Mean-square consensus of heterogeneous multi-agent systems with communication noises

This paper addresses the mean-square consensus problems of continuous-time heterogeneous multi-agent systems with communication noises. First, in order to attenuate the communication noises, time-varying consensus gains are applied in the consensus algorithm. Then, by using the tools of algebraic graph theory and stochastic analysis, sufficient conditions for the mean-square consensus are given for the cases with and without a leader. Finally, simulations are provided to demonstrate the effectiveness of the proposed algorithms.     

Bipartite output consensus for heterogeneous linear multi-agent systems with fully distributed protocol

This paper addresses the problem of bipartite output consensus of heterogeneous multi-agent systems over signed graphs. First, under the assumption that the sub-graph describing the communication topology among the agents is connected, a fully distributed protocol is provided to make the heterogeneous agents achieve bipartite output consensus. Then for the case that the topology graph has a directed spanning tree, a novel adaptive consensus protocol is designed, which also avoids using any global information. Each of these two protocols consists of a solution pair of the regulation equation and a homogeneous compensator. Numerical simulations show the effectiveness of the proposed approach.     

Event-based consensus for second-order multi-agent systems with actuator saturation under fixed and Markovian switching topologies

This paper studies the event-based consensus problem of second-order multi-agent systems with actuator saturation under fixed topology and Markovian switching topologies. By a model transformation, the consensus problem is first converted into the stability problem of the error system. Using discontinuous Lyapunov functional approach, two sufficient conditions on the consensus are derived for second-order multi-agent systems with fixed topology and Markovian switching topologies, respectively. The discontinuous Lyapunov functions take full account of the characteristics of the sawtooth delay, and thus lead to a less conservative consensus criterion. It is shown that the consensus condition depends on the parameters of sampling period, Laplacian matrix, and event-triggered parameter. In addition, this paper provides an effective method to co-design both the consensus controller and the event-triggered parameter. Finally, two numerical examples are provided to illustrate the effectiveness and feasibility of the proposed algorithm.     

Fault diagnosis and fault-tolerant tracking control for discrete-time systems with faults and delays in actuator and measurement

In this paper, the fault diagnosis (FD) and fault-tolerant tracking control (FTTC) problem for a class of discrete-time systems with faults and delays in actuator and measurement is investigated. In the first step, a discrete delay-free transformation approach is introduced for an constructed augmented system such that the two-point-boundary-value (TPBV) problem with advanced and delayed items can be avoided. Then, the optimal fault-tolerant tracking controller (OFTTC) is proposed with respect to an equivalent reformed quadratic performance index. Moreover, by using the real-time system output rather than the residual errors, a reduced-order-observer-based fault diagnoser for the augmented system is designed to diagnose faults in actuator and measurement, and solve the physically unrealizable problem of proposed OFTTC. Finally, the effectiveness of the proposed fault diagnoser and OFTTC is illustrated by a realistic design example for industrial electric heater.     

Explicit condition for consensus of third-order discrete-time multi-agent systems without accelerated velocity measurements

This paper investigates the consensus problem for third-order discrete-time multi-agent systems in directed networks. For the case when each agent can only receive the information of position and velocity from its neighbors, necessary and sufficient conditions for consensus have been proposed. In contrast to the preceding work, we not only present the exact consensus value, but also illustrate the influence of scaling parameters and nonzero eigenvalues of the involved Laplacian matrix on consensus. Two numerical examples are given to demonstrate the effectiveness of the obtained results.     

Event-based discrete-time multi-agent consensus over signed digraphs with communication delays

The ability to ensure the desired performance of the cooperative-antagonistic multi-agent networks (MANs) in the presence of communication constraints is an important task in many applications of real systems. In this paper, under the proposed event-triggered condition (ETC), different types of consensus are obtained under different network topology. We concentrates on the event-based bipartite consensus. It is shown that under the proposed ETC (i) the addressed cooperative-antagonistic network with arbitrary communication delays reaches bipartite consensus provided that the network is balanced; (ii) the network model reaches zero if the network is unbalanced. Further, to avoid the continuously verifying the triggering condition, a self-triggered algorithm is proposed for realizing the bipartite consensus of the network model. A numerical example is given to illustrate the effectiveness of the theoretical results.     

Leader-following consensus of multi-agent systems with connectivity-mixed attacks and actuator/sensor faults

This study investigates the leader-following consensus issue of multi-agent systems subject to simultaneous connectivity-mixed attacks, actuator/sensor faults and disturbances. Connectivity-mixed attacks are remodeled into connectivity-maintained and connectivity-paralyzed topologies in a switched version, and actuator/sensor faults are established with unified incipient-type and abrupt-type characteristics. Then, unknown input observer-based decoupling and estimation are incorporated to achieve unknown state and fault observations with the normalized technique, and the leader-following consensus-based compensation to faults, resilience to attacks and robustness to disturbances are also realized with the neighboring output information and sensor fault estimation through the distributed framework. Criteria of achieving exponential leader-following consensus of multi-agent systems under cyber-physical threats are derived with dual attack frequency and activation rate indicators. Simulation example is conducted to exemplify the validation and merits of the proposed leader-following consensus algorithm.     

Consensus for heterogeneous networked multi-agent systems with switching topology and time-varying delays

This paper investigates consensus problem for heterogeneous discrete linear time-invariant (LTI) multi-agent systems subjected to time-varying network communication delays and switching topology. A new two-stage consensus protocol is proposed based on stochastic, indecomposable and aperiodic (SIA) matrix and pseudo predictive scheme. With pseudo predictive scheme the network delay is compromised. Consensus analysis based on seminorm is provided. Results give conditions for such systems with periodic switching topology and time-varying delays to reach consensus. Highlights of the paper include: the protocol can be implemented in a distributed manner; the pseudo predictive approach requires less computation and communication; the verification of consensus convergence does not require the global information about the communication topology; the protocol allows delay to be time-varying, topology to dynamically and asymmetrically switch and system mode to be unstable. Numerical and practical examples demonstrate the effectiveness of the theoretical results.     

Adaptive tracking control for nonlinear heterogeneous multi-agent systems with unknown dynamics

This paper is concerned with the tracking control problem for nonlinear heterogeneous multi-agent systems with a static leader, where the leader’s state is only available to a small portion of follower agents. The considered multi-agent system is composed of first- and second-order follower agents with unknown nonlinearities and unknown disturbances, and the communication graph of follower agents is fixed and directed. A robust adaptive neural network controller is designed for each follower agent. By applying the Lyapunov theory with the singular value analysis method, it is shown that all follower agents will synchronize to the leader agent with bounded residual errors. A numerical example is presented to demonstrate the effectiveness of the theoretical findings.     

Leader-following consensus of multi-agent systems with limited data rate

This paper investigates the leader-following consensus problem of time-invariant linear multi-agent systems with limited data rate. Based on the idea of assigning a priority level for each agent of the concerned multi-agent system, a novel distributed control law has been proposed. The proposed control law has two distinctive advantages. That is, it is fully distributed in the sense that it does not rely on the eigenvalues of the Laplace matrix associated with the topology. Moreover, the required data rate is independent of the number of agents and remains small even if the number of the agents in multi-agent systems is large. An example is finally given to illustrate the effectiveness of the proposed controller.     

Event-triggered consensus of nonlinear multi-agent systems with stochastic switching topology

This paper is concerned with a leader-follower consensus problem for networked Lipschitz nonlinear multi-agent systems. An event-triggered consensus controller is developed with the consideration of discontinuous state feedback. To further enhance the robustness of the proposed controller, modeling uncertainty and switching topology are also considered in the stability analysis. Meanwhile, a time-delay equivalent approach is adopted to deal with the discrete-time control problem. Particularly, a sufficient condition for the stochastic stabilization of the networked multi-agent systems is proposed based on the Lyapunov functional method. Furthermore, an optimization algorithm is developed to derive the parameters of the controller. Finally, numerical simulation is conducted to demonstrate the effectiveness of the proposed control algorithm.     

Containment control of singular heterogeneous multi-agent systems

In this paper, we first consider the containment control problem of singular heterogeneous multi-agent systems, where all the followers converge to the convex hull spanned by the leaders. To solve this problem, we propose two distributed control laws: one is based on the state feedback control framework, which is suitable for the case that the full state information of each follower is accessible; and the other is based on the output regulation framework, where each follower only can access to its output. Furthermore, the distributed observers are designed for every follower to estimate the convex combination of the leader states which is determined by the communication graph. It should be noted that our results can also regard the non-singular multi-agent systems’ containment control problem as a special case. Finally, simulation results corroborate the effectiveness of our analytical results.     

Event-triggered group consensus for multi-agent systems subject to input saturation

This paper investigates group consensus for leaderless multi-agent systems with non-identical dynamics. The consensus protocol is put forward in the form of the distributed event-triggered control subject to saturation, which depends on information from neighboring agents at event-triggered instants. In order to exclude the Zeno behavior and save resources, the given event-triggered condition is detected only at discrete sampling times, where the sampling intervals can be variable. Based on the graph theory, Lyapunov–Krasovskii functional method and by adopting the free-weighting matrix technique, some sufficient group consensus criteria in terms of linear matrix inequalities are derived. Furthermore, optimization problems aiming at maximizing the event-triggered parameter and the consensus region are proposed. Finally, numerical simulations illustrate the effectiveness of the theoretical results.     

Robust multi-tracking of heterogeneous multi-agent systems with uncertain nonlinearities and disturbances

A robust multi-tracking problem is solved for heterogeneous multi-agent systems with uncertain nonlinearities and disturbances. The nonlinear function satisfies a Lipschitz condition with a time-varying gain, the integral of which is bounded by a linear function. A distributed impulsive protocol is proposed, where the position data and velocity data of desired trajectories are needed only at sampling instants. Based on the system decomposition technique, the error dynamic system of achieving multi-tracking is decomposed into two impulsive dynamic systems with vanishing perturbation and nonvanishing perturbation, respectively. Constructing a nominal model, then the multi-tracking problem is converted into the stability of impulsive dynamic system with nonvanishing perturbation under some conditions. It is proved that the proposed impulsive protocol is robust enough to solve the multi-tracking problem. Numerical examples are presented to illustrate the effectiveness of our theoretical results.     

Finite-time consensus for nonlinear multi-agent systems with time-varying delay: An auxiliary system approach

This paper investigates the finite-time consensus problem of uncertain nonlinear multi-agent systems with asymmetric time-varying delays and directed communication topology. An auxiliary system is firstly designed to deal with the continuous or discontinuous time-varying communication delays. Based on the finite-time input-to-output framework, a novel consensus scheme relying on local delayed information exchange is proposed. Moreover, by utilizing an auxiliary integrated regressor matrix and vector method, the system uncertainties can be accurately estimated. Then the consensus of multi-agent systems can be achieved within finite time by selecting the control gains simply. Finally, numerical simulations are provided to demonstrate the effectiveness of the proposed control algorithms.     

Reliable control for event-triggered singular Markov jump systems with partly unknown transition probabilities and actuator faults

In this paper, the problem of reliable controller design for event-triggered singular Markov jump systems with partly known transition probabilities, nonlinear perturbations and actuator faults is studied. To mitigate the burden of data transmissions over network, two event-triggered schemes with different triggering conditions are introduced. The switch law between the two event-triggered schemes is governed by a random variable with Bernoulli distribution. Taking nonlinear perturbations and actuator faults into account, the resulting closed-loop system is converted into a time-delay singular Markov jump system with partly known transition probabilities. Sufficient conditions of stochastically admissible for the resulting closed-loop system are obtained in terms of a group of linear matrix inequalities. The co-design of desirable reliable controller and weighting matrices of event-triggered schemes is presented. Finally, two numerical examples are given to show the effectiveness of the developed results.     

Quantized consensus in second-order multi-agent systems via event-trigger control with sampled data

This paper addresses the quantized consensus problem of second-order multi-agent systems (MASs) where the topology has a directed spanning tree. An event-trigger control protocol (ETCP) is proposed by designing a combined threshold. The combined threshold not only reduces more event triggers than the state-dependent threshold, but also is more practical than the time-dependent threshold. For further reducing computation resources and transmission cost, the sampled data, self-trigger scheme and data quantization are employed together. Under the proposed ETCP, the sufficient condition is derived to guarantee the quantized consensus of second-order MASs. Finally, the comparison experiments are conducted to demonstrate the superiority of ETCP based on the combined threshold.     

Adaptive fault-tolerant control for a class of nonlinear multi-agent systems with actuator faults

This paper considers the distributed adaptive fault-tolerant control problem for linear multi-agent systems with matched unknown nonlinear functions and actuator bias faults. By using fuzzy logic systems to approximate the unknown nonlinear function and constructing a local observer to estimate the states, an effective distributed adaptive fault-tolerant controller is developed. Furthermore, different from the traditional method to estimate the weight matrix, only the weight vector needs to be estimated by exchanging the order of weight vectors and fuzzy basis functions in the fuzzy logic systems. In contrast to the existing results, the assumption that the dimensions of input vector and output vector are equal is removed. In addition, it is proved that the proposed control protocol guarantees all signals in the closed-loop systems are bounded and all agents converge to the leader with bounded residual errors. Finally, simulation examples are given to illustrate the effectiveness of the proposed method.     

Distributed impulsive control for heterogeneous multi-agent systems based on event-triggered scheme

In this paper, the distributed impulsive control for heterogeneous multi-agent systems based on event-triggered approach is investigated. According to whether the information transfer of the dynamic compensator is continuous or not, two different kinds of impulsive controllers are designed, respectively. Based on these two kinds of controllers, the corresponding distributed event-triggered conditions are provided, which make the impulsive instants of all agents do not need occur simultaneously. Moreover, the lower bound of impulsive intervals can also be guaranteed for all the event-triggered conditions, which means that the control schemes given in this paper can avoid the Zeno-behavior successfully. Eventually, a simulation example is proposed to support the effectiveness of the results obtained in this paper.     

Event-based dynamic output-feedback controller design for networked control systems with sensor and actuator saturations

This paper is concerned with the problem of event-triggered dynamic output-feedback H_∞ control for networked control system with sensor and actuator saturations. The event-triggered scheme combined with sensor saturation is first introduced to judge whether the newly sampled signal should be transmitted to the dynamic output-feedback controller or not. Under this scheme, the concurrent closed-loop system is first modeled as a control system with an interval time-varying delay and nonlinear items. Through constructing the Lyapunov–Krasovskii functional and employing linear matrix inequality approach, sufficient conditions for H_∞ asymptotical stability are derived for the networked control system; furthermore, under the above stability condition, a dynamic output-feedback controller and the corresponding event-triggered parameters are co-designed through linear matrix inequality approach. Lastly, a numerical example is employed to prove the practical utility of this method.