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This article studies the problem of formation tracking control in multi-agent systems, achieved in finite time, under challenging conditions such as strong nonlinearity, aperiodic intermittent communication, and time-delay effects, all within a hybrid impulsive framework. The impulses are categorized as either stabilizing control impulses or disruptive impulses. Furthermore, by integrating Lyapunov-based stability theory, graph theory, and the linear matrix inequality (LMI) method, new stability criteria are established. These criteria ensure finite-time intermittent formation tracking while considering weak Lyapunov inequality conditions, intermittent communication rates, and time-varying gain strengths. Additionally, the approach manages an indefinite number of impulsive moments and adjusts the control domain's width based on the average impulsive interval and state-dependent control width. Numerical simulations are provided to validate the applicability and effectiveness of the proposed formation tracking control protocols.
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Coordinating the movements of a robotic fleet using consensus-based techniques is an important problem in achieving the desired goal of a specific task. Although most available techniques developed for consensus-based control ignore the collision of robots in the transient phase, they are either computationally expensive or cannot be applied in environments with dynamic obstacles. Therefore, we propose a new distributed collision-free formation tracking control scheme for multiquadcopter systems by exploiting the properties of the barrier Lyapunov function (BLF). Accordingly, the problem is formulated in a backstepping setting, and a distributed control law that guarantees collision-free formation tracking of the quads is derived. In other words, the problems of both tracking and interagent collision avoidance with a predefined accuracy are formulated using the proposed BLF for position subsystems, and the controllers are designed through augmentation of a quadratic Lyapunov function. Owing to the underactuated nature of the quadcopter system, virtual control inputs are considered for the translational (x and y axes) subsystems that are then used to generate the desired values for the roll and pitch angles for the attitude control subsystem. This provides a hierarchical controller structure for each quadcopter. The attitude controller is designed for each quadcopter locally by taking into account a predetermined error limit by another BLF. Finally, simulation results from the MATLAB-Simulink environment are provided to show the accuracy of the proposed method. A numerical comparison with an optimization-based technique is also provided to prove the superiority of the proposed method in terms of the computational cost, steady-state error, and response time.
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The formation tracking of the leader-follower multi-agent systems (MASs) under switching topologies is investigated. The considered system is exposed to both the mismatched and matched disturbances in the dynamics of the leader and followers, which places higher requirements for the robustness of the control protocol. In the presence of disturbances and leader's unknown control input, an innovative distributed observer embedded with robust terms is designed firstly to estimate leader's states in finite time. Taking account of the switching topologies, a novel analysis scheme that divides the convergence process into two stages is proposed to establish the finite-time (FT) convergence of estimation errors. Then, by virtue of a constructed auxiliary variable, a FT controller with an event-triggered mechanism is put forward, in which multiple robust feedback terms are designed wisely to suppress the mismatched and matched disturbances effectively. As a result, the FT formation tracking can be achieved with saved resources, despite perturbed environments and switching topologies. Simulation examples are presented to confirm the effectiveness of the proposed algorithm.
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Time-varying formation tracking problems for multi-agent systems (MASs) under distributed Denial-of-Service (DDoS) attacks and actuator faults are studied. To deal with the hybrid threats at the cyber and physical layers, an estimator-based fault-tolerant hierarchical control scheme is introduced, which is applicable to channel-wise asynchronous communication. Sufficient conditions for formation tracking of maneuvering leader with ultimately bounded error are obtained, and the particular case of periodic communication and attacks with constrained duration and frequency is further analyzed. Comparative physical simulations based on ROS and Gazebo are first conducted to show the resilience of our scheme against the threats. Finally, an experimental platform containing DJI Tello quadrotors and a self-developed ground control station is built, based on which practical experiments with four quadrotors are carried out to evaluate the effectiveness and engineering practicability of the proposed control framework.
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This paper studies the distributed time-varying output formation tracking problem for heterogeneous multi-agent systems with both diverse dimensions and parameters. The output of each follower is supposed to track that of the virtual leader while accomplishing a time-varying formation configuration. First, a distributed trajectory generator is proposed based on neighboring interactions to reconstitute the state of virtual leader and provide expected trajectories with the formation incorporated. Second, an optimal tracking controller is designed by the model-free reinforcement learning technique using online off-policy data instead of requiring any knowledge of the followers' dynamics. Stabilities of the learning process and resulting controller are analyzed while solutions to the output regulator equations are equivalently obtained. Third, a compensational input is designed for each follower based on previous learning results and a derived feasibility condition. It is proved that the output formation tracking error converges to zero asymptotically with the biases to cost functions being restricted arbitrarily small. Finally, numerical simulations verify the proposed learning and control scheme.
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This work investigates fixed-time time-varying output formation-containment control of heterogeneous general multi-agent systems, which comprises one virtual leader, multiple leaders, and followers. First, fixed-time nonlinear control law is constructed, such that leaders can achieve time-varying output formation in a finite time. Meanwhile, leaders can track the virtual leader's output trajectory. Next, two complete distributed adaptive fixed-time observers are designed aiming to recover a convex hull. This is key to control issue in this paper. Further, nonlinear control law is constructed for followers, such that followers can move into the convex hull formed by multiple leaders. Finally, two examples are provided to verify the feasibility of the theoretical results.
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In this paper, a flexible shape generator (FSG) is designed to achieve the divinable transformation process of the time-varying formation, and consider the FSG-based time-varying formation tracking (TVFT) problem of multiple Lagrangian agents with unknown disturbances and directed graphs. A hierarchical control algorithm is newly designed to achieve the control goal without using the prior information of the system model and bounded disturbances, and the specific implementation of the proposed hierarchical algorithms is also provided. By using the Hurwitz criterion and adaptive system theory, the sufficient conditions are derived and the stability analysis show that the formation tracking errors of the considered system are uniform ultimate bounded. Several simulation examples are performed on five two-degree-of-freedom mechanical arms to show the effectiveness of theoretical results.
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The paper proposes a formation tracking control method for the uncertain artificial swarm systems under the inequality constraints. Not only can the agents perform swarm behaviors (e.g., convergence, formation and avoidance of collision), but they can also track the fixed targets in a constrained area (which is formulated as the inequality constraints, such as unilateral constraint and bilateral constraint.). The swarm behaviors are creatively considered as the servo constraints or the control objectives for the swarm agents. Based on the Udwadia-Kalaba (U-K) equation, those prescribed behaviors are realized by a model-based control design (that is the servo constraints force model-based feedforward control). To deal with the inequality constraints in the formation tracking process, a differential homeomorphism transformation is used to relieve the environmental constraints for the swarm agents. Moreover, the uncertainty of the swarm agents (i.e., the parameter uncertainty in modeling and the external disturbances) is considered, which is time-varying and unknown (but bounded). An uncertainty estimation method with dead-zone and leakage term is designed to calculate the possible upper bound of the uncertainty. In virtue of the estimated upper bound of the uncertainty, a robust control is designed for the uncertain swarm agents to obey the prescribed swarm behaviors in the formation tracking task. The system performances of the artificial swarm systems under the proposed control are theoretically guaranteed by a range of rigorous theorems and numerically verified by the simulations of three agents.
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The distributed formation tracking with preview information is investigated for discrete-time heterogeneous linear multi-agent systems (MASs) over directed communication networks. Firstly, by constructing an augmented system containing virtual regulation output and previewable information, the original problem is converted into a state regulation problem. Secondly, due to the coupling restriction of the eigenvalues of the exosystem matrix and the communication topology matrix, a linear distributed observer is proposed by introducing two extra parameters to realize asymptotic estimation. Using the output information of the observer, the problem was further formulated in the form of feedforward output regulation. Moreover, by solving the output regulation problem, the sufficient conditions are deduced for ensuring the achievement of the formation preview tracking. Meanwhile, numerical simulations show that the distributed design with preview actions has positive effect on the improvement of the transient response.
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This paper presents a distributed constant bearing guidance and model-free disturbance rejection control method for formation tracking of autonomous surface vehicles subject to fully unknown kinetic model. First, a distributed constant bearing guidance law is designed at the kinematic level to achieve a consensus task. Then, by using an adaptive extended state observer (AESO) to estimate the total uncertainties and unknown input coefficients, a simplified model-free kinetic controller is designed based on a dynamic surface control (DSC) design. It is proven that the closed-loop system is input-to-state stable The stability of the closed-loop system is established. A salient feature of the proposed method is that a cooperative behavior can be achieved without knowing any priori information. An application to formation control of autonomous surface vehicles is given to show the efficacy of the proposed integrated distributed constant bearing guidance and model-free disturbance rejection control.
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In this study, an event-triggered fixed-time multiple stratospheric airship formation trajectory tracking controller is designed, and it is composed of two parts: the airship leader trajectory tracking controller (ALTTC) and the airship follower formation tracking controller (AFFTC). First, based on the framework of backstepping, the fixed-time ALTTC is designed to allow the trajectory tracking error to converge to zero within a fixed time. Subsequently, the event-triggered fixed-time AFFTC is designed to reduce the formation tracking error to zero within a fixed time. Two event-triggering conditions are designed to reduce the transmission times of control inputs and calculation times of control outputs. The fixed-time stability and the trajectory-tracking and formation-tracking performance of event-triggered closed-loop systems are theoretically shown to be ensured, and Zeno behavior is excluded in the proposed asynchronous event-triggering mechanism. Finally, simulations indicate the effectiveness of the proposed controller.
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With the rapid development of UAV technology, the research of optimal UAV formation tracking has been extensively studied. However, the high maneuverability and dynamic network topology of UAVs make formation tracking control much more difficult. In this paper, considering the highly dynamic features of uncertain time-varying leader velocity and network-induced delays, the optimal formation control algorithms for both near-equilibrium and general dynamic control cases are developed. First, the discrete-time error dynamics of UAV leader-follower models are analyzed. Next, a linear quadratic optimization problem is formulated with the objective of minimizing the errors between the desired and actual states consisting of velocity and position information of the follower. The optimal formation tracking problem of near-equilibrium cases is addressed by using a backward recursion method, and then the results are further extended to the general dynamic case where the leader moves at an uncertain time-varying velocity. Additionally, angle deviations are investigated, and it is proved that the similar state dynamics to the general case can be derived and the principle of control strategy design can be maintained. By using actual real-world data, numerical experiments verify the effectiveness of the proposed optimal UAV formation-tracking algorithm in both near-equilibrium and dynamic control cases in the presence of network-induced delays.
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This paper studies the energy-constraint output formation control for swarm systems with leaderless and leader-following topology structures. Most existing results on output formation with the dynamic output feedback protocols focus on the swarm systems without the energy constraint, but it is well known that the energy constraint is critically important for practical applications. In order to analyze the impacts of the energy constraint, a new energy-constraint output formation protocol is proposed. First, by the observable decomposition approach, a dynamic output formation protocol is presented, which contains an energy-constraint term to restrict the whole consumption. Then, sufficient conditions for leaderless energy-constraint output formation are presented via establishing the relationship of the energy constraint and the matrix variables, where it is found that the designed gain matrices of the output formation protocol can ensure that the actual energy consumption is lower than the total energy supply. Especially, a partition checking algorithm is proposed to check those conditions, which can ensure the scalability and solvability of a swarm system. Moreover, the output formation center function is derived to depict the whole macroscopic movement of a swarm system. A nonsingular transformation approach is presented to unify leaderless energy-constraint output formation and energy-constraint output formation tracking into the same framework, which are usually discussed in different theoretical frameworks. Finally, two simulation examples are illustrated to show that the theoretical results about leaderless energy-constraint output formation and energy-constraint output formation tracking are correct.
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This paper investigates formation tracking control for multi-agent networks with fixed time convergence. The control task is that the follower agents are required to form a prescribed formation within a fixed time and the geometric center of the formation moves in sync with the leader. First, an error system is designed by using the information of adjacent agents and a new control protocol is designed based on the error system and terminal sliding mode control (TSMC). Then, via employing the Lyapunov stability theorem and the fixed time stability theorem, the control task is proved to be possible within a fixed time and the convergence time can be calculated by parameters. Finally, numerical results illustrate the feasibility of the proposed control protocol.
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Practical time-varying output formation tracking (PTVOFT) analysis and design task of high-order nonlinear strict-feedback multi-agent systems (MASs) containing control saturation is processed, in which PTVOF error is confined to a narrow range. Distinct with former achievements, agents' model characteristics are high-order nonlinear strict-feedback form with mismatched uncertain nonlinearities and control saturation constraints while multi-follower system is required for achieving PTVOFT for a maneuvering leader. Firstly, hierarchical distributed extended state observer (DESO) is put forward which only employs information between adjacent individuals for approximating mismatched nonlinearities of followers together with mismatched nonlinearities of the leader. Secondly, the practical time-varying output formation tracking protocol can be raised. Backstepping techniques are applied in design procedures to provide primary variables for each control loop, where hierarchical DESOs are utilized for dealing with comprehensive uncertainties. Distributed auxiliary systems are designed for providing compensating signals to achieve the input saturation. Then, the design processes of PTVOFT protocol and hierarchical DESOs are summarized within three steps in an algorithm. Thirdly, the stability and the properties of the proposed protocol and algorithm are analyzed through employing graph theories and Lyapunov theories. Finally, numerical simulation results illustrate the effectiveness of achieved protocol and algorithm.
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This paper studies the time-varying formation tracking problem for general linear multi-agent systems with multiple leaders in the presence of both actuator failure and input saturation. The followers are required to uniquely determine and track the convex combination of the states of leaders, while maintaining a predefined time-varying formation. A hyperbolic tangent function is firstly introduced to modify the actuator model with input saturation constraint. Then, an augmented plant for dynamics of each follower is constructed to derive the control protocol by exploiting the dynamic surface control technique. The proposed control protocol deals with faults of bias and unknown bounded loss of effectiveness by means of adaptive fault-tolerant strategies, while a formation feasible condition should be satisfied. With the control signal generated by the augmented plant, the time-varying formation error is proved to be semi-globally uniformly bounded under the faults and input saturation, based on standard Lyapunov theory. Finally, a numerical simulation is implemented to demonstrate the effectiveness of the proposed algorithm.
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This paper considers the adaptive time-varying formation tracking control of unmanned aerial vehicles (UAVs) with quantized input. Uncertainties and nonholonomic constraint are involved in the UAV model. With a novel transformation of the final control signal, a very coarse quantization can be achieved. Adaptive quantized controllers are proposed by employing backstepping technique. It is proved that, with our proposed strategy, all signals of the closed-loop system are globally uniformly bounded, and the formation tracking error converges to an arbitrarily small residual set. Simulation results are given to illustrate the effectiveness of the proposed strategy.