Zeno Phenomenon Research Articles

Bumpless transfer control of switched systems: A dynamic event-triggering switching control approach

This paper studies the bumpless transfer (BT) control issue for switched systems with event-triggered (ET) control input. The aim is to reduce the jumps in control input at both switching and triggering points, while capturing the stability of the switched systems. First, a dynamic ET program is constructed with the triggering condition based on the level of suppression of input signal jumps. This not only reduces input jumps at triggering points, but also prevents Zeno behavior caused by triggering within the operation time interval of subsystems. Second, a sampled state-dependent switching signal is designed to ensure a dwell time for subsystems to prevent Zeno phenomenon induced by switching. Further, a switched ET controller with alleviated jumps is designed. Third, conditions are obtained to simultaneously reach both stabilization and BT of switched systems. Finally, the effectiveness of the theoretical results is demonstrated through a simulation of an engine model.

Robust synchronization of Markovian jump complex dynamical networks under link attacks: Delay-dependent dynamic event-triggered control approach

This paper investigates the synchronization problem for Markovian jump complex dynamical networks (MJCDNs) subject to link attacks. An extended dynamic event-triggered (DET) control is proposed that takes into account limited network resources and time-varying delay constraints. The proposed method enhances the robustness and resource-saving ability of the DET mechanism, and avoids the Zeno phenomenon. It provides MJCDNs to have a buffering ability for external interference. Additionally, this paper introduces a robust model-based strategy to address scenarios where network attackers inject false data into the link channels between nodes. This approach reduces the complexity of processing MJCDNs subject to link attacks. By leveraging network topology and Lyapunov functions, the criteria are derived to achieve robust synchronization of MJCDNs under link attacks. Finally, simulation examples including Chua’s circuit are presented to verify the validity and superiority of the results.

Double adaptive event-triggered strategy for leader-following group consensus of heterogeneous multi-agent systems in cooperative–competitive networks

This article investigates adaptive event-triggered control for leader-following group consensus of hybrid heterogeneous multi-agent systems (HMASs) composed of single- and double-integrator agents under cooperative–competitive relationships. By using fully distributed control protocol and adaptive protocol, the leader-following group consensus can be achieved without global information. Additionally, a novel adaptive double dynamic event-triggered mechanism (DDETM) is proposed, in which two independent adaptive event-triggered conditions are devised to maintain events of communication and updates of controllers. Furthermore, adaptive parameters and internal dynamic variables are employed to reduce the number of triggers and exclude Zeno phenomenon. By utilizing Lyapunov stability theory, some sufficient conditions are acquired for the leader-following group consensus of the HMASs. Finally, simulation examples are given to prove the effectiveness of the proposed method.

Bipartite formation control of second-order multi-agent systems with antagonistic interactions under dynamic event-triggered adaptive schemes

This article examines the adaptive leader-following bipartite formation (LBF) of second-order nonlinear multi-agent systems (MASs) with antagonistic interactions over a directed signed graph. To save the scarce communication resources efficiently, a novel distributed controller is designed for the LBF of the MASs, where a dynamic event-triggered (DET) control protocol with dynamic parameters is proposed. Meanwhile, the optimal control gains for realizing adaptive bipartite formation are obtained in accordance with the designed adaptive updating laws. By employing the DET mechanism and the Lyapunov functionals in conjunction, sufficient criteria for the adaptive LBF of the second-order MASs with antagonistic interactions and a directed signed graph are obtained. Furthermore, it has been demonstrated that Zeno phenomenon doesn't exist. Finally, the efficacy of the theoretical outcomes and the control protocol is validated through a numerical simulation.

H∞ adaptive ETF control for degenerate jump systems under actuator faults and impulsive deception attacks with application to DCMIP device

This article considers the issue of H∞ adaptive event-triggered feedback control for degenerate jump systems under actuator faults and impulsive deception attacks. Based on periodic sampling strategy, a mode-dependent adaptive event-triggered scheme is developed, which can save communication resources, avoid the Zeno phenomenon and take full advantage of Markovian mode information. By constructing the neoteric Lyapunov-Krasovskii (L-K) functional containing piecewise linear impulsive auxiliary functions and applying singular value decomposition (SVD) technique, the fresh stochastic admissibility conditions for degenerate Markovian jump systems under actuator faults and impulsive deception attacks are obtained under the framework of linear matrix inequalities (LMIs), and then the adaptive event-triggered scheme with weighted matrices and feedback controller are designed simultaneously. By applying freedom weight matrix method and the property that the network-induced delay derivative is one, the non-strict LMI conditions are transformed into strict ones, such that the stochastic admissibility of the degenerate jump systems and state feedback controller gains are realized adequately. Finally, a direct current motor-controlled inverted pendulum (DCMIP) device is used to confirm the feasibility of the presented approach.

Event-triggered and quantised feedback stabilisation of switched networked control systems

In order to conserve network resources, this paper investigates the event-triggered control and quantised feedback stabilisation of switched networked control systems by introducing the vector quantizer technique. The state information undergoes quantisation and is transmitted to the controller after being sampled by the event-triggering technology. The designed event-triggered mechanism relies on quantised state values, and the generation of each quantised value also depends on the event-triggered condition. Addressing the asynchronous issue between the controller and the subsystem, we provide a sufficient condition for ensuring exponential stability of the closed-loop system and outline the controller gain design method by employing the multiple Lyapunov function and average dwell time methods. Besides, we demonstrate the explicit exclusion of the Zeno phenomenon in the event-triggered mechanism. Finally, the viability of our approach is demonstrated through simulation examples.

Non-fragile event-triggered control for switched positive linear systems using state-dependent switching method

This article is concerned with the issues of stability and L1-gain characteristic for switched positive linear systems utilizing bumpless transfer (BT) technique and event-triggered (ET) strategy. Under the state-driven switching policy, a regulatory approach that couples BT and ET is introduced to attenuate the hybrid bumps stemming from switching and triggering moments. Compared with traditional state-driven switching, the proposed hysteresis switching can delay the occurrence of switching. Based on multiple copositive Lyapunov functions, a state feedback controller with an ET mechanism is constructed for positive systems, which reduces the update frequency of the actuator, and this control strategy is extended to the case of actuator faults. It is confirmed that the proposed control scheme can assure the positivity, stability, and L1-gain performance of the system. Additionally, the Zeno phenomenon is addressed via establishing a positive lower bound for the ET interval. Ultimately, simulation examples containing a turbofan engine model are provided to demonstrate the effectiveness of the proposed approach.

Adaptive Neurodynamic Approach to Multiple Constrained Distributed Resource Allocation.

In this article, an adaptive neurodynamic approach over multiagent systems is designed to solve nonsmooth distributed resource allocation problems (DRAPs) with affine-coupled equality constraints, coupled inequality constraints, and private set constraints. It is to say, agents focus on tracking the optimal allocation to minimize the team cost under more general constraints. Among the considered constraints, multiple coupled constraints are dealt with by introducing auxiliary variables to make Lagrange multipliers reach consensus. Furthermore, aiming to address private set constraints, an adaptive controller is proposed with the aid of the penalty method, thus avoiding the disclosure of global information. Through using the Lyapunov stability theory, the convergence of this neurodynamic approach is analyzed. In addition, to reduce the communication burden of systems, the proposed neurodynamic approach is improved by introducing an event-triggered mechanism. In this case, the convergence property is also explored, and the Zeno phenomenon is excluded. Finally, a numerical example and a simplified problem on a virtual 5G system are implemented to demonstrate the effectiveness of the proposed neurodynamic approaches.

Event-triggered adaptive fault-tolerant control with pre-specified performance for AUVs trajectory tracking

This paper investigates the problem of fault-tolerant control of the preset performance of autonomous underwater vehicles (AUVs) in case of external disturbances and actuator failures. To begin with, a specific new nonlinear auxiliary function with dual performance constraints is designed to establish the foundation for achieving prescribed performance in the closed-loop system. Subsequently, an event-triggered fault tolerant controller employing Nussbaum gain technique is introduced to accomplish the precision trajectory tracking control of the AUVs by predetermining control index. It is shown that the effect by resulting in actuator faults is on-line compensated by an adaptive estimator. Theoretical analyses demonstrate the boundedness of the signals of the designed closed-loop control system, and the Zeno phenomenon can be effectively avoided. Finally, simulation experiments are conducted to verify the effectiveness of the proposed methods.

Fault-Tolerant Synchronization for Memristive Neural Networks With Multiple Actuator Failures.

By using the fault-tolerant control method, the synchronization of memristive neural networks (MNNs) subjected to multiple actuator failures is investigated in this article. The considered actuator failures include the effectiveness failure and the lock-in-place failure, which are different from previous results. First of all, the mathematical expression of the control inputs in the considered system is given by introducing the models of the above two types of actuator failures. Following, two classes of synchronization strategies, which are state feedback control strategies and event-triggered control strategies, are proposed by using some inequality techniques and Lyapunov stability theories. The designed controllers can, respectively, guarantee the realization of synchronizations of the global exponential, the finite-time and the fixed-time for the MNNs by selecting different parameter conditions. Then the estimations of settling times of provided synchronization schemes are computed and the Zeno phenomenon of proposed event-triggered strategies is explicitly excluded. Finally, two experiments are conducted to confirm the availability of given synchronization strategies.

Cluster consensus for nonlinear multi‐agent systems restricted with input saturation by event triggered control

AbstractThis article studies the cluster consensus problem for the nonlinear multi‐agent systems subject to input saturation under the context of event triggered control. Taking ordinary consensus object as a special case, this article considers the problem of cluster consensus. The event triggered mechanism is designed and the Zeno phenomenon is ruled out. The sufficient conditions of control protocol and range estimation of domain of attraction are formulated by the linear matrix inequalities for the constraints of input saturation and nonlinear terms existed in the system dynamics. Finally, the proposed results are validated by one example in the background of spring damping system.

Disturbance-observer-based adaptive neural event-triggered fault-tolerant control for uncertain nonlinear systems against sensor faults

In this article, the adaptive event-triggered fault-tolerant control (FTC) issue of uncertain nonlinear systems suffering from sensor and actuator faults as well as external disturbances is studied. A disturbance observer (DO) is constructed to compensate for external disturbances and approximation errors generated by neural networks (NNs). Then, switching event-triggered control and command filtering techniques are introduced to balance the communication frequency and tracking performance of the controlled systems while avoiding “explosion of complexity” issue caused by iterative derivations of virtual controllers. Furthermore, compensation signals are designed to eliminate filtered errors. Finally, it is proven that the developed FTC scheme can esure that all signals are bounded and free from Zeno phenomenon. Simulation results of a spring damping mechanical system verifies the merits of the designed control algorithm.

Disturbance observer-based event-triggered impulsive control for nonlinear systems with unknown external disturbances

Input-to-state practical stability (ISpS) of a kind of nonlinear systems suffering from unknown exogenous disturbances is explored in this article, where a disturbance observer is established to estimate the information of the exogenous disturbances. To achieve ISpS of the system, the impulsive controller as well as state-feedback controller are both considered to regulate the discrete and continuous dynamics of the system, respectively. Especially, a novel disturbance observer-based event-triggered mechanism is devised to decide the release of impulsive control signal. Furthermore, several adequate conditions are given for excluding the occurrence of Zeno phenomenon. To confirm the feasibility of the proposed results, two numerical instances and their corresponding simulation results are presented.

Event-triggered quasi-time-varying [formula omitted] filtering for switched systems via multiple trigger-dependent Lyapunov functionals

This paper investigates the event-triggered filtering problem for switched systems from the perspective of switched impulsive systems (SISs) by exploiting the characteristics of trigger and impulse behavior. By constructing multiple trigger-dependent Lyapunov functionals (MTDLFs), an event-triggered quasi-time-varying (ET-QTV) H∞ filtering scheme is developed. Since the MTDLFs properly capture the event-induced impulse property of SISs, they release less conservatism. The filtering stability in the scenario of frequent plant switching during an interevent interval is also guaranteed by incorporating the average dwell time switching. The filtering synthesis condition is formulated as a set of QTV matrix inequalities defined over a finite time horizon, based on which a sum of squares-based filter design algorithm is presented further. Additionally, the derivation of a lower bound on interevent intervals is clarified for the event-triggering mechanism (ETM) to exclude the Zeno phenomenon. Finally, the effectiveness and potential practicability of the proposed filtering scheme are validated using a morphing aircraft model.

RBF-based event-triggered fixed-time stable and chattering-free controller for load following of the pressurized water reactor

Preventing chattering phenomenon in load following control of the Pressurized Water Reactor (PWR) is still a main challenge. This article focuses on the chattering-free and rapid load following control strategy for PWR. Firstly, by proposing a newly adaptive updated law, the Radial Basis Function Neural Networks (RBFNNs) is employed to compensate the unmeasured states of relative delayed neutron precursor density, average fuel temperature and uncertain disturbances simultaneously online. On this basis, a fixed-time stable controller including saturation function is constructed to guarantee that the actual output power (OP) of nuclear reactor can follow the desired power (DP) within a fixed-time and the chattering phenomenon is alleviated. Additionally, to save the limited network resource and reduce the cost of computation, an event-triggered mechanism is constructed. Based on it, a chattering-free fixed-time stable controller is structured to ensure that the actual reactivity of control rod (ARCR) converges to the desired control rod reactivity (DCRR) within a fixed-time, meanwhile, it can eliminate Zeno phenomenon during the control process. Finally, the effectiveness and feasibility of the theoretical results are demonstrated through simulation examples.

Dynamic event-triggered time-varying formation control for heterogeneous unmanned swarm systems with scaling attacks

This paper addresses the problem of time-varying formation control for heterogeneous unmanned swarm systems (USSs) consisting of multiple unmanned aerial vehicles (UASs) and unmanned surface vehicles (USVs) based on a directional switching topology. Firstly, a novel USSs model is established, involving the effect of multiple network attacks, network bandwidth constraints and input saturation. In particular, a scaling attack model is proposed to account for denial-of-service (DoS) and deception attacks. Secondly, a distributed controller based on a dynamic event triggering mechanism is designed to reduce the communication load by adjusting the communication frequency between individuals, and the Zeno phenomenon is effectively avoided. Finally, the Lyapunov function is used to obtain sufficient conditions for system stability and bounds on the frequency and duration of network attacks. The experiments and comparison results verify the proposed strategy's effectiveness and superiority.

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.

Dynamic event‐triggered control of 2‐D continuous systems in Roesser model

AbstractIn this paper, a dynamic event‐triggered control problem is discussed for 2‐D continuous systems by the Roesser model. In order to reduce communication frequency and avoid dependence on global information, a dynamic event‐triggered mechanism is constructed, which is more flexible than some existing event‐triggered schemes with fixed event‐triggered thresholds. Utilizing the dynamic event‐triggered mechanism, a state feedback controller is designed. By constructing a 2‐D Lyapunov function, sufficient conditions expressed in terms of linear matrix inequalities (LMIs) are firstly established such that the 2‐D system is asymptotically stable with a disturbance attenuation performance. It is also proved that the Zeno phenomenon is excluded. Finally, two examples are provided to illustrate the effectiveness of the proposed method.

Action-dependent heuristic dynamic programming for hybrid-order systems based on dynamic event-triggered mechanism

We investigate the distributed optimal consensus control problem based on action-dependent heuristic dynamic programming (ADHDP). In order to strike a stable balance between the learning cost of reinforcement learning and the resource utilization efficiency of the hybrid-order multi-agent systems (MASs), we propose an improved dynamic event-triggered ADHDP (dET-ADHDP) method. This approach can non-periodically explore the control policy distribution using the online action-dependent actor–critic (ADAC) learning framework. Meanwhile, it can dynamically adjust the trigger lower bound by exploiting the designed trigger threshold function, and adaptively decide the signal trigger moment during the ADAC learning process. In addition, we demonstrate the boundedness of the ADAC network weights and show that under the designed dynamic event-triggering rules, the MASs can asymptotically achieve optimal tracking control without Zeno phenomenon. Finally, compared with the traditional static counterparts, simulation experiments demonstrate that the proposed dynamic event-triggered ADAC (dET-ADAC) algorithm has more efficient resource utilization while maintaining satisfactory learning performance.

Composite error event-triggered-based finite-time safe formation control of underactuated vessels

For the problems of limited communication bandwidth and frequent triggering of actuators during the formation navigation, comprehensively considering the safety performance and coordinated control performance, a novel composite error event-triggered-based formation control strategy is proposed. Firstly, design an event-triggered-based finite-time extended state observer, which can not only quickly estimate the compound disturbances and velocity information simultaneously, but also reduce the communication frequency between sensor and observer. Secondly, considering the communication frequency and coordinated control performance of the whole formation system, a composite error based on the state information of adjacent underactuated vessels is defined, and it is used as a factor of the event-triggered mechanism. Then, by combining the exponential potential energy function, the composite error event-triggered-based formation controller is designed. And through stability analysis, we known that all signals of the system are uniformly ultimately bounded. Furthermore, the Zeno phenomenon that exists in event-triggered control can also be avoided completely. Finally, through simulation results and comparative analysis, the effectiveness of the composite error event-triggered-based formation control scheme for safe navigation control and reducing communication frequency and triggering frequency has been verified.