Distributed consensus tracking for multiple uncertain nonlinear strict-feedback systems under a directed graph.

This study investigates a distributed adaptive consensus tracking problem for multiple non-linear strict-feedback systems with parametric uncertainties under a directed communication graph topology. It is assumed that the information of a leader is available for only a limited subset of followers. The distributed adaptive dynamic surface design approach is presented to design the local controller of each follower to guarantee that all networked followers with unmatched parametric uncertainties synchronise to the leader regardless of a lack of the shared information on the communication links. From the Lyapunov stability theorem, it is shown that the consensus tracking errors are cooperatively semiglobally uniformly ultimately bounded and converge to an adjustable neighbourhood of the origin.

This article proposes a neural-network-based adaptive asynchronous event-triggered design strategy for the distributed consensus tracking of uncertain lower triangular nonlinear multi-agent systems under a directed network. Compared with the existing event-triggered recursive consensus tracking designs using multiple neural networks for each follower and continuous communications among followers, the primary contribution of this study is the development of an asynchronous event-triggered consensus tracking methodology based on a single-neural network for each follower under event-driven intermittent communications among followers. To this end, a distributed event-triggered estimator using neighbors' triggered output information is developed to estimate a leader signal. Subsequently, the estimated leader signal is used to design local trackers. Only a triggering law and a single-neural network are used to design the local tracking law of each follower, irrespective of unmatched unknown nonlinearities. The information of each follower and its neighbors is asynchronously and intermittently communicated through a directed network. Thus, the proposed asynchronous event-triggered tracking scheme can save communicational and computational resources. From the Lyapunov stability theorem, the stability of the entire closed-loop system is analyzed and the comparative simulation results demonstrate the effectiveness of the proposed control strategy.

Consensus tracking for higher-order multi-agent systems with switching directed topologies and occasionally missing control inputs

In this article, the asymptotic tracking consensus problem of higher-order multiagent systems (MASs) with general directed communication graphs is addressed via designing event-triggered control strategies. One common assumption utilized in most existing results on such tracking consensus problem that the inherent dynamics of the leader are the same as those of the followers is removed in this article. In particular, two cases that the dynamics of the leader are subjected, respectively, to bounded input and unknown nonlinearity are considered. To do this, distributed event-triggered observers are first constructed to estimate the state information of the leader. Then, local event-triggered tracking control protocols are designed for each follower to complete the goal of tracking consensus. One distinguishing feature of the present distributed observers lies in the fact that they could avoid the continuous monitoring for the states of the neighbors' observer states. It is also worth pointing out that the present tracking consensus control strategies are fully distributed as no global information related to the directed communication graph is involved in designing the strategies. Two simulation examples are finally presented to verify the efficiency of the theoretical results.

A distributed coordinated tracking problem is solved via a variable structure approach when there exists a dynamic virtual leader who is a neighbor of only a subset of a group of followers, all followers have only local interaction, and only partial measurements of the states of the virtual leader and the followers are available. In the context of coordinated tracking, we focus on both consensus tracking and swarm tracking algorithms. In the case of first-order kinematics, we propose a distributed consensus tracking algorithm without velocity measurements under both fixed and switching network topologies. In particular, we show that distributed consensus tracking can be achieved in finite time. The algorithm is then extended to achieve distributed swarm tracking without velocity measurements. In the case of second-order dynamics, we first propose two distributed consensus tracking algorithms without acceleration measurements when the velocity of the virtual leader is varying under, respectively, a fixed and switching network topology. In particular, we show that the proposed algorithms guarantee at least global exponential tracking. We then propose a distributed consensus tracking algorithm and a distributed swarm tracking algorithm when the velocity of the virtual leader is constant. When the velocity of the virtual leader is varying, distributed swarm tracking is solved by using a distributed estimator. For distributed consensus tracking, a mild connectivity requirement is proposed by adopting an adaptive connectivity maintenance mechanism in which the adjacency matrix is defined in a proper way. Similarly, a mild connectivity requirement is proposed for distributed swarm tracking by adopting a connectivity maintenance mechanism in which the potential function is defined in a proper way. Several simulation examples are presented as a proof of concept.

This paper focuses on fixed-time event-triggered consensus tracking of high-order MAS over digraph and under DOS attack. The considered DOS attack is divided into connectivity-maintained attack and connectivity-broken attack. To detect connectivity-broken attack under event-triggered environment, a new cyberattack detection algorithm is presented. Next, using cyberattack detection results, a fixed-time event-triggered distributed observer is developed to estimate the leader’s states in the presence of DOS attack, which conducts event-triggered update in the normal condition and under connectivity-maintained attack and stops updating in the presence of connectivity-broken attack. Then, an adaptive event-triggered prescribed-time dynamic surface consensus tracking control protocol is proposed to eliminate mismatched disturbances caused by estimation error and achieve prescribed-time convergence of the tracking error. Stability analysis proves fixed-time convergence of the developed consensus tracking strategy and non-zeno analysis shows the developed distributed observer and consensus tracking control strategy exclude zeno behavior. This paper contributes to proposing a fixed-time leader-follower consensus control strategy for MAS under DOS attack via event-triggered approach, which eliminates the effect of DOS attack, achieves consensus tracking within a fixed time and reduces resources consumption. Finally, simulation results show the effectiveness and superiority of the developed consensus tracking approach.

In this article, we focus on the problems of consensus control for nonlinear uncertain multiagent systems (MASs) with both unknown state delays and unknown external disturbances. First, a nonlinear function approximator is proposed for the system uncertainties deriving from unknown nonlinearity for each agent according to adaptive radial basis function neural networks (RBFNNs). By taking advantage of the Lyapunov-Krasovskii functionals (LKFs) approach, we develop a compensation control strategy to eliminate the effects of state delays. Considering the combination of adaptive RBFNNs, LKFs, and backstepping techniques, an adaptive output-feedback approach is raised to construct consensus tracking control protocols and adaptive laws. Then, the proposed consensus tracking scheme can steer the nonlinear MAS synchronizing to the predefined reference signal on account of the Lyapunov stability theory and inequality properties. Finally, simulation results are carried out to verify the validity of the presented theoretical approach.

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.

Adaptive fuzzy output feedback FTC for nonstrict-feedback systems with sensor faults and dead zone input

Event-triggering mechanisms reported in the existing prescribed-time (PT) control do not adequately capture the dynamic nature of network environments, and are not applied to distributed consensus tracking problems with unknown time delays. Therefore, designing a dynamic event-triggering mechanism is crucial to ensuring PT stability, even in the presence of unknown time delays. This article focuses on developing a dynamic event-triggering mechanism to achieve adaptive practical PT output-feedback consensus tracking for nonlinear uncertain multiagent systems with unknown time delays. Firstly, a delay-independent PT state observer using a time-varying gain function is designed to estimate the immeasurable states. Following this, a novel distributed delay-independent PT consensus tracking scheme is constructed, incorporating a dynamic event-triggered mechanism through the command-filtered backstepping approach. In this design, dynamic variables based on a time-varying gain function are developed to support the event-triggering mechanism, ensuring practical stability within the prescribed settling time. Consequently, the proposed output-feedback control protocol can achieve practical PT stability, meaning that consensus tracking errors are constrained to a neighborhood around zero within a pre-specified time, regardless of the initial states of the agents or design parameters, while also avoiding the Zeno phenomenon. Finally, the effectiveness of the proposed strategy is validated through an illustrative example, which includes a comparative analysis.

Controlling stochastic multi-agent systems (MAS) is a promising branch of systems engineering owing to its ability to solve complex practical problems by taking inspiration from the social behavior of living organisms. Consensus on more than one state is a less considered problem in the framework of leader-following control of high-order uncertain nonlinear stochastic multi-agent systems with unknown dynamics. To this end, in this paper, a sliding surface integrates a tracking error polynomial with consensus error between states of the connected agents. Accordingly, a new distributed fuzzy sliding mode controller is designed for a class of stochastic multi-agent systems with partially unknown deterministic dynamics and unknown bounded stochastic dynamics. The proposed control protocol steers agents to reach agreement on states of the leader and concurrently approximates the unknown part of their deterministic dynamics by using fuzzy systems with adaptive parameters. In the sense of Lyapunov, it is proved that consensus error and all of the closed-loop signals of each agent are semi-globally uniformly ultimately bounded (SGUUB) in mean square. Under the designed controller, nonlinear closedloop experimental dynamics behave well in both tracking and reaching state consensus.

Containment control is one of critical issues in multiagent systems (MASs). A recursive sliding-mode dynamic surface control (DSC) strategy with a nonlinear gain is addressed for the containment problem of uncertain MASs in strict-feedback form. Two factors, a recursive dynamic sliding-mode surface and a nonlinear gain function, are introduced to solve the contradiction between control accuracy and dynamic performance in the traditional DSC method. The function approximation technique, by radial basis function neural networks, is employed to compensate unknown dynamics. On the basis of the backstepping and graph theory, a full-state feedback containment control strategy is presented. Subsequently, we propose an output feedback containment control strategy via a state observer for individual followers. From the Lyapunov stability theorem, we construct an improvement Lyapunov function for the MAS, and it is proven that all followers converge to a convex hull formed by leaders for both full-state feedback and output feedback cases. Simulation examples are presented for verification of the effectiveness of the strategy.

This study proposes an adaptive approximation‐based control approach for non‐linear pure‐feedback systems in the presence of full state constraints. Completely non‐affine non‐linear functions are considered and assumed to be unknown. The dynamic surface design based on integral barrier Lyapunov functionals is provided to achieve both the desired tracking performance and the constraints satisfaction, in consideration of the full‐state‐constrained non‐affine non‐linearities. In this design procedure, simple sufficient conditions for choosing control gains, which can be checked off‐line, are established to guarantee the feasibility of the controller. The function approximation technique is employed to estimate unknown non‐linearities induced from the controller design procedure where the adaptive laws using the projection operator are designed to ensure the boundedness of the function approximators in the feasibility conditions. It is shown that all the signals in the closed‐loop system are uniformly ultimately bounded and the tracking error converges to an adjustable neighbourhood of the origin while all state variables always remain in the constrained state space.

This paper considers the distributed consensus disturbance rejection problem for general linear multiagent systems with deterministic disturbances under directed communication graphs. Based on the relative state information of the neighboring agents, the consensus protocols, which consist of two observers, including a state observer and a separate disturbance observer, are designed to guarantee that the consensus error goes to zero with complete disturbance rejection. Furthermore, the state observer is designed in a fully distributed fashion with adaptive coupling gain, which has the advantage that the consensus controller design is independent of the Laplacian matrix associated with the communication network. The distributed observer-based consensus disturbance rejection protocols are further extended to containment control. Finally, an example is provided to demonstrate the effectiveness of the proposed strategies.

This paper investigates a minimal-function-approximation (MFA)-based decentralized event-triggered tracking problem for uncertain interconnected systems with completely unknown nonaffine nonlinearities. It is assumed that events are triggered to transmit state variables in the sensor-to-controller channel. The existing approximation-based event-triggered control schemes for single lower-triangular nonlinear systems require multiple neural-network-based or fuzzy-based function approximators and multiple event-triggering conditions that are equal to the order of the system. Thus, all error surfaces using virtual control laws should be computed to verify the triggering conditions in the sensor part. To overcome the complexity in using these multiple function approximators and event-triggering conditions, we propose an event-triggered tracking strategy using one function approximator and one event-triggering condition for each subsystem in the decentralized control framework, regardless of the order of pure-feedback nonlinear subsystems. The proposed strategy is based on the MFA design technique and thus one event-triggering condition using a local tracking error is established for the local tracking law of each subsystem. Using the impulsive system approach and the Lyapunov stability theorem, the total closed-loop stability is analyzed rigorously and the minimum interevent times for each subsystem are derived to exclude the unexpected Zeno behavior.