Impulsive Control Theory Research Articles

Time-varying formation of uncertain nonlinear multi-agent systems via adaptive feedback control approach with event-triggered impulsive estimator

The time-varying formation problem under directed topology is investigated for the uncertain nonlinear multi-agent systems (MASs) via the neural networks-based adaptive feedback control (NNAFC). Compared with the simple adaptive control, the designed control protocol consists of two parts: NNAFC and the event-triggered impulsive estimator. To save communication costs, communications among followers are only carried out at discrete instants determined by the event-triggered impulsive rule. Two kinds of estimators and controllers are designed for two cases with or without communication delay, respectively. Further, NNAFC can be further improved to eliminate errors due to uncertain function approximation for some special cases. Utilizing the Lyapunov stability theory and impulsive control theory, we obtain some sufficient conditions to implement time-varying formation task. Finally, three examples are given to show the feasibility of theoretical analysis.

Finite-Time Synchronization of Fractional-Order Nonlinear Systems with State-Dependent Delayed Impulse Control

This paper delves into the topics of Finite-Time Stabilization (FTS) and Finite-Time Contractive Stabilization (FTCS) for Fractional-Order Nonlinear Systems (FONSs). To address these issues, we employ a State-Dependent Delayed Impulsive Controller (SDDIC). By leveraging both Lyapunov theory and impulsive control theory, we establish sufficient conditions for achieving stability criteria for fractional-order systems. Initially, we employ the aforementioned sufficient conditions to derive stability criteria for general FONSs within the SDDIC framework, employing Linear Matrix Inequality (LMI) techniques. Furthermore, we apply these theoretical findings to tackle the challenge of finite-time synchronization in fractional-order chaotic systems using the proposed SDDIC. We substantiate the efficacy of these theoretical advancements through numerical simulations that vividly demonstrate their capability to achieve finite-time synchronization in fractional-order cellular neural networks and fractional-order Chua’s circuits. Moreover, we introduce an innovative chaos-based multi-image encryption algorithm, thereby contributing significantly to the field. To ensure the algorithm’s robustness, we subject it to rigorous statistical tests, which confidently affirm its capacity to provide the requisite level of security.

Finite-Time Consensus of Second-Order Multi-Agent Systems via Event-Triggered Impulsive Control

In this study, the finite-time consensus problem of second-order multi-agent systems via event-triggered impulsive control is investigated. We leverage a novel approach that combines impulsive control, event-triggered communication, and finite-time stability theory. This successful combination achieves finite-time consensus while minimizing communication. In addition, the event-triggered condition determines both the impulsive instants and the update times for the finite-time control. Furthermore, it is shown that the Zeno-behavior and chattering phenomenon can be eliminated under our work. Numerical examples and simulations are provided to validate the effectiveness of the proposed control strategy.

Dynamic event-triggered boundary control for exponential consensus of multi-agent systems of impulsive PDEs with switching topology

This paper is concerned with the exponential consensus issue for multi-agent systems (MASs) of impulsive partial differential equations (PDEs) with switching topology. A new observer-based dynamic event-triggered boundary control (DETBC) protocol is designed to realize the exponential consensus objective. By Lyapunov functional method, impulse control theory and inequality analysis technique, some conditions are addressed to ensure that the considered MASs achieve the exponential consensus in terms of linear matrix inequalities (LMIs). In addition, the theoretical analysis with respect to the exclusion of Zeno behaviors is given for the designed DETBC mechanism. Finally, two examples are established to indicate the validity of the obtained results.

Optimal Treatment Strategy for Cancer Based on Mathematical Modeling and Impulse Control Theory

Adaptive therapy is a new type of cancer treatment in which time and dose are dynamically changed according to different individuals, which is very different from conventional cancer treatment strategies that use the maximum dose to kill the tumor cells. However, how to determine the time and dose of drug treatment is a challenging problem. In this paper, a competition model between drug-sensitive cells and drug-resistant cells was established, in which pulse intervention was introduced. In addition, based on the theory of pulse optimal control, three pulse optimal control strategies are proposed in the process of cancer treatment by controlling the pulse interval and dose, minimizing the number of tumor cells at the end of the day at minimal cost. Finally, three optimization strategies were compared, using numerical simulation, in terms of tumor burden and the effect on drug-resistant cells. The results show that the hybrid control strategy has the best effect. This work would provide some new ideas for the treatment of cancer.

Quasi-Synchronization of Timescale-Type Delayed Neural Networks With Parameter Mismatches via Impulsive Control

Most synchronization criteria are scale-free on time evolution, whose main research objects are discrete-time/continuous-time systems. Unlike these theoretical results, in order to develop impulsive control schemes for discrete-time and continuous-time neural networks (NNs) in a unified framework. This article investigates impulsive control design of timescale-type NNs (TNNs) with parameter mismatches and time-varying delays (TVDs). First, several timescale impulsive differential inequalities are demonstrated by the timescale theory, which offer new inequality techniques for the investigation of timescale-type impulsive systems. Next, some criteria are proved for discrete-time NNs and TNNs by utilizing impulsive control theory, timescale inequality techniques, and the average impulsive interval method. Unlike the published works, this article gives some impulsive control schemes to ensure quasi-synchronization (QS) even if there exist TVDs in TNNs. In the end, four simulation examples are offered to demonstrate the validness of the obtained theoretical results.

Event-triggered impulsive control of lower-triangular large-scale nonlinear systems based on gain scaling technique

This paper investigates the event-triggered impulsive control problem for a class of large-scale nonlinear systems in lower-triangular form. Based on gain scaling technique and impulsive control theory, a novel decentralized event-triggered impulsive control strategy is first put forward by introducing a static scaling gain, where no control input exists between two consecutive triggering points. Moreover, when the large uncertainties exist in system nonlinearities, we further develop a new control strategy by introducing a time-varying scaling gain. It is proved that the proposed closed-loop control strategies exclude the Zeno behavior without sacrificing the global convergence of system states. Compared with the existing results, it is the first time to apply impulsive control to lower-triangular large-scale nonlinear systems, and the advantages of event-triggered impulsive control and gain scaling technique are subtly combined in the proposed control strategies. Finally, two simulation examples are used to demonstrate the effectiveness of the proposed schemes.

Exponential stabilization of nonlinear systems under saturated control involving impulse correction

This paper studies the problem of locally exponential stabilization (LES) of nonlinear systems under a class of hybrid control in the framework of actuator saturation, where the limitation of actuator saturation on both continuous state feedback control and impulsive control are fully considered. Based on impulsive control theory and differential inclusion approach, some sufficient conditions for LES are derived, where a novel set inclusion relation is proposed to handle the double saturation nonlinearities. Different from the existing results that each part of saturated hybrid control (SHC) is required to stabilize the system individually, our results relax the requirement by making full use of the correction effect of the impulse. Moreover, the maximum of estimation of domain of attraction is obtained by a convex optimal problem and corresponding algorithm. The result is applied to the robustness for a class of nonlinear systems. Finally, the validity of the results is shown by two examples and their simulations, where the synchronization problem of Chua’s oscillator is illustrated in the framework of actuator saturation.

Hybrid output regulation for linear impulsive systems with aperiodic jumps: A discrete-time feedback controller design approach

This paper is concerned with the problem of hybrid output regulation for a class of linear impulsive systems with aperiodic jumps. Firstly, by leveraging time-dependent Lyapunov function technique and impulsive control theory, sufficient conditions for achieving output regulation are obtained in state feedback case. Then, the results are extended to error feedback case by constructing an impulsive observer. In this framework, two novel hybrid controllers are designed. Such controllers only need the discrete-time system state or error signal for feedback. The complete procedures for controller designs are also presented. Finally, two illustrative examples, including a numerical example and an LC circuit, are given to show the validity and applicability of the proposed control laws.

Impulsive Artificial Defense Against Advanced Persistent Threat

Advanced persistent threat (APT) as a new type of cyber espionage poses a severe threat to modern organizations. Artificial APT defense, in which an organization engages experienced cybersecurity experts to artificially check if there exist rootkits implanted by APT actors within the organizational internet and, if so, artificially remove the discovered rootkits, is recognized as an indispensable part of APT defense. There are two different ways of artificial APT defenses: continuous artificial defense (CAD), where the defense work is conducted at all time points, and impulsive artificial defense (IAD), where the defense work is conducted at a scheduled sequence of time points. IAD is superior to CAD in terms of the overall service cost. In the context of IAD, we refer to each sequence of service costs as an IAD policy. This paper addresses the problem of developing a cost-effective IAD policy (the IAD problem). First, by introducing an impulsive state evolutionary model for the organizational intranet, the IAD problem is reduced to an optimal impulsive control model (the IAD model). Second, by deriving the optimality system for the IAD model, an iterative algorithm for solving the IAD model (the IAD algorithm) is presented. Next, the convergence and effectiveness of the IAD algorithm are validated through numerical experiments. Finally, the effect of some factors is inspected. To our knowledge, this is the first time IAD is inspected from the perspective of optimal impulsive control theory.

Fast fixed-time impulsive bipartite synchronization of TS fuzzy complex networks with signed graphs

This dissertation mainly discusses the fast fixed-time bipartite synchronization (FFDT-BS) of TS fuzzy complex networks (TS FCNs) with signed graphs under impulsive control, where the communications between adjacent nodes are both cooperative and competitive. Different from most control protocol, the control process can be divided into two steps (impulsive control before settling time T and fixed-time control after T), and both the impulsive controller and FFDT controller are designed as fuzzy logic systems. By adopting impulsive control theory and mathematical induction, and constructing comparison system, some novel sufficient criteria are presented to guarantee the FFDT-BS of the TS FCNs within bounded time independent of the initial conditions. It is noting that the bipartite synchronization achieves faster convergence than most existing results, which is more practical and efficient. The performance comparisons of pure impulsive control, pure FFDT control, exist both impulsive control and FFDT control demonstrate the correctness of the theoretical analysis.

Finite-/fixed-time bipartite consensus for first-order multi-agent systems via impulsive control

This paper studies the finite-/fixed-time bipartite consensus (FNTBC and FXTBC) of multi-agent systems (MASs) over signed graph via discontinuous impulsive control while considering both leaderless and leader-following MASs. In contrast to the existing methods of FNTBC and FXTBC, the impulsive control has a better performance in convergence speed and less state information transmission, which is more practical and flexible in real applications. To realize FNTBC and FXTBC for leaderless and leader-following MASs, a class of distributed impulsive control protocols is proposed. Then by utilizing impulsive control theory and finite-/fixed-time stability theory, some sufficient criteria and the settling time which are based on the proposed impulsive control protocols for FNTBC and FXTBC for leaderless and leader-following MASs are derived. It has been shown that the settling time for FNTBC depends on initial conditions of systems, while this limitation is removed for FXTBC. Finally, the proposed impulsive protocols are validated by some simulations, separately.

Optimal impulse dividend and capital injection model with proportional and fixed transaction costs

In this paper, a hybrid strategy with optimal proportional reinsurance, dividends, and capital injections is discussed by a diffusion model with impulse process of discrete dividend events and discrete capital injections. Due to the presence of fixed transaction costs, the problem is formulated as a more complicated impulse stochastic control problem. By using methodologies from impulse control theory and the techniques of translation transformation, we obtain the explicit solutions of the value function and the corresponding optimal strategy. Firstly, the original problem is transformed into two types of suboptimal impulse control problems, one of which is “the case without capital injections” and the other one of which is “the case with compulsory capital injections.” Then, by verification theorem and the expressions of value functions of these two suboptimal problems, we verify that the optimal solution of the original problem is either “keeping bankruptcy without injections” or “never bankruptcy with injections.” It depends on the parameters of the model.

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.

Event-triggered control for nonlinear systems involving hybrid impulses

In this paper, we apply event-triggered control to nonlinear systems with impulses, and investigate the problem of ensuring globally exponential stability (GES) of the systems, where events and impulses may occur at different time. Moreover, two types of impulses (i.e., stabilizing and destabilizing) can coexist. On the basis of Lyapunov method and impulsive control theory, some sufficient conditions ensuring GES are derived, and the Zeno behaviour can be excluded. These conditions are presented in the form of linear matrix inequalities (LMI). In particular, inspired by average dwell-time methods, conditions for restriction of impulses are proposed, which guarantee GES of nonlinear systems involving single stabilizing and destabilizing or multiple impulses, respectively. Furthermore, the problem of designing event-triggered mechanism and control gains are solved by using LMI method. Lastly, two numerical simulation examples are given to represent the effectiveness of our results.

Saturated impulsive control of nonlinear systems with applications

The problem of saturated impulsive control of nonlinear systems is studied, where the saturation structure of impulse action is fully considered. Based on impulsive control theory and average dwell time (ADT) method, sufficient conditions for local exponential stabilization (LES) are derived. An optimization problem on designing controller is presented in order to maximize the domain of attraction. To get a less conservative estimate of the domain of attraction, a linear matrix inequality (LMI) based algorithm is proposed to solve such kind of optimization problems. The applications of the developed results are illustrated through examples from a Chua’s circuit and a problem of pulse transmission of a simple ball motion model.

A New Chaotic System with Coexisting Attractors

The investigation of new chaotic systems in spherical coordinates has been one of the present exciting research directions in exploring new chaotic systems. In this paper, a new system in spherical coordinates is presented. The appealing feature of the proposed system is that the dynamics of the system cannot pass through a sphere of a specific radius and stop as soon as the solution crosses the sphere in Cartesian coordinates. So, the system’s attractors are limited to be located on one side of the sphere and cannot touch it. Moreover, the reason for this phenomenon is that the velocity of a system’s variable becomes zero for a specific value of that variable. The proposed system has three unstable equilibrium points and four hidden attractors, including a limit cycle and a strange attractor inside and a limit cycle and a strange attractor outside the sphere. The system’s dynamical properties are investigated with the help of bifurcation diagrams and the calculation of Lyapunov exponents. The basin of attraction for the system’s attractors is also studied. Finally, the system is controlled or stabilized using the impulsive control theory.

Analysis and control of a delayed population model with an Allee effect

Based on the population model with an Allee effect, the corresponding delayed model is built up. According to the qualitative theory of differential equations, the model is analyzed completely to describe various intriguing dynamic properties as singular point of high order, Hopf bifurcation, etc. Next, combined impulse control theory with the ecological principles, the control models with impulse effects are proposed and the corresponding controllers are designed not only to avoid the extinction of the populations but also to prevent outbreak of the populations. The study would not only reveal the complexity dynamic behavior of ecosystems, but also provide the theory reference for the management of populations.

Hybrid Event-Triggered Approach for Quasi-Consensus of Uncertain Multi-Agent Systems With Impulsive Protocols

Quasi-consensus tracking problems of uncertain multi-agent systems are investigated in this paper. By integrating impulsive control theory with event-triggered mechanism, a new hybrid event-triggered impulsive consensus protocol is presented, under which the information transmission of agents occurs at a sequence of state-dependent instants. Based on Lyapunov method, several quasi-consensus criteria of uncertain multi-agent systems are constructed, as well as the relation among control gains, event parameters, consensus error level, and convergence rate is established. It shows that the hybrid event-triggered control strategy benefits to save the energy cost of information transmission and control cost between agents compared with the time-triggered scheme, and it is effective to achieve quasi-consensus tracking objective of considered systems. Finally, the Zeno behavior is shown to be ruled out, and some simulation examples are proposed to demonstrate the validity of the theoretical analysis.

Finite-Time Synchronization for Delayed Complex Dynamical Networks With Synchronizing or Desynchronizing Impulses.

In this article, the finite-time synchronization problem of delayed complex dynamical networks (CDNs) with impulses is studied, where two types of impulses, namely, synchronizing impulses and desynchronizing impulses, are fully considered, respectively. Since the existence of impulses makes the discontinuity of the states, which means that the classical result for finite-time stability is inapplicable in such a case, the key challenge is how to guarantee the finite-time stability and estimate the settling time in impulse sense. We apply impulsive control theory and finite-time stability theory to CDNs and establish some sufficient conditions for finite-time synchronization, where two kinds of memory controllers are designed for synchronizing impulses and desynchronizing impulses, respectively. Moreover, the upper bounds for settling time of synchronization, which depends on the impulse sequences, are effectively estimated. It shows that the synchronizing impulses can shorten the settling time of synchronization; conversely, the desynchronizing impulses can delay it. Finally, the theoretical analysis is verified by two simulation examples.