Leader-following Consensus Problem Research Articles

A new control method for leader-follower consensus problem of uncertain constrained nonlinear multi-agent systems

A new control method for leader-follower consensus problem of uncertain constrained nonlinear multi-agent systems

Consensus for nonlinear multi-agent systems with actuator saturation by adaptive event-triggered scheme

This paper studies the leader-follower consensus problem for nonlinear multi-agent systems with actuator saturation by adaptive event-triggered scheme. This adaptive mechanism allows parameters in triggereded mechanism to change automatically compared to fixed ones in traditional strategies. The paper introduces two distinct approaches to address the issue of saturation. The first approach is sector bounded condition, while the second relies on convex hull representation. Compared with the former one, the latter one can reduce the conservatism of controller design effectively. Furthermore, it is assumed that the nonlinear function adheres to incremental quadratic limitations, thereby offering a more comprehensive depiction of its nonlinear properties. Finally, the validity of the proposed approaches is demonstrated by one numerical example in the background of mechanical systems.

Stubborn Observer for Leader-Following Consensus of Nonlinear Multiagent Systems With Application to Spacecraft.

In this article, the leader-following consensus problem is investigated for a class of nonlinear multiagent systems with transmission outliers. First, through the relative output information and observer states of neighbor agents, a distributed stubborn reduced-order observer is proposed to estimate the leader-following consensus error which is affected by abnormal and isolated transmission outliers. Moreover, considering that the leader agent in practice is a controllable plant, another distributed stubborn reduced-order observer is designed by using the relative information and inputs of neighbor agents. Sufficient conditions are established in terms of the Laplacian matrix such that two stubborn reduced-order observers are convergent and the studied nonlinear multiagent system could achieve leader-following consensus with directed topology. Finally, an example of the multispacecraft system is provided to illustrate the effectiveness of the proposed methodology.

Output Feedback-Based Consensus for Nonlinear Multiagent Systems: The Event-Triggered Communication Strategy.

The current investigation explores the leader-following consensus problem for nonlinear multiagent systems under the output feedback control mechanism and the event-triggered communication mechanism. Owing to the physical instrument constraints, a significant portion of the state variables is not readily available. Therefore, this article put forward a distributed event-based leader-following consensus protocol only using agents' relative output measurements and underlying neighbors. Furthermore, this article develops two event-triggered mechanisms simultaneously, one is the event-triggered communication mechanism in the sensor-to-controller channel, and another is the event-triggered controller update in the controller-to-actuator track. Besides that, it is proven that the developed event-triggered control protocol can settle the leader-following consensus problem of the nonlinear multiagent systems, and the Zeno behavior is excluded in both the channels. Finally, we perform two simulation examples to illustrate the efficacy of the obtained results.

Distributed Leader-Following Consensus of Feedforward Nonlinear Delayed Multiagent Systems via General Switched Compensation Control.

This work examines the distributed leader-following consensus problem of feedforward nonlinear delayed multiagent systems involving directed switching topologies. In contrast to the existing studies, we focus on time delays acting on the outputs of feedforward nonlinear systems, and we permit that the partial topology dissatisfy the directed spanning tree condition. In the cases, we present a novel output feedback-based general switched cascade compensation control method that addresses the above-mentioned problem. First, we put forward a distributed switched cascade compensator by introducing multiple equations, and we design the delay-dependent distributed output feedback controller with the compensator. Subsequently, when the control parameters-dependent linear matrix inequality is met and the switching signal of the topologies obeys a general switching law, we prove that the established controller can render that the follower's state asymptotically tracks the leader's state by employing an appropriate Lyapunov-Krasovskii functional. The given algorithm allows output delays to be arbitrarily large and increases the switching frequency of the topologies. A numerical simulation is presented to demonstrate the practicability of our proposed strategy.

Distributed Event-Triggered Quantized Fault-Tolerant Control of Linear Multiagent Systems With External Disturbances and Parameter Uncertainties.

In this article, the issue of fault-tolerant leader-following consensus under a distributed dynamic event-triggered mechanism is addressed for linear multiagent systems (MASs) in the presence of unknown parameter uncertainties, external disturbances, and actuator faults, including loss of effectiveness and bias, in which the mechanism is with quantized state measurements. Due to the fact that information is transmitted via a bandwidth-limited communication network, a quantized control scheme with a uniform quantizer is introduced for leader-following consensus. In order to decrease the communication load and save the limited communication network resources, a distributed event-triggered mechanism is studied for leader-following consensus problem of linear MASs with quantized state measurements. In the presence of actuator faults, external disturbances, and unknown parameter uncertainties, an adaptive coupling gain for the controller is presented. Based on the Lyapunov function approach, the stability of the closed-loop system and the convergence of consensus errors are proved. Furthermore, the Zeno behavior is excluded for the triggering time sequences. Finally, simulation studies are given to verify the effectiveness of the proposed event-triggered fault-tolerant control scheme.

Fuzzy control of singular fractional order multi-agent systems with actuator saturation

In this paper, a T-S fuzzy model is established to describe nonlinear fuzzy singular fractional order multi-agent systems (SFOMASs) exhibiting actuator saturation when the order is between 0 and 2. We focus on the case where the system state is difficult to measure or cannot be directly measured, so it needs to be estimated based on other measurable signals. To this end, a fuzzy observer is designed, which can process fuzzy or imprecise input and output signals through fuzzy processing. Then the observer-based leader-following consensus problem of fuzzy SFOMASs with actuator saturation is addressed. To address input saturation, we use some mathematical tools to represent the saturated linear feedback on the convex hull, which is then transformed into seeking the optimal solution of linear matrix inequalities (LMIs). Finally, the effectiveness of the proposed approach is verified through the adoption of a numerical example.

Guaranteed-performance consensus control for multi-agent systems with external disturbances via event-triggered strategy

In this paper, we investigate the leader-following guaranteed performance consensus problem for multi-agent systems(MASs) controlled by event-triggered under external disturbances. First, a disturbance observer is designed for each follower, which can be used to efficiently estimate external disturbances. Second, to reduce the waste of communication resources, a new distributed event-triggered strategy based on the state estimation of neighboring agents is presented, which does not need continuous communication among agents. And the growing estimation error is reset by communication updates. The analysis illustrates that Zeno behavior can be effectively averted by formulating a lower bound on the number of normals for the minimum inter-event interval. Also, based on the above proposed state feedback consensus protocol with guaranteed performance, sufficient conditions are derived to guarantee that a MASs can achieve leader-following consensus. In addition, the consensus criterion with guaranteed performance is put forward in the form of a linear matrix inequality. The cost of guaranteed performance with leader-following structural properties is also established. At last, an example of numerical simulation is presented to confirm the derived analytical solution.

Hybrid protocols for leader–follower consensus of multi-agent systems with distributed delays

The primary focus of this paper is to investigate the leader–follower consensus problem of multi-agent systems (MASs) with discrete and distributed delays in complex domains. We propose a new hybrid consensus protocol that incorporates a continuous-time protocol based on the communication topology of follower agents, along with an event-triggered pinning impulsive control (ETPIC) protocol. Using the Lyapunov functional method in complex domains, we establish delay-dependent sufficient conditions for leader–follower consensus of delayed complex-valued MASs. Our results demonstrate that the proposed hybrid protocol can ensure leader–follower consensus even when the size of discrete and distributed delays exceeds the length of intervals between two consecutive triggering instants. Furthermore, we prove that the Zeno phenomenon can be excluded under the proposed control protocol. In particular, as a special case, we derive the leader–follower consensus result for delay-free complex-valued MASs based on a reduced hybrid control protocol. Two numerical examples are presented to validate the effectiveness of the proposed control scheme.

Resilient dynamic output feedback control for leader-following consensus of high-order uncertain multi-agent systems under sensor–actuator attacks

This paper investigates the resilient leader-following consensus problem for a class of high-order multi-agent systems subject to unmatched lower triangular uncertainty dynamics and sensor–actuator attacks. Compared with previous work, the sensor and actuator attacks are modeled to be both time-varying and state-dependent, which makes the resilient consensus control more challenging. To deal with the unmatched uncertainties and sensor–actuator attacks, a new compensator with two online tuned dynamic gains is proposed relying only on the relative output measurements of neighboring agents. Then, using only the local compensation information, a fully distributed output feedback resilient protocol is designed to guarantee the leader-following consensus. Sufficient conditions in terms of matrix inequalities are derived to determine control gains and compensator parameters and simulation studies are presented to demonstrate the proposed theoretical results.

Adaptive Dynamic Event-Triggered Distributed Output Observer for Leader-Follower Multiagent Systems Under Directed Graphs.

Leader-follower consensus problem for multiagent systems (MASs) is an important research hotspot. However, the existing methods take the leader system matrix as a priori knowledge for each agent to design the controller and use the leader's state information. In fact, only the output information may be available in some practical applications. On this basis, this article first designs a novel adaptive distributed dynamic event-triggered observer for each follower to learn the minimum polynomial coefficients of the leader system matrix instead of the leader system matrix. The proposed method is scalable and suitable for large-scale MASs and can reduce the information transmission dimension in observer design. Then, an adaptive dynamic event-triggered compensator based on the observer and leader output information is designed for each follower, thereby solving the leader-follower consensus problem. Finally, several simulation examples are given to verify the effectiveness of the proposed scheme.

Distributed Estimator-Based Event-Triggered Neuro-Adaptive Control for Leader-Follower Consensus of Strict-Feedback Nonlinear Multiagent Systems.

This article investigates the leader-follower consensus problem for strict-feedback nonlinear multiagent systems under a dual-terminal event-triggered mechanism. Compared with the existing event-triggered recursive consensus control design, the primary contribution of this article is the development of a distributed estimator-based event-triggered neuro-adaptive consensus control methodology. In particular, by introducing a dynamic event-triggered communication mechanism without continuous monitoring neighbors' information, a novel distributed event-triggered estimator in chain form is constructed to provide the leader's information to the followers. Subsequently, the distributed estimator is utilized to consensus control via backstepping design. To further decrease information transmission, a neuro-adaptive control and an event-triggered mechanism setting on the control channel are codesigned via the function approximate approach. A theoretical analysis shows that all the closed-loop signals are bounded under the developed control methodology, and the estimation of the tracking error asymptotically converges to zero, i.e., the leader-follower consensus is guaranteed. Finally, simulation studies and comparisons are conducted to verify the effectiveness of the proposed control method.

Sampled-Data-Based Distributed Output Feedback Leader–Following Consensus for Time-Delay Multiagent Systems

This paper addresses the distributed output feedback leader-following consensus problem for high-order nonlinear multiagent systems (MASs) with time delays and disturbances under the directed network. Using sampled relative outputs to neighbors and the discrete control input, the continuous-discrete time compensator is constructed in each agent to compensate for the consensus errors, where the sampling time instants can be asynchronous and aperiodic without exceeding an explicit upper bound of sampling intervals. Based on the compensator, we propose a co-design algorithm for constructing the dynamic event-triggered protocol with a corresponding event-triggering mechanism which is a combination of discrete-time control input, continuous dynamic variables of each agent's own compensator, and a given threshold. The proposed methods can not only achieve consensus tracking under the effects of time delays in states and communications but also implement the discrete-time execution of measurement, communication, and control. Based on the novel lemmas, it is proved that the resulting closed-loop consensus error system is globally stable. Finally, a simulation is given to illustrate the effectiveness of proposed methods.

Output Reachable Set-Based Leader-Following Consensus of Positive Agents Over Switching Networks.

This work addresses the output reachable set-based leader-following consensus problem, focusing on a group of positive agents over directed dwell-time switching networks. Two types of non-negative disturbances, namely, 1) L1 -norm bounded disturbances and 2) L∞,1 -norm bounded disturbances are studied. Meanwhile, a class of directed dwell-time switching networks for modeling the communication protocol of positive agents is investigated. To deal with the presence of disturbances, an output-feedback control protocol is developed to achieve a robust consensus with positivity preserved based on the output reachable set. By exploiting the positive characteristics, switched linear copositive Lyapunov functions are adopted to establish output reachable set-based consensus conditions. These conditions can facilitate the control protocol design by solving a bilinear programming problem, and also generate hyperpyramidal regions to confine the output consensus error. A particle swarm optimization-based (PSO-based) algorithm is applied to compute the controller gains and optimize the volume of the hyperpyramids. The proposed methods are verified by the presented numerical case studies.

Observer-Based Distributed Adaptive Consensus Tracking of Nonlinear Multi-agent Systems on Directed Graphs

This paper studies the leader-following consensus problem of nonlinear multi-agent systems (MAS) with one-sided Lipschitz conditions under the directed graph, and a novel observer-based distributed tracking protocol that only utilizes the relative output information of adjacent agents is proposed. To avoid the disadvantage of solving Laplace matrix eigenvalues, a fully distributed adaptive consensus scheme is constructed. The sufficient conditions for linear matrix inequalities (LMIs) for the consensus of MAS systems are derived using the Lyapunov function and the properties of one-sided Lipschitz nonlinear systems. Finally, the effectiveness of the proposed control method can be verified by two examples-based simulations with a leader and five followers.

Distributed Observer-Based Leader-Follower Consensus of Multiple Euler-Lagrange Systems.

This article investigates the leader-follower consensus problem of multiple Euler-Lagrange (EL) systems, where each agent suffers uncertain external disturbances, and the communication links among agents experience faults. Besides, we consider a more general case that only a portion of followers can measure partial components of leader's output and access the dynamic information of leader. The main idea of solving the consensus problem in this article is proceeded in two steps. First, we design an adaptive distributed observer to estimate the full state information of leader in real time with resilience to communication link faults. Second, based on the proposed distributed observer, we propose a proportional-integral (PI) control protocol for each agent to track the trajectory of leader, which is model-independent and robust to uncertain external disturbances. Distinct from the existing leader-follower consensus protocols of multiple EL systems, the proposed distributed observer-based PI consensus protocol in this article is model-independent, which is irrelevant to the structures or features of EL system model. Finally, we present a simulation example to show the resilience of the above adaptive distributed observer and the robustness of the distributed observer-based consensus protocol.

Distributed Dynamic Event-Triggered Leader-Following Consensus for Nonlinear Multiagent Systems Over Fading Channel.

This article investigates the leader-following consensus problem of discrete-time nonlinear multiagent systems (MASs) over fading channels. With the consideration of the transmission among followers maybe affected by the fading networks, the nonidentical fading channels model is constructed. To reduce the transmission network burden, the dynamical event-triggered mechanism (DETM) is developed. Different from most of existing event-triggered strategies, the threshold parameter in the developed dynamical event-triggering condition is dynamically adjusted according to a dynamic rule. Based on the DETM, a distributed consensus control protocol is designed under fading channels. Then, sufficient criteria are provided to ensure that MASs can achieve the leaser-following consensus, and satisfy the H∞ performance index in the presence of fading channels. The desired controller parameters can be derived in terms of solutions of matrix inequalities that are lightly solvable. In the end, simulation results show that the designed dynamical event transmission policy is capable of diminishing communication burden more promptly and effectively than some existing ones.

Leader-Following Consensus of Multiple Uncertain Euler-Lagrange Systems via Fully Distributed Event-Triggered Adaptive Fuzzy Control.

This article deals with the leader-following consensus problem of multiple uncertain Euler-Lagrange systems with unknown nonlinear dynamics. By introducing a dynamic compensator for each agent, a fully distributed control strategy is developed based on the fuzzy approximation approach, which is independent of any priori global information associated with the communication topology. Meanwhile, a distributed event-triggering mechanism (ETM) is designed such that each agent broadcasts its states only when an event occurs. It is shown that with the proposed ETM, the leader-following consensus is achieved with aperiodic intermittent communication and Zeno behavior is excluded by contradiction. Moreover, the consensus tracking errors converge to small sets around the origin. Finally, an example is provided to illustrate the effectiveness of the obtained theoretical results.

Adaptive output feedback event-triggered consensus control for networked reaction-diffusion PDE systems

This paper explores the adaptive output feedback event-triggered consensus control of a network of parabolic systems modelled by partial differential equations (PDEs). An infinite-dimensional state observer is established to estimate the state based on the relative output information. On the basis of the adaptive state observer, two novel distributed event-triggered controllers are proposed to address the leaderless consensus and leader-follower consensus problem. Based on the Lyapunov method and PDE theory, it is shown that the asymptotic consensus control can be achieved. Compared to the related works, a distinctive feature of the designed event-triggered consensus protocols is fully distributed which does not demand any global information of the graph. In addition, the absence of Zeno behaviour is demonstrated. Lastly, the obtained results are demonstrated using two simulations.

Observer-Based Adaptive Consensus Protocol Design for Multi-Agent Systems with One-Sided Lipschitz Nonlinearity

This paper considers the observer-based leader–follower consensus problem of multi-agent systems with one-sided Lipschitz conditions and quadratic inner-boundedness nonlinearity. Based on the relative outputs of neighboring agents, an adaptive protocol over a directed graph is designed via assigning a time-varying coupling weight to each node. Compared with the existing protocols, the proposed protocol can not only be utilized in the unidirectional flow of information, but it does not require any global graph information for its design. It has been shown that the established criteria can not only make the observer error tendency zero, but one can also achieve the leader–follower consensus of such nonlinear multi-agent systems. Furthermore, the gains of observer and protocol parameters can be constructed by solving the linear matrix inequalities (LMIs), which are conveniently checked. The results are illustrated by numerical simulations.