Distributed impulsive control consensus for a class of unknown nonlinear multi-agent systems based on event-triggered scheme

In this study, we are concerned with the impulsive consensus control problem for a class of nonlinear multi-agent systems (MASs) which have unknown dynamics and directed communication topology. The neural networks (NNs) method is the first utilized to construct distributed event-triggered impulsive consensus protocol. In contrast to the existing impulsive consensus protocol, the consensus protocol proposed in this paper does not need the dynamics of agents, which enhances the system robustness, and realizes distributed event-triggered communication between agents, which can reduce unnecessary consumption of communication resources. Sufficient conditions are derived to ensure the consensus of the controlled MASs and the exclusion of Zeno-behavior. Finally, simulation examples are presented to illustrate the effectiveness of the proposed control protocol.     

Second-order cluster consensus of multi-agent dynamical systems with impulsive effects

This paper discuss the cluster consensus of multi-agent dynamical systems (MADSs) with impulsive effects and coupling delays. Some sufficient conditions that guarantee cluster consensus in MADS are derived. In each cluster, agents update their position and velocity states according to a leader’s instantaneous information, and interactions among agents are uncertain. Furthermore, switching topology problem in MADS is considered by impulsive stability and adaptive strategy. Finally, numerical simulations are given to verify our theoretical analysis.     

Impulsive consensus of one-sided Lipschitz nonlinear multi-agent systems with Semi-Markov switching topologies

Many real systems involve not only parameter changes but also sudden variations in environmental conditions, which often causes unpredictable topologies switching. This paper investigates the impulsive consensus problem of the one-sided Lipschitz nonlinear multi-agent systems (MASs) with Semi-Markov switching topologies. Different from the existing modeling methods of the Markov chain, the Semi-Markov chain is adopted to describe this kind of randomly occurring changes reasonably. To cope with the communication and control cost constraints in the multi-agent systems, the distributed impulsive control method is applied to address the leader–follower consensus problem. Beyond that, to obtain a wider nonlinear application range, the one-sided condition is delicately developed to the controller design, and the results are different from the ones obtained in the traditional method with the Lipschitz condition (note that the existing results are usually only applicable to the case with small Lipschitz constant). Based on the characteristics of cumulative distribution functions, the theory of Lyapunov-like function and impulsive differential equation, the asymptotically mean square consensus of multi-agent systems is maintained with the proposed impulsive control protocol. Finally, an explanatory simulation is presented to validate the correctness of the proposed approach conclusively.     

Distributed adaptive switching consensus control of heterogeneous multi-agent systems with switched leader dynamics

In this paper, the leader-following distributed consensus control problem is addressed for general linear multi-agent systems with heterogeneous uncertain agent dynamics and switched leader dynamics. Different from most existing results with a single linear time-invariant (LTI) leader dynamics, the leader dynamics under consideration is composed by a family of LTI models and a switching logic governing the switches among them, which is capable of generating more diverse and sophisticated reference signals to accommodate more complicated consensus control design tasks. A novel distributed adaptive switching consensus protocol is developed by incorporating the model reference adaptive control mechanism and arbitrary switching control technique, which can be synthesized by following a two-layer hierarchical design scheme. A numerical example has been used to demonstrate the effectiveness of the proposed approach.     

Robust fixed-time consensus protocols for multi-agent systems with nonlinear state measurements

This paper solves the robust fixed-time consensus problem for multi-agent systems with nonlinear state measurements. Sufficient conditions are established for the proposed protocol to reach fixed-time consensus under time-varying undirected and fixed directed topology with the aid of Lyapunov functions. It is proved that the finite settling time of the presented protocol for robust consensus is uniformly bounded for any initial condition, which makes it possible for people to design and estimate the convergence time off-line. Numerical simulations are preformed to show the effectiveness of our proposed protocol.     

Stabilization of switched linear systems using an improved event-triggered control scheme

This paper is concerned with the event-triggered control of switched linear systems. The coupling of system switching and event-triggered communication raises two phenomena: (1) the update of controller cannot always catch up with the active subsystem; (2) the switching may lead to additional triggers. The first phenomenon is called the asynchronous switching induced by network communication and the second one brings great difficulty to avoid the Zeno behavior of event-triggered mechanism (ETM). To address the above problem, we propose a new ETM which contains the switching signal of models and controllers and the discontinuity of triggering error at switching time instants. A relative threshold strategy, combined with a jump function, is designed as a new threshold function. By introducing a compensation term, the linear feedback control law is extended to avoid the Zeno behavior of ETM and improve the solvability of control algorithm. Based on the proposed event-triggered control scheme, the exponential stabilization of switched systems is achieved with relaxed constraints on the triggering and switching conditions. The obtained results are validated by a numerical example.     

Hybrid consensus for multi-agent systems with time-driven jumps

In this paper, the behavior of scalar multi-agent systems over networks subject to time-driven jumps. Assuming that all agents communicate through distinct communication digraphs at jump and flow times, the asymptotic multi-consensus behavior of the hybrid network is explicitly characterized. The hybrid multi-consensus is shown to be associated with a suitable partition that is almost equitable for both the jump and flow communication digraphs. In doing so, no assumption on the underlying digraphs is introduced. Finally, the coupling rules making the multi-consensus subspace attractive are established. Several simulation examples illustrate the theoretical results.     

Resilient self/event-triggered consensus based on ternary control

This paper considers the problem of multi-agent consensus in the presence of adversarial agents. Such adversaries may try to introduce undesired influence on the coordination of the regular agents and to even prevent them from reaching consensus. To our setting, we extend the so-called mean subsequence reduced algorithms with the aim to reduce the use of computation and communication resources of the agents. In particular, by employing self- and event-triggered communication, the frequencies of state updates as well as data transmissions are kept low. Moreover, the control inputs of the agents take the form of ternary signals, allowing them to further reduce the amount of information at each transmission. We will observe that in hostile environments with adversaries, the self-triggered approach can bring certain advantages over the event-triggered counterpart. Moreover, a novel switching scheme is introduced to mix the two protocols to further enhance the performance of the agents.     

Variable impulsive consensus of nonlinear multi-agent systems

In this paper, the consensus problem for nonlinear multi-agent systems with variable impulsive control method is studied. In order to decrease the communication wastage, a novel distributed impulsive protocol is designed to achieve consensus. Compared with the common impulsive consensus method with fixed impulsive instants, the variable impulsive consensus method proposed in this paper is more flexible and reliable in practical application. Based on Lyapunov stability theory and some inequality techniques, several novel impulsive consensus conditions are obtained to realize the consensus of multi-agent systems. Finally, some necessary simulations are performed to validate the effectiveness of theoretical results.     

Impulsive consensus problem of second-order multi-agent systems with switching topologies

The paper proposes an impulsive consensus protocol to solve the consensus problem of the second-order multi-agent systems with fixed and switching topologies. Some sufficient conditions are obtained for the states of follower agents converging to the state of leader asymptotically. Two numerical simulations are also given to verify the effectiveness of the theoretical analysis.     

Dynamic periodic event-triggered gain-scheduling control co-design for quasi-LPV systems

This paper investigates dynamic periodic event-triggered gain-scheduling control co-design for nonlinear systems subject to disturbances. The considered class of nonlinear systems is such that an equivalent polytopic quasi-LPV model is obtained. Based on the co-design approach, gain-scheduled control law and dynamic event-triggering mechanism (ETM) are jointly designed. The proposed co-design condition is formulated in terms of linear matrix inequality (LMI) conditions which are derived from the Bessel–Legendre inequality and the delay-dependent reciprocally convex combination lemma. As the state information is available to the gain-scheduled controller at specific instants determined by the ETM, it induces the asynchronous phenomenon between the parameters of the controller and the plant’s quasi-LPV model. To reduce the conservativeness induced by this asynchronous phenomenon, an LMI relaxation is proposed. Numerical examples illustrate the advantages of the proposed dynamic periodic event-triggered control co-design approach over its static counterpart.     

Quantized control for networked switched systems under denial-of-service attacks via a barrier event-triggered mechanism

This paper studies the quantized control problem for networked switched systems (NSSs) under denial-of-service (DoS) attacks. The quantized state information, together with the switching signal, is transmitted to the controller through a network. In order to reduce communication consumption and controller update frequency, a barrier event-triggered mechanism is utilized to monitor the state at discrete time. Because of the event-triggered mechanism and the DoS attacks on the network, the mismatch between the system mode and the controller mode is thus frequently encountered, which may lead to quantization saturation and system instability. To solve the problem, an update rule is presented for the dynamic quantizer by switching between zooming in and zooming out of the zooming variable, and a feedback controller is proposed with a jointly designed event-triggered mechanism and a dynamic quantizer. Sufficient conditions on the constraints of DoS frequency and duration are obtained to ensure the exponential stability of the switched system. The effectiveness of the obtained results is illustrated by simulation examples and comparative studies.     

A multi-agent inventory problem with general transportation costs

This paper addresses the cost allocation problem that arises from an inventory system with multiple item and several agents that place joint orders according to an EOQ policy. In this setting, the cost per a new order has two components: a fixed cost and a variable cost. We assume that the variable part is given by a general function, not necessarily additive. We obtain the optimal policy and we evaluate some proposals of allocation rule for the ordering costs.     

Randomly changing leader-following consensus control for Markovian switching multi-agent systems with interval time-varying delays

This paper considers the problem of leader-following consensus stability and also stabilization for multi-agent systems with interval time-varying delays. The randomly occurring interconnection information of the leader and the Markovian switching interconnection information of the agent are matters of concern in the systems. Through construction of a suitable Lyapunov–Krasovskii functional and utilization of the reciprocally convex approach, new delay-dependent consensus stability and stabilization conditions for the systems are established in terms of linear matrix inequalities (LMIs) which can be easily solved by using various effective optimization algorithms. Two numerical examples are given to illustrate the effectiveness of the proposed methods.     

Sampled-data-based consensus of multi-agent systems under asynchronous denial-of-service attacks

This paper investigates the sampled-data-based consensus problem of multi-agent systems (MASs) under asynchronous denial-of-service (DoS) attacks. In order to describe asynchronous DoS attacks, a new definition of complete DoS attack and novel double-layer switched systems are proposed. A complete DoS attack refers to a DoS attack that consists of several consecutive successful DoS attacks. While a successful DoS attack denotes an attack that can break the connected communication topology into several isolated subgraphs. Based on this, the original system is transformed into a double-layer switched systems with a stable mode and several unstable modes. It should be pointed out that each unstable subsystem is also composed of finite second-level unstable subsystems that represent consecutive successful DoS attacks. Moreover, a new double-mode-dependent Lyapunov function (DMDLF) method is employed to obtain the lower and upper bounds of the corresponding average dwell time (ADT) of subsystems. It is proved that the consensus of MASs under asynchronous DoS attacks can be achieved by using the feedback consensus controllers which can be designed simultaneously. Finally, an illustrative example is provided to illustrate the effectiveness of the results proposed in this paper.     

Small-gain technique-based adaptive output constrained control design of switched networked nonlinear systems via event-triggered communications

This paper investigates the problem of event-triggered tracking control for switched networked nonlinear systems with asymmetric time-varying output constraints. To handle the output constraints, an output-dependent generic constraint function is constructed to describe relationship between the output and the performance requirement. Meanwhile, an event-triggering rule is designed to reduce communication frequency between the controller and the actuator, thereby reducing the burden of the network communication. Based on the common Lyapunov function method and event-triggered control strategy, an adaptive control method is designed, which can guarantee that the closed-loop signals are bounded and avoid the Zeno behavior. Different from existing results considering constraints, the proposed scheme not only relaxes the restricted condition of constraint boundaries but also both the cases with and without output constraints can be addressed simultaneously. Furthermore, the stability of the system can be guaranteed by the small-gain technique. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed scheme.     

An improved convergence rate of Glimm scheme for general systems of hyperbolic conservation laws

We study the convergence rate of Glimm scheme for general systems of hyperbolic conservation laws without the assumption that each characteristic field is either genuinely nonlinear or linearly degenerate. We first give a sharper estimate of the error arising from the wave tracing argument by a careful analysis of the interaction between small waves. With this key estimate, the convergence rate is shown to be , which is sharper compared to given in [T. Yang, Convergence rate of Glimm scheme for general systems of hyperbolic conservation laws, Taiwanese J. Math. 7 (2) (2003) 195-205]. However, it is still slower than given in [A. Bressan, A. Marson, Error bounds for a deterministic version of the Glimm scheme, Arch. Ration. Mech. Anal. 142 (2) (1998) 155-176] for systems with each characteristic field being genuinely nonlinear or linearly degenerate. Here s is the mesh size and α is any positive constant.     

Practical scaled consensus for nonlinear multiagent systems with input time delay via a new distributed integral-type event-triggered scheme

This paper studies scaled-based practical consensus issue for multiagent systems with input time delay by a fully continuous communication-free integral-type event-triggered scheme. By choosing the proper scales, scaled consensus can be induced to synchronization, bipartite consensus or cluster consensus. By defining a continuous communication-free measurement error for the integral-type event-triggered mechanism, the new integral-type event-triggered condition is proposed which can not only reduce the energy consumption but also prolong the interevent time. Then, with time domain analysis method, the distributed integral-type event-triggered control problem for nonlinear general multiagent systems involving input time delay is investigated and then the second-order counterpart, with a calculated upper-bound for time-delay. Moreover, it is concluded that with such event-triggered protocols, practical scaled consensus can be achieved without the exhibition of Zeno behavior. At last, simulations are shown to support the results.     

Stability analysis of cyclic switched nonlinear systems via event-triggered method

In this paper, the exponential stability problem is addressed for a class of cyclic switched nonlinear systems with unstable modes. A novel event-triggered cyclic switching scheme (ETCSS) is proposed to generate a cyclic switching signal that exponentially stabilizes the considered system for any given initial configuration. Some easily verifiable stability criteria for switched nonlinear and linear systems are established, and the effects of event parameters on the convergence rate are also analyzed. Different from the existing studies, here the developed switching scheme is not only cyclic but also event-triggered and thereby the switching frequency is relatively low. Finally, a numerical example is given to verify the efficiency of the method.