Time-varying Formation Tracking Research Articles

Observer-based adaptive time-varying formation tracking of one-sided Lipschitz nonlinear multi-agent systems

In this article, the problem of time-varying formation (TVF) tracking for nonlinear multi-agent systems (MASs) is investigated. The agent dynamics are described by one-sided Lipschitz (OSL) and quadratic inner-boundedness (QIB) function. Adaptive continuous TVF tracking protocols for nonlinear MASs are proposed. Compared to prior nonlinear system, this approach is more general and less conservative than nonlinear system with large Lipschitz constant. In addition, the continuous protocols are proposed to avoid undesirable chattering from non-zero inputs of the leader. Finally, the expected theoretical results are achieved through effective numerical simulations.

Time-varying formation tracking of multi-agent systems with multiple leaders based on aperiodic time-triggered intermittent control

In this article, the distributed aperiodic time-triggered intermittent control protocol (DATICP) is presented for the time-varying formation tracking of multi-agent systems (MASs) with multiple leaders. Firstly, we present the mathematical description of DATICP. The characteristic of DATICP lies in that for each agent, its control signal is updated at aperiodic sampling instants on work time intervals and disappears on rest time intervals. Secondly, based on a mixed time-dependent Lyapunov functional (MTLF), the exponential stability theorem of the derived system is established. Thirdly, according to the theorem, sufficient conditions are given to achieve time-varying formation tracking for MASs with multiple leaders by DATICP. As a result, a corollary is obtained which compromises conservativeness and complexity. Finally, two simulation examples are offered for illustration.

Observer-based leader-centric time-varying formation tracking control for nonlinear multi-agent systems with collision avoidance

The article introduces a novel control design methodology to achieve leader-centric time-varying formation tracking (TVFT) with collision avoidance in Lipschitz nonlinear multi-agent systems (MASs) equipped with a leader-driven formation system. This methodology addresses challenges such as actuator bias faults and leader maneuvering within this MASs setup. It employs two control schemes: collision avoidance and a novel formation observer-based time-varying formation tracking (FO-based TVFT) control. These control schemes work in tandem. The collision avoidance scheme ensures safe operation by preventing inter-agent collisions, while the novel FO-based TVFT control scheme enables followers to achieve leader-driven formations while tracking the leader’s movements. To achieve this capability, each follower employs a formation observer (FO) that continuously estimates the leader’s dynamically driven formations throughout runtime, facilitating responsive formation tracking by the followers. Notably, this FO-based TVFT control scheme establishes a novel framework for integrated leader-driven formation switching and leader tracking (i.e., leader-centric TVFT) in MASs. Furthermore, this control methodology is specifically designed for Lipschitz nonlinear MASs susceptible to challenges like actuator bias faults and leader maneuvering. It guarantees that the followers’ collective formation tracking error is uniformly ultimately bounded (UUB), based on Lyapunov’s stability theory. Finally, an illustrative example validates the proposed approach’s effectiveness.

Resilient Time-Varying Formation Tracking Control for General Linear Multiagent Systems With a Nonautonomous Leader and Adversarial Followers.

This article is concerned with resilient formation tracking problems for general linear multiagent systems, where the leader's control input is unavailable to all the followers and partial followers' behaviors are malicious due to the node attacks. Despite the presence of the nonautonomous leader and the adversarial followers, the remaining benign followers are still expected to track the leader's trajectory with the prescribed time-varying formation. To this end, a resilient scheme comprising an attack detection and isolation strategy and a formation tracking protocol is proposed. The detection strategy enables every benign follower to identify its adversarial neighbors with two-hop communication information, as long as the underlying topology meets given conditions. Then, the detected adversarial agents are directly removed to avoid the spread of their influence, which induces a new problem called node loss. To accommodate possible node loss events, the designed tracking protocol is independent of certain global knowledge, and its convergence is demonstrated by means of the impulsive Lyapunov functions. Finally, the proposed resilient scheme is verified by two simulation examples.

Adaptive output feedback time‐varying formation tracking of multi‐agent system with a leader of unknown input

AbstractThis paper researches the time‐varying formation tracking (TVFT) problem of linear multi‐agent systems (MASs). By designing a compensator, the problem of time‐varying formation can be considered as the output regulation problem. Thereby, the distributed output feedback controller combined with an adaptive technique is proposed. With this controller, follower agents achieve the desired time‐varying formation and follow the trajectory of the leader agent. Furthermore, extending the designed controller to the case where the leader agent equips with unknown control input. Using Lyapunov stability theory, it is demonstrated that under proper conditions the given protocol is implementable. Simulation example is presented at the end of the paper to illustrate the effectiveness of designed control mechanism.

Integral Event-triggered Time-varying Formation Tracking for UAV Swarm Systems With Switching Directed Topologies

Integral Event-triggered Time-varying Formation Tracking for UAV Swarm Systems With Switching Directed Topologies

Observer-based guaranteed-cost bipartite time-varying formation tracking control for multiagent systems subject to communication delays

The paper centers on the guaranteed-cost bipartite time-varying formation tracking control for multiagent systems with nonuniform time-varying communication delays under the framework of a distributed observer. An integral quadratic cost function is presented, founded on formation tracking and observation error. Firstly, distributed state observers, using the relative measurement output between neighbors, are established so that the leader and follower can accurately estimate each agent's unmeasurable state. Subsequently, a bipartite formation tracking protocol is proposed, incorporating estimation information and nonuniform time-varying communication delays. This protocol aims to achieve bipartite time-varying formation tracking for multiagent systems. Next, a new augmented Lyapunov-Krasovskii functional with delay-product and triple integral terms is constructed. By integrating the second-order Bessel-Legendre inequality technique, the delay-dependent reciprocally convex combination inequality method, and the free weight matrix technique, a new guaranteed-cost bipartite time-varying formation tracking criterion is developed, offering less conservatism. Compared to certain existing delay conditions, the stability conditions assure a greater allowable upper bound of delay. Finally, a numerical example is conducted to confirm the validity and superiority of the theoretical findings.

Time-Varying Formation Tracking Control of Multi-Leader Multiagent Systems With Sampled-Data

In this paper, the time-varying formation tracking (TVFT) problem of multi-leader multi-agent systems (MASs) under sampled-data control is studied. First, an improved TVFT criterion is derived by employing a general looped-functional and a zero integral functional. Then a new TVFT controller is designed based on our proposed method. Unlike the existing works, the TVFT controller can allow for bigger sampling intervals of multi-leader MASs. The results demonstrate that the states of the followers can form the designated formation and rotate around the convex combination formed by the multiple leaders. In addition, we generalize the results of TVFT to the sampled-data consensus for MASs, a sampled-data consensus controller which can reduce communication consumption is designed. Meanwhile, the values of the allowable maximum sampling intervals (AMSIs) are calculated. Finally, the superiority and availability of the theoretical results are verified by two simulation experiments. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The motivation of this paper is to address the problem of TVFT for MAS with multiple leaders. It has been applied to several practical engineering systems, e.g., satellite formation control and unmanned air vehicles (UAVs) formation control. Note that information exchange is a prerequisite to ensure safe and stable control of multi-UAV formation. However, continuous-time communication is difficult to be realized in the actual environment, and it will inevitably consume a lot of energy. In addition, sampled-data controller for MAS with a small sampling interval may cause network congestion. Therefore, a sampled-data controller which allows for a bigger sampling interval for MAS is designed to save network resources in this paper. Through simulation experiments, it can be proved that the followers not only track the leaders, but also form the designated formation.

Predefined-Time Bipartite Time-Varying Formation Tracking Control of Networked Autonomous Surface Vehicles via Hierarchical Control Approach

Predefined-Time Bipartite Time-Varying Formation Tracking Control of Networked Autonomous Surface Vehicles via Hierarchical Control Approach

Formation tracking control with disturbance rejection in leader-follower multi-agent systems under dynamic event-triggered mechanism

This paper investigates the problem of time-varying formation tracking (TVFT) in a linear multi-agent systems (MASs) with external disturbance in a type of directed network topology, and proposes a formation control strategy in a leader-follower control framework with disturbance rejection under a dynamic event-triggering mechanism (DETM). Firstly, in order to improve the overall performance of the system, an extended state observer is used to estimate the status of the follower and the presence of external disturbance in real time. Secondly, a DETM is designed to avoid continuous communication between adjacent intelligent agents. And the formation tracking error between adjacent multi-agents is used to formulate a distributed TVFT control strategy. Furthermore, a compensation function is designed to actively offset the impact of time-varying disturbances on system. A Lyapunov function is then established for stability analysis, verifying the absence of Zeno behavior with this DETM. Finally, a comparative numerical simulation was conducted using an unmanned aerial vehicle (UAV) cluster case to verify that the proposed method can save communication resources to a greater extent and has good control performance.

Dynamic Self-Triggered Fuzzy Bipartite Time-Varying Formation Tracking for Nonlinear Multiagent Systems With Deferred Asymmetric Output Constraints

Dynamic Self-Triggered Fuzzy Bipartite Time-Varying Formation Tracking for Nonlinear Multiagent Systems With Deferred Asymmetric Output Constraints

Finite-Time Time-Varying Formation Tracking for Heterogeneous Nonlinear Multiagent Systems Using Adaptive Output Regulation.

The finite-time output time-varying formation tracking (TVFT) problem for heterogeneous nonlinear multiagent system (MAS) is investigated in this article, where the dynamics of the agents can be nonidentical, and leader's input is unknown. The target of this article is that the outputs of followers need to track leader's output and realize the desired formation in finite time. First, for removing the assumption that all agents are required to know the information of leader's system matrices and the upper boundary of its unknown control input in previous studies, a kind of finite-time observer is constructed by exploiting the neighboring information, which can estimate not only the leader's state and system matrices but also can compensate for the effects of unknown input. On the basis of the developed finite-time observers and adaptive output regulation method, a novel finite-time distributed output TVFT controller is proposed with the help of the technique of coordinate transformation by introducing an extra variable, which removes the assumption that the generalized inverse matrix of follows' input matrix needs to be found in the existing results. By means of the Lyapunov and finite-time stability theory, it is proven that the expected finite-time output TVFT can be realized by the considered heterogeneous nonlinear MASs within a finite time. Finally, simulation results demonstrate the efficacy of the proposed approach.

Resilient Output Formation-Tracking of Heterogeneous Multiagent Systems Against General Byzantine Attacks: A Twin-Layer Approach.

This work solves the countermeasure design problems of distributed resilient output time-varying formation-tracking (TVFT) of heterogeneous multiagent systems (MASs) against general Byzantine attacks (GBAs). Inspired by the concept of Digital Twin, a hierarchical protocol equipped with a twin layer (TL) is proposed, which decouples the above problem into the defense against Byzantine edge attacks (BEAs) on the TL and the defense against Byzantine node attacks (BNAs) on the cyber-physical layer (CPL). First, a secure TL with respect to (w.r.t.) the high-order leader dynamics is designed, which achieves resilient estimation against BEAs. A trusted-node strategy against BEAs is proposed, which promotes network resilience by protecting almost the smallest fraction of crucial nodes on the TL. It is proven that strongly (2f+1) -robustness w.r.t. the above trusted nodes is sufficient for the resilient estimation performance of the TL. Second, a decentralized adaptive and chattering-free controller against potentially unbounded BNAs is designed on the CPL. This controller has the merit of uniformly ultimately bounded (UUB) convergence and an assignable exponential decay rate when converging into the above UUB bound. To the best of our knowledge, this article is the first to achieve resilient output TVFT against GBAs, rather than under GBAs. Finally, the practicability and validity of this new hierarchical protocol are illustrated via a simulation example.

Distributed Adaptive Time-Varying Formation Tracking for Input Saturated Multi-Agent Systems With Multiple Leaders

Distributed Adaptive Time-Varying Formation Tracking for Input Saturated Multi-Agent Systems With Multiple Leaders

Resilient Time-Varying Formation Tracking for Heterogeneous High-Order Multiagent Systems With Multiple Dynamic Leaders

This paper investigates time-varying output formation tracking problems for heterogeneous multiagent systems in an adversarial environment, where both leaders and followers are vulnerable to cyber-attacks. Despite the presence of adversarial agents, the normal followers not suffering from cyber-attacks seek to achieve a desired for-mation configuration and track a safe trajectory generated by normal leaders' outputs simultaneously. To this end, a resilient time-varying output formation (RTVOF) tracking scheme is presented in this work. Firstly, to counteract the effect of adversarial agents, a safety strategy is proposed for general linear heterogeneous systems, which is a syn-thesis of the mean-subsequence-reduced family algorithms and an attack detection procedure. Secondly, using the neighboring interaction, a resilient distributed observer and a local formation controller are designed for each normal follower to estimate the state and track the output of the safe formation reference. Then, it is proved that the hetero-geneous multiagent system with multiple dynamic leaders and time-varying topologies can accomplish the RTVOF tracking if specific graph-theoretic properties and forma-tion feasibility conditions are satisfied. Finally, simulation examples are given to demonstrate the effectiveness of obtained results.

Energy-Constraint Adaptive Time-Varying Formation Tracking for Multi-Agent Systems With Multiple Leaders and Bounded Unknown Inputs

Energy-Constraint Adaptive Time-Varying Formation Tracking for Multi-Agent Systems With Multiple Leaders and Bounded Unknown Inputs

Predictive State Observer-Based Aircraft Distributed Formation Tracking Considering Input Delay and Saturations

This paper investigates a fully distributed time-varying formation tracking problem for a group of fixed-wing aircraft. The fixed-wing aircraft formation control system consists of an outer-loop trajectory control subsystem and an inner-loop attitude control subsystem. For fixed-wing aircraft, it is crucial to consider the time delay of the engine response, the model uncertainties, the tracking capability of the attitude commands in the inner loop, and other agility performances of the aircraft. To address the problems related to the input time delay and model uncertainties, a predictive extended state observer-based fully distributed time-varying formation tracking control (PESO-TVFTC) protocol is proposed. To satisfy the constraints set by the attitude tracking quickness and the trajectory tracking smoothness, the low gain feedback technique is introduced in the protocol to keep the control inputs for the outer loop within the desired saturation constraints. Through theoretical analysis, it is proved that the multiple aircraft systems can achieve time-varying formation tracking consensus under specific initial conditions and feasibility conditions, and it is shown that the upper bounds of the PESO gains are restricted by the time delay. Numerical simulations are used to demonstrate the effectiveness of and the improvements in the proposed method.

Time-varying formation tracking control for multi-agent systems using distributed multi-sensor multi-target filtering

Time-varying formation tracking control issues for multi-agent systems are investigated based on the distributed multi-sensor multi-target filtering algorithm. In order to estimate the states of targets, a distributed multi-sensor multi-target filtering algorithm based on cubature Kalman filtering is investigated. Subsequently, the state estimations calculated by the filtering algorithm are used to design a time-varying formation tracking protocol for multi-agent systems, enabling the agents to form a time-varying formation and track the convex combination of uncooperative targets. The estimation errors of the filtering algorithm are proved to be bounded in mean square by introducing a stochastic process and the boundedness of the formation tracking errors is further proved. Simulation results illustrates the effectiveness of the proposed algorithm and protocol.

Robust Decentralized Formation Tracking Control of Complex Multiagent Systems

This article investigates the decentralized formation tracking problem for complex multiagent systems in finite settling time, subjected to output constraints and external disturbances. The barrier Lyapunov function is used to constrain the output of each agent. Therefore, starting inside a closed boundary, the agents are guaranteed to remain inside it for all future time. Under directed communication topology, decentralized time-varying formation tracking is achieved in finite time. Furthermore, in the proposed work, the linear sliding manifold is employed to mitigate the singularity problem that occurs in the conventional robust finite-time methods, i.e., terminal sliding mode-based control schemes. The stability properties of the proposed framework are established through the Lyapunov method which not only ensures the finite-time formation tracking of nonlinear multiagent systems under directed communication but also guarantees that for all time the agents remain inside a closed boundary if they are initially inside it. Consequently, the uniqueness of this article is that it presents a novel formation tracking control framework for multiagent systems that simultaneously considers three performance metrics of robustness, finite-time convergence, and output constraints while mitigating the singularity problem. The proposed topology is validated by implementing the numerical examples in MATLAB/SIMULINK.

Multiple time-varying formation tracking of multiple heterogeneous Euler–Lagrange systems via prescribed-time hierarchical control algorithms in task space

Multiple time-varying formation tracking of multiple heterogeneous Euler–Lagrange systems via prescribed-time hierarchical control algorithms in task space