy. Moreover, topology switching and strong nonlinearity are taken into account for more practical application. Based on transmission topology structure, impulsive control theory, and Lyapunov based event-triggered strategy, some improved theorems are derived to guarantee convergence of the corresponding error dynamics without exhibiting Zeno behaviour. Compared with most existing results on continuous or impulsive systems, the obtained stability criteria are more general as they are applicable to systems involving both delayed coupling feedback and delayed impulses. In addition, a novel approach using braking and gyroscopic forces is utilized for collision avoidance purposes. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical analysis.

An improved two-layer model for rumor propagation considering time delay and event-triggered impulsive control strategy

The rapid development of the Internet has broadened the existing channels of rumor propagation, it has added many new features during the dynamic process of the rumor propagation that are different from those in the past. In this paper, we construct an improved XYZ−ISR two-layer model considering time delay to describe the dynamic process of rumor propagation in multiple channels. Firstly, we obtain the basic regeneration number R0 by the next generation matrix method. Secondly, we derive the stability condition of the equilibrium point by constructing Lyapunov functions. In order to reduce the negative impact caused by rumor propagation at minimum cost, we design an event-triggered impulsive control strategy and optimize the control parameters by using a particle swarm optimization algorithm. Then, by comparing the rumor propagation process in the XYZ−ISR two-layer model and the classical rumor DK model, we find that although rumors propagate faster in the XYZ−ISR model in the initial stage, the rumor spreads on a smaller scale than in the DK model in terms of the whole life cycle of the rumor due to the official supervision and timely release of corresponding rumor-debunking information. Besides, individuals need a certain amount of careful consideration time between receiving the information and deciding whether to forward it or not, and this time delay slows the behavior spreading and reduces its scale. Finally, we verify the reasonableness of the above theoretical results through numerical simulations. Moreover, by simulating a rumor case on the microblog with real data, we find that the model proposed in this paper can fit the real rumor propagation process well, and the event-triggered impulsive control strategy can control the rumor propagation more effectively in multiple channels.

Rapid exponential stabilization of nonlinear continuous systems via event-triggered impulsive control

Abstract This article investigates the problem of rapid exponential stabilization for nonlinear continuous systems via event-triggered impulsive control (ETIC). First, we propose a trigger mechanism that, when triggered by a predefined event, causes the closed-loop system exponentially stable. Then, the exponential stabilization is achieved by the designed ETIC with or without data dropout. The case where there are delays in the ETIC signals is also studied, and the exponential stabilization is proved. Finally, a numerical study is presented, along with numerical illustrations of the stability results.

Event-triggered delayed impulsive control for input-to-state stability of nonlinear impulsive systems

This paper studies the input-to-state stability (ISS) and integral input-to-state stability (iISS) of nonlinear impulsive systems in the framework of event-triggered impulsive control (ETIC), where the stabilizing effect of time delays in impulses is fully considered. Some sufficient conditions which can avoid Zeno behavior and guarantee the ISS/iISS property of impulsive systems are proposed, where external inputs are considered in both the continuous dynamics and impulsive dynamics. A novel event-triggered delayed impulsive control (ETDIC) strategy which establishes a relationship among event-triggered parameters, impulse strength and time delays in impulses is presented. It is shown that time delays in impulses can contribute to the stabilization of impulsive systems in ISS/iISS sense. Finally, the effectiveness of the proposed theoretical results is illustrated by two numerical examples.

Event-Triggered Impulsive Control for Stochastic Networked Control Systems Under Cyber Attacks

The event-triggered impulsive control (ETIC) problem is studied for stochastic networked control systems (NCSs) under random cyber attacks. The random cyber-attacks model is proposed to integrate denial-of-service (DoS) attacks and deception attacks into a unified framework by means of two independent Bernoulli random sequences. In ETIC systems, the impulsive control time sequence is generated by the event-triggered mechanism (ETM). Both continuous ETM and periodic ETM are developed by continuous measuring and periodic sampling, respectively. In order to exclude the Zeno behavior, an easy and effective method is provided to choose the waiting time of continuous ETM and the sampling period of periodic ETM. According to the proposed ETMs, sufficient conditions of the mean-square exponential stability are derived for stochastic NCSs. An example of Chua’s circuits is given to explain our ETIC schemes.

Finite-Time Stabilization of Switched Systems Under Mode-Dependent Event-Triggered Impulsive Control

This article studies the event-triggered finite-time stabilization problem of nonlinear switched systems in which the time derivatives of Lyapunov functions of modes are indefinite. Based on a mode-dependent average dwell time constraint and event-triggered impulsive control (ETIC) strategy, a new type of the mode-dependent event-triggered mechanism (MDETM) which can efficiently avoid Zeno behavior for switched systems is presented. Some Lyapunov-based criteria for finite-time stability (FTS) and finite-time contractive stability (FTCS) are obtained, respectively, where a relationship between the prescribed bound and event-triggered mechanism is established. Then, we apply these proposed ETIC strategies to impulsive switched systems and design a class of LMI-based MDETMs to guarantee the FTS/FTCS property. Finally, the effectiveness of presented ETIC strategies is illustrated by two examples.

Impulsive Control for Nonlinear Systems Under DoS Attacks: A Dynamic Event-Triggered Method

In this brief, the impulsive control problem is addressed for a class of unstable nonlinear systems under denial-of-service (DoS) attacks. A dynamic event-triggered impulsive control (DETIC) method is proposed to achieve asymptotic stability for the resulting closed-loop systems. A new class of impulsive control systems with dynamic event-triggered impulse instants are formulated, and some easily verifiable conditions are provided. The introduction of internal dynamic variable facilitates the regulation of the control frequency. Here, Zeno behaviors can be easily excluded by the proposed method. Finally, two examples, which include a Chua’s circuit and a numerical example, are given to demonstrate the efficiency of the method.

Bipartite event-triggered impulsive output consensus for switching multi-agent systems with dynamic leader

This paper studies the output consensus of heterogeneous switching linear multi-agent systems (LMASs). The considered switching topology in a signed graph is jointly connected. An event-triggered impulsive control algorithm is proposed, in which the event-triggered time sequence is allowed to be different from the impulsive sequence. Specifically, the leader’s control inputs in the LMASs model are allowed to be designed for the followers. In a fully distributed manner, a general compensator consisting of an impulsive and dynamic event-triggered mechanism is proposed to estimate the state of the leader. Based on the designed compensator and observer, a distributed control law is proposed to realize the bipartite output consensus by using an iterative method. Under the event triggering strategy, the combined measurement method is used, so that each agent only needs to update input information at the moment of its event triggering. Finally, our theoretical results are demonstrated through a numerical example.

Quasisynchronization of Memristive Neural Networks With Communication Delays via Event-Triggered Impulsive Control.

This article considers the quasisynchronization of memristive neural networks (MNNs) with communication delays via event-triggered impulsive control (ETIC). In view of the limited communication and bandwidth, we adopt a novel switching event-triggered mechanism (ETM) that not only decreases the times of controller update and the amount of data sent out but also eliminates the Zeno behavior. By using an appropriate Lyapunov function, several algebraic conditions are given for quasisynchronization of MNNs with communication delays. More important, there is no restriction on the derivation of the Lyapunov function, even if it is an increasing function over a period of time. Then, we further propose a switching ETM depending on communication delays and aperiodic sampling, which is more economical and practical and can directly avoid Zeno behavior. Finally, two simulations are presented to validate the effectiveness of the proposed results.