Class Of Nonlinear Multi-agent Systems Research Articles

Event‐triggered leader‐following consensus for a class of nonlinear multiagent systems with time‐varying delay

AbstractThis article studies the consensus problem for discrete‐time nonlinear multiagent systems with time delay. Based on an asynchronous event‐triggered mechanism where local information of a communication graph is involved, a distributed consensus protocol is proposed to reduce the network communication congestion for achieving state consensus for multiagent systems with nonlinear perturbations. To avoid complications involving data fusion, this distributed consensus protocol allows every agent to broadcast its state at its own triggering condition instead of using continuous updates and without continuous monitoring of the triggering condition. To save the energy consumption involved in a consensus protocol, the proposed event‐triggering guaranteed cost is investigated in this article for multiagent systems. We select an agent as a leader that is constrained by its neighbors and controlled by the proposed protocol as other agents. It has been theoretically demonstrated that the consensus problem of multiagent systems with nonlinear perturbation and time delays can be achieved if the control gains and the triggering parameters are appropriately selected. Sufficient conditions are given to guarantee that the agents achieve consensus. Moreover, the gain matrix and triggering parameters of the proposed protocol are cast into matrix inequalities conditions. A simulation example is given to illustrate the effectiveness of the theoretical results.

Adaptive consensus control for a class of nonlinear multi-agent systems with unknown time delays and external disturbances

This paper investigates a class of unknown nonlinear multi-agent systems with unknown time delays and external disturbances. The external disturbance considered in this paper is completely unknown, and the accurate mathematical expression cannot be obtained. To eliminate the external disturbance, a disturbance observer is constructed by the Disturbance-Observer-Based-Control (DOBC) method. By utilizing Young’s inequality scaling technique, the problem of time delay is solved. By assuming that the communication graph among the agents is directed and connected, a novel distributed adaptive consensus control protocol is established based on the relative output information to achieve the goal of consensus control. Furthermore, the stability of the multi-agent system is analyzed by selecting an appropriate Lyapunov function; it is certified that with the proposed control protocol, all signals are guaranteed to be globally uniformly bounded, and the considered multi-agent systems can reach consensus even in the presence of time delay and external disturbance. Finally, two simulation examples are given to support the proposed control strategy.

Observer-based event-triggered adaptive containment control for multiagent systems with prescribed performance

This paper focuses on the problem of the event-triggered adaptive containment control for a class of nonlinear multiagent systems (MASs) with prescribed performance and immeasurable states. First, the radial basis function neural networks (RBFNNs) are adopted to approximate the uncertain smooth nonlinear function, and the neural network-based state observer is designed to estimate the unmeasurable state. Besides, to reduce the control resource consumption and get a better balance between the system performance and network constraints, the switching threshold-based event-triggered control strategy is introduced. Based on this, the novel distributed containment controller is designed by utilizing the adaptive backstepping technique and the dynamic surface control (DSC) technique to guarantee that the output of each follower converges to the convex hull formed by multileader. Moreover, the containment errors can be converged to the prescribed boundary and all signals in closed-loop system are semi-global uniformly ultimately bounded (SGUUB) as well. Finally, the simulation examples are carried out to illustrate the efficiency of the proposed controller.

Sampled-based bipartite tracking consensus of nonlinear multiagents subject to input saturation

This paper is concerned with the sampled-data bipartite tracking consensus problem for a class of nonlinear multiagent systems (MASs) with input saturation. Both competitive and cooperative interactions coexist among agents in the concerned network. By resorting to Lyapunov stable theory and linear matrix inequality (LMI) technique, several criteria are obtained to ensure that the considered MASs can achieve the bipartite tracking consensus. Besides, with the help of the decoupled method, the dimensions of LMIs are reduced for mitigation of the computation complexity so that the obtained results can be applied to large-scaled MASs. Furthermore, the controller gain matrix is explicitly expressed in terms of solutions to a set of LMIs. We also provide with an estimate of elliptical attraction domain of bipartite tracking consensus. Finally, numerical simulation is exploited to support our theoretical analysis.

Dynamic event-based finite-horizon [formula omitted] secure consensus control of a class of nonlinear multi-agent systems

In this paper, we investigate the H∞ consensus control issue for nonlinear multi-agent systems (MASs) subject to multiple attacks over a finite time interval. A novel and comprehensive model to characterize the multiple attacks is presented that includes denial-of-service (DoS) attacks, scaling attacks and replay attacks. With the hope of easing the communication burdens, we implement a dynamic event-triggered scheme to schedule the process of data sharing among the individual subsystems, which helps judge if the collected data should be shared to neighboring agents for control input update. The aim of the proposed problem is to develop an output feedback strategy to meet the desired H∞ consensus performance despite the existence of multiple attacks. Some conditions are presented for the solvability of the investigated problem, and the feedback gains are obtained via certain convex optimization algorithms. The proposed theoretical result is finally demonstrated by virtue of two illustrative simulation examples.

Output-feedback distributed consensus for nonlinear multi-agent systems with quantization

In this paper, we investigate the distributed consensus problem for a class of nonlinear multi-agent systems. Firstly, the uniform quantizer with scaling function is considered in the communication channels to reduce the communication burden. Secondly, noting that the state’ information of each agent cannot be directly obtained, we design a suitable observer to rebuild the states of the nonlinear systems with the help of dynamic gain function. Since the information of communication quantization and state observation is coupled to each other, it is necessary to jointly design uniform quantizer with scaling function and the observer. Based on this, a distributed control protocol is proposed, which leads to a distributed asymptotic consensus of overall nonlinear systems with either known or unknown Lipschitz constant through ⌈log2(2R)⌉-bit information exchange between each pair of agents. Finally, to validity the feasibility of the control scheme, a simulation example is provided.

Consensus for clusters of agents with cooperative and antagonistic relationships

In this paper we address the consensus problem in the context of networked agents whose communication graph splits into clusters: interactions between agents in the same cluster are cooperative, while interactions between agents belonging to different clusters are antagonistic. This problem set-up arises in the context of social networks and opinion dynamics, where reaching a consensus means that the opinions of the agents in the same cluster converge to the same decision, that is typically different for the different clusters. Under the assumption that agents belonging to the same cluster have the same amount of trust (/distrust) to be distributed among their cooperators (/adversaries), we propose a modified version of DeGroot’s law. By simply constraining how much agents in each group should be conservative about their own opinions, it is possible to achieve a nontrivial solution by means of a distributed algorithm. The result is then particularized to unweighted complete communication graphs, and subsequently extended to a class of nonlinear multi-agent systems.

Event-triggered surrounding adaptive control of nonlinear multi-agent systems

This paper investigates an event-triggered control method for a class of nonlinear multi-agent systems, in which a group of followers surround a group of leaders. Dynamics of leaders and followers are assumed to be heterogeneous and to have unknown parameters. To deal with this problem, some adaptive laws and also controllers including event-triggered estimator of leaders’ geometric center are proposed. In order to reduce some dispensable data exchange among the follower agents and save the limited communication resources, event-triggered control protocols are used to attain better performance of resources. The proposed control scheme guarantees that all the closed loop signals are globally bounded and surrounding error converges toward a compact set, exponentially. Moreover, Zeno behavior is also excluded under certain conditions. Eventually, numerical simulations are provided to verify theoretical results and demonstrate that the triggering laws cause decrement of the number of controller updates and inter-agent communications.

Fuzzy fault-tolerant containment control for multi-agent systems with unknown nonlinear dynamics

This paper studies the containment control problem for a class of nonlinear multi-agent systems (MASs) with actuator faults (AFs) and external disturbance under switching communication topologies. To address this problem, a new fuzzy fault-tolerant containment control method is developed via utilizing adaptive mechanisms. Furthermore, a sufficient condition is obtained to guarantee the stability of the considered closed-loop system by the dwell time technique combined with Lyapunov stability theory. Unlike the traditional method to estimate the weight matrix, the fuzzy logic system is used to estimate the norm of weight vectors. Thus, the difficulty that the unknown nonlinear function cannot be compensated for when the actuator produces outage or stuck fault is solved. Compared with the existing controllers for nonlinear MASs, the proposed controller is more suitable for the considered problem under the influence of AFs that are detrimental to the operation of each agent system. Besides which, the closed-loop system is proven to be stable by using the developed controller, and all followers converge asymptotically to the convex hull formed by the leaders. Finally, an example based on a reduced-order aircraft model is presented to verify the effectiveness of the designed control scheme.

Fault-Tolerant Fuzzy Formation Control for a Class of Nonlinear Multiagent Systems Under Directed and Switching Topology

The fault-tolerant formation control problem of a class of nonlinear multiagent systems with actuator/sensor faults under directed and switching network topology is addressed in this article. The main contributions are as follows: 1) the developed controller is effective to compensate for actuator/sensor faults and unknown nonlinearity simultaneously and 2) in contrast to the existing fault-tolerant formation control results, the more general directed and switching network topology is considered. In particular, by using a fuzzy logic system to approximate unknown nonlinearity and by introducing fault estimators to estimate actuator/sensor faults, a novel distributed fuzzy formation controller is developed. By virtue of introducing a modification technique in adaptive law, the phenomenon of strictly increase in adaptive law caused by actuator/sensor faults and unknown nonlinearity can be avoided. In addition, the uniformly ultimately bounded of the formation errors can be shown by introducing a novel Lyapunov function and a new analysis method. The efficiency of the developed method can be shown by an illustrative example demonstrates.

Distributed control for output-constrained nonlinear multi-agent systems with completely unknown non-identical control directions

This paper studies the consensus problem for a class of nonlinear multi-agent systems with asymmetric time-varying output constraints and completely unknown non-identical control directions. Firstly, in order to deal with the problem of asymmetric time-varying output constraints, the original output-constrained multi-agent systems are transformed into new unconstrained multi-agent systems by constructing the state transformation for each agent. Secondly, the emergence of multiple Nussbaum-type function terms is avoided by introducing novel sliding-mode-esque auxiliary variables and consensus estimate variables, which allows the control directions to be completely unknown non-identical. Thirdly, a novel control strategy is proposed by combining novel variables with state transformation method for the first time, which makes the design of distributed consensus protocol more concise. Through Lyapunov stability analysis, the proposed distributed protocol ensures that the output constraints are never violated and the consensus can be achieved asymptotically. Finally, a practical simulation example is given to demonstrate the effectiveness of the proposed distributed consensus protocol.

On designing a distributed event‐triggered output feedback consensus protocol for nonlinear multiagent systems

AbstractIn this article, the leader–follower consensus problem is considered for a class of nonlinear multiagent systems with event‐triggered inputs. A novel time‐varying gain compensator is designed for each follower by only utilizing the output information of the follower and its neighbors. Based on a time‐varying threshold strategy and a directed communication topology, a distributed event‐triggered output feedback controller is designed for each follower. It is proved by the Lyapunov theory that the leader–follower consensus of the multiagent systems is achieved and the Zeno‐behavior is avoided. Compared with the existing results, it is the first time that a time‐varying gain control algorithm is proposed for the multiagent systems subject to event‐triggered inputs. The effectiveness of the proposed consensus protocol is validated by the chemical reactor systems.

State consensus cooperative control for a class of nonlinear multi-agent systems with output constraints via ADP approach

A state consensus cooperative adaptive dynamic programming (ADP) control strategy is proposed for a nonlinear multi-agent system (MAS) with output constraints. On the basis of the transformation function, state models of leader and followers are transformed into affine ones. By using a monotonically increasing mapping function, the state-consensus cooperative control problem for an MAS with output constraints is equivalently transformed into a cooperative approximately optimal control one for an affine MAS. Then, a neural network observer is constructed for estimation of inner states, and, by graph theory and ADP method, the state consensus cooperative ADP control strategy is developed. The proposed strategy guarantees the performance index of the transformed system is approximately optimal. Furthermore, the stability analysis of whole closed-loop system is presented. Through the Lyapunov Theorem, we prove that the states of the MAS achieve consensus and the output signals of the followers satisfy the constraints. Also, all signals of the closed-loop MAS are bounded, and the trajectory of the leader node is cooperative bounded. The theoretical analysis and effectiveness of the strategy are verified by both a physical and a numerical example.

Consensus control for nonlinear multi-agent systems with event-triggered communications

This paper investigates the consensus problems for a class of nonlinear multi-agent systems (MASs) by distributed event-based control protocols. Firstly, we design the static distributed event-triggered control protocols to achieve leader-follower and leaderless consensus problems, respectively, and the systems exclude Zeno behavior under the proposed control schemes. In order to avoid utilizing the global information of the system networks, that is, the minimum eigenvalues of the correlation matrices. Then, the fully distributed event-based control schemes are designed by introducing the time-varying coupling weights to achieve the leader-follower and leaderless consensus problems, respectively. It has been shown that the Zeno behavior is ruled out in the MASs under the fully distributed event-based control protocols. All static and dynamic event-based control schemes are able to be constructed based on the solvability of linear matrix inequalities (LMIs). Finally, the rationality of the theoretical results is illustrated by the example.

Mean Square Consensus of Nonlinear Multi-Agent Systems under Markovian Impulsive Attacks

This paper focuses primarily on the mean square consensus problem of a class of nonlinear multi-agent systems suffering from stochastic impulsive deception attacks. The attacks here are modeled by completely stochastic destabilizing impulses, where their gains and instants satisfy all distributions and the Markovian process. Compared with existing methods, which assume that only gains are stochastic, it is difficult to deal with systems with different types of random variables. Thus, estimating the influence of these different types on the consensus problem is a key point of this paper. Based on the properties of stochastic processes, some sufficient conditions to solve the consensus problem are derived and some special cases are considered. Finally, a numerical example is given to illustrate the main results. Our results show that the consensus can be obtained if impulsive attacks do not occur too frequently, and it can promote system stability if the gains are below the defined threshold.

Neural-Network Based Adaptive Self-Triggered Consensus of Nonlinear Multi-Agent Systems With Sensor Saturation

This paper aims to propose a self-triggered consensus control scheme for a class of nonlinear multi-agent systems with sensor saturation. Because of the existence of unknown nonlinear dynamics, this study borrows the approximation capability of neural networks to design the consensus control protocol. This paper adopts neural network to approximate the ideal controller, instead of using the combination of neural network and adaptive method to approximate the unknown system dynamics. Thus, the extended approximation property of neural network for event-based sampling can be beneficially introduced. Moreover, the designed controller only updates at discrete time, which enables that the system can be modeled as a hybrid system with impulsive dynamics. Thus, the stability theory of impulsive systems can be used to analyze the convergence of the system. It should be noted that this is the first time to propose an effective event-triggered consensus control algorithm based on neural network. Furthermore, this paper also considers a frequently encountered phenomenon of sensor saturation. The convex hull method is adopted to deal with sensor saturation problem, instead of the widely used sector condition method. Finally, the performance of the proposed neural-network based self-triggered consensus control algorithm is demonstrated by the numerical examples.

Distributed robust fault-tolerant consensus control for a class of nonlinear multi-agent systems with intermittent communications

This paper considers the H∞ consensus problem for a class of nonlinear multi-agent systems in the presence of multiple faults, including intermittent communications and actuator faults, under the switching communication topologies. Aiming at this problem, a new distributed robust fault-tolerant controller is designed by utilizing an adaptive mechanism to remove the interference of nonlinear functions and multiple faults. Furthermore, the closed-loop system is proven to be stable by applying the topology-based average dwell time technique and the Lyapunov stability theory. Compared with existing controllers for nonlinear multi-agent systems, the developed scheme is efficient for solving the fault-tolerant H∞ consensus problem of nonlinear multi-agent systems even under the influence of intermittent communications, actuator faults, and switching communication topologies. Finally, an example based on the B747-100/200 aircraft model is given to validate the proposed control scheme’s effectiveness.

Adaptive cooperative dynamic surface control of non-strict feedback multi-agent systems with input dead-zones and actuator failures

This paper discusses the consensus tracking problem for a class of nonlinear multi-agent systems (MASs) with output constraints, unmodeled dynamics, nonsymmetric input dead-zones and actuator failures under directed graphs, and proposes an adaptive cooperative neural dynamic surface control (DSC) strategy. Using the properties of invertible nonlinear mapping and Gaussian function, output constraints and non-strict feedback terms are separately dealt with. A measurable dynamic signal produced by an auxiliary first-order system is used to eliminate the influence of unmodeled dynamics on the system. Two input models of input dead-zone and actuator failure are linearized, each follower control signal is constructed via DSC. All the signals of the closed-loop system are proved to be cooperative semi-globally uniformly ultimately bounded, and all the followers can accomplish a desired consensus results. Finally, the simulation results are provided to illustrate the availability of the presented adaptive control approach.

Fixed-time time-varying formation tracking for nonlinear multi-agent systems under event-triggered mechanism

This study focuses on the fixed-time event-triggered time-varying formation tracking issue for a class of nonlinear multi-agent systems with multi-dimensional dynamics, uncertain disturbances and non-zero control input of leader. Firstly, a distributed fixed-time event-triggered control scheme is proposed such that the time-varying formation tracking can be achieved with intermittent controller updates and intermittent communication. To reduce the chattering phenomenon, a novel control protocol with saturation function is designed. It should be noted that continuous triggering condition monitoring is needed in the triggering mechanism. To address above issue, a novel triggering mechanism is further proposed. Moreover, the fixed-time event-triggered time-varying formation containment with multiple leaders is considered. It is verified that the Zeno behavior can be excluded. Finally, two examples are presented to demonstrate the feasibility of the main theoretical findings.

Neural Network Observer Based Consensus Control of Unknown Nonlinear Multi-agent Systems with Prescribed Performance and Input Quantization

This paper investigates the consensus tracking problem with predefined performances requirements for a class of unknown nonlinear multi-agent systems with hysteresis quantizer and external disturbances under a directed graph topology. Neural network observers are designed to estimate unmeasurable states and the the consensus tracking problem with performance requirements is transformed to a stabilization problem by prescribed performance error transformation schemes. The novel consensus protocol can be applied to a more general class of nonlinear multi-agent systems since the Lipschitz condition is avoided and state information is not required. It is strictly proved that all signals in the closed-loop systems are cooperatively uniformly ultimately bounded and both the transient and steady performances of the consensus tracking satisfy prescribed performance requirements. Finally, two numerical examples are presented to validate the effectiveness of the proposed strategy.