Tracking Control For Multi-agent Systems Research Articles

Connectivity enhancing coordinated tracking control of multi-agent systems with a state-dependent jointly-connected dynamic interaction topology

We revisit the problem of virtual leader tracking by a group of agents of second order dynamics when only a portion of the agents are informed of the information of the virtual leader, under a state-dependent interaction topology. By proposing a simpler controller structure, we obtain results on coordinated tracking control under a jointly connected topology, both in the presence and in the absence of the virtual leader velocity information. The simplification in control protocols also enables us to arrive at our second contribution on connectivity enhancing coordinated control. In comparison with the existing connectivity preserving control algorithms, our proposed connectivity enhancing mechanism is effective in maintaining both the initially existent topology edges and those newly formed topology edges that were not initially existent. Besides, our proposed algorithms are designed in such a way that the local Lipschitz condition is satisfied and thus technical issues on solution uniqueness of the closed-loop system are avoided. Our proposed technique applies to both consensus tracking and flocking.

Delay-dependent distributed event-triggered tracking control for multi-agent systems with input time delay

This paper addresses delay-dependent distributed event-triggered tracking control for general linear multi-agent systems. First, both fixed and time-varying input delays are taken into consideration of tracking consensus protocol design due to the network transmission delay among agents, respectively. Correspondingly, a new delay-dependent triggering mechanism is proposed, by which the protocols of agent are only updated at the violation of the pre-defined triggering mechanism. One of its advantages is that the triggering instant can not be affected by its neighbours’ state of last triggering instant, which can reduce effectively the frequency of control updates. Then, the co-design method of the control protocol gains and the triggering parameters are developed and delay-dependent event-triggered tracking consensus criteria are obtained by Lyapunov stability theory, respectively. Moreover, the Zeno-behavior of event-triggered mechanisms is excluded effectively by showing the existence of the strictly positive consecutive triggering interval. Last, two comparison examples are provided to demonstrate the effectiveness of the developed method.

Distributed Observer-Based Formation Tracking Control of Multi-Agent Systems with Multiple Targets of Unknown Periodic Inputs

This paper studies the distributed formation tracking control problem of heterogeneous multi-agent systems where the multiple targets have unknown inputs with finite dimensional Fourier decompositions and each target’s measurement output is just available to partial agents. A distributed observer-based formation tracking control algorithm is proposed. The distributed observers are based on the consensus protocol and designed to estimate the inputs and states of all targets from the available measurement outputs and neighbor information. The tracking controller is a state feedback based on the estimated state center of the targets. It is proved that the estimation errors of all agents converge to zero, if and only if each target node in the extended topology is reachable from each agent node and the consensus gain is larger than certain value. It is further proved that under the formation tracking control algorithm, the agents can asymptotically achieve predesigned formation and encircle the targets. A numerical simulation example is given to verify the validity of the algorithm.

Event-Triggered Adaptive Tracking Control for Multiagent Systems With Unknown Disturbances.

This paper considers the event-triggered tracking control problem of nonlinear multiagent systems with unknown disturbances. The event-triggering mechanism is considered in the controller update, which decreases the amount of communication and reduces the frequency of the controller update in practice. By designing a disturbance observer, the unknown external disturbances are estimated. Moreover, a part of adaptive parameters are only dependent on the number of followers, which weakens the computational burden. It is shown that all the signals are bounded, and the consensus tracking errors are located in a small neighborhood of the origin based on the Lyapunov stability theory and backstepping approach. Finally, the effectiveness of the approach proposed in this paper is proved by simulation results.

Event-triggered simultaneous fault detection and tracking control for multi-agent systems

ABSTRACTThe main aim of this study is to design distributed simultaneous fault detection and control units for multi-agent systems subject to limited communication and energy resources. For this purpose, each agent is equipped with a single module that generates both the residual signal for the fault detection task, as well as the control input of each agent for the tracking objective. To reduce the communication among the agents, an event-triggered data transmission paradigm is considered by using a dynamic triggering rule which results in higher data transmission reduction in comparison with the static triggering condition. Moreover, the proposed dynamic observer-based structure for the detector-controller module provides more degrees of freedom compared to the static Luenberger observer. The design parameters are obtained by solving a multi-objective optimisation problem considering the fault detection, tracking, and communication objectives. Simulation results illustrate the effectiveness and capabilities of the proposed method.

Formation tracking control for multi-agent systems: A wave-equation based approach

This paper considers the formation tracking control problem of large-scaled Multi-Agent Systems (MAS) for which the model is based on a system of mutually independent wave Partial Differential Equations (PDEs). The spatial derivatives in the equation correspond to the underlying communication topology of the agents. A leader-follower mode is employed in the control algorithm, with which the agents on the boundary of PDEs are chosen as leaders knowing the tracking trajectory and all the other agents are followers. Each follower has only the information of its own relative position and velocity to its topological neighbors. With a designed distributed controller, the formation tracking error is bounded by a constant proportional to the acceleration of the desired trajectory. Robustness of the control law to a perturbation in the velocity measurement is also discussed. Furthermore, some simulation studies are provided to show the effectiveness of the control algorithm.

Distributed adaptive tracking control for multi-agent systems with uncertain dynamics

In this paper, the adaptive observer-based tracking problem for multi-agent system with uncertain dynamics is considered. The communication topology among the agents is assumed to be directed and connected. To track the active leader, a distributed adaptive consensus protocol based on the relative output information with its neighboring agents is proposed for each following agent. To deal with uncertain dynamics, an adaptive learning law is included in the proposed protocol. Furthermore, to implement the protocol in a fully distributed fashion, distributed adaptive laws are adopted to adjust the coupling weights. By using Lyapunov method, the multi-agent system can be proved to achieve consensus via the proposed protocols. The established convergence condition is in term of linear matrix inequalities, by which the control protocol can be constructed effectively. Simulation results show the effectiveness of the proposed method for multi-agent systems with uncertain dynamics.

Leader–follower optimal coordination tracking control for multi-agent systems with unknown internal states

This paper investigates optimal coordination tracking control for nonlinear multi-agent systems (NMASs) with unknown internal states by using an adaptive dynamic programing (ADP) method. Actually, the optimal coordination control for MASs depends on the solutions to the coupled Hamilton–Jacobi–Bellman (HJB) equations which are almost impossible to be solved analytically. And what’s worse is that the accurate system models are either infeasible or difficult to obtain in practical applications. To surmount these deficiencies, a neural network (NN) based observer is designed for each agent to reconstruct its internal states by utilizing the measurable input–output data rather than accurate system models. Based on the observed states and Bellman optimality principle, we derive optimal coordination control policies from the coupled HJB equations. In order to implement the proposed ADP method, a critic network framework is proposed for each agent to approximate its value function and help calculate the optimal coordination control policy. Then we prove the local coordination tracking errors and weight estimation errors are uniformly ultimately bounded (UUB) while the approximated control policies converge to their target values. Finally, two simulation examples are given to show the effectiveness of the proposed ADP method.

Event-triggered leader-following tracking control for multivariable multi-agent systems

The paper considers event-triggered leader–follower tracking control for multi-agent systems with general linear dynamics. For both undirected and directed follower graphs, we propose event triggering rules which guarantee bounded tracking errors. With these rules, we also prove that the systems do not exhibit Zeno behavior, and the bounds on the tracking errors can be tuned to a desired small value. We also show that the combinational state required for the proposed event triggering conditions can be continuously generated from discrete communications between the neighboring agents occurring at event times. The efficacy of the proposed methods is discussed using a simulation example.

Robust fault-tolerant cooperative control of multi-agent systems: A constructive design method

This paper investigates the distributed cooperative controller design problem for multi-agent systems in the presence of actuator faults. Both the partial loss of actuator effectiveness and the actuator bias faults are considered. A constructive design method is presented to achieve the synchronization and/or tracking control of multi-agent systems. The control protocol for each agent consists of three modules: the actuator fault detection module, the nominal control module, and the auxiliary control module. The auxiliary control module is activated as soon as the actuator faults are detected. The control protocols are locally distributed in the sense that the control modules designed for each agent only require the information of itself and its neighbors. The loss of symmetry in the digraph Laplacian matrix is also considered. The analysis is suitable for the multi-agent systems with a general directed communication graph. The proposed fault-tolerant control schemes are applied in the formation control of multi-robot systems. Numerical simulation results are presented to show the effectiveness of the proposed control methods.

Robust consensus tracking control for multiagent systems with initial state shifts, disturbances, and switching topologies.

This paper deals with the consensus tracking control issues of multiagent systems and aims to solve them as accurately as possible over a finite time interval through an iterative learning approach. Based on the iterative rule, distributed algorithms are proposed for every agent using its nearest neighbor knowledge, for which the robustness problem is addressed against initial state shifts, disturbances, and switching topologies. These uncertainties are dynamically changing not only along the time axis but also the iteration axis. It is shown that the matrix norm conditions can be developed to achieve the convergence of the considered consensus tracking objectives, for which necessary and sufficient conditions are presented in terms of linear matrix inequalities to guarantee their feasibility in the sense of the spectral norm. Furthermore, simulation examples are given to illustrate the effectiveness and robustness of the obtained consensus tracking results.

Neural network-based adaptive consensus tracking control for multi-agent systems under actuator faults

In this paper, a distributed output feedback consensus tracking control scheme is proposed for second-order multi-agent systems in the presence of uncertain nonlinear dynamics, external disturbances, input constraints, and partial loss of control effectiveness. The proposed controllers incorporate reduced-order filters to account for the unmeasured states, and the neural networks technique is implemented to approximate the uncertain nonlinear dynamics in the synthesis of control algorithms. In order to compensate the partial loss of actuator effectiveness faults, fault-tolerant parts are included in controllers. Using the Lyapunov approach and graph theory, it is proved that the controllers guarantee a group of agents that simultaneously track a common time-varying state of leader, even when the state of leader is available only to a subset of the members of a group. Simulation results are provided to demonstrate the effectiveness of the proposed consensus tracking method.

Distributed Tracking Control for Multi-Agent Systems Under Two Types of Attacks

This paper studies a distributed consensus tracking control problem for a class of stochastic linear multi-agent systems subject to two types of attacks. The problem boils down to how to achieve robust consensus tracking of multi-agent systems with switching connected and disconnected directed topologies under attacks. The attacks on the edges instead of nodes lead to the loss of consensus tracking security. Based on a multi-step design procedure for designing a distributed secure algorithm, sufficient conditions on robust mean-square exponential consensus tracking are derived via the idea of average dwell time switching between some stable and unstable subsystems obtained from graph theory analysis. An applicaton to a practical power system is considered. It is proved that each distributed generator (DG) modeled as an agent in a microgrid can successfully synchronize their terminal voltage amplitude to a prespecified reference value under these two types of attacks.

Finite-Time Distributed Tracking Control for Multi-Agent Systems With a Virtual Leader

This paper aims at further investigating the finite-time distributed tracking control problems for multi-agent systems with a virtual leader under the conditions of fixed and switching topologies, respectively. Two continuous distributed tracking protocols are designed for tracking the virtual leader in finite time. Compared with the traditional distributed tracking protocols, the proposed distributed tracking protocols can reach consensus in finite time. In particular, to eliminate the chattering phenomenon occurred in non-Lipschitz dynamical systems, this paper introduces a saturation function to replace the original sign function in the proposed distributed tracking protocols. The improved protocols can guide all agents to track the virtual leader without chattering phenomenon in finite time for the same position. Numerical simulations are also given to validate the proposed distributed tracking protocols.

Distributed finite-time tracking control for multi-agent systems: An observer-based approach

This paper addresses the distributed finite-time tracking control problem for second-order multi-agent systems. First, we propose a finite-time tracking protocol for multi-agent systems by using state feedback. Then, a new class of observer-based control algorithms are designed for achieving finite-time consensus tracking in multi-agent systems with a single active leader, where each agent can only share its position states with its neighbors. Within the same context, the present control algorithms are then extended to solve the finite-time containment tracking problem for multi-agent systems in the presence of multiple active leaders. It is theoretically shown that the position states of the followers will converge to that of the leader or a convex hull spanned by those of the leaders, respectively, in finite time. Furthermore, the finite-time formation control problem is discussed. The effectiveness of the results is also illustrated by numerical simulations.

Collective tracking control for multi-agent system on balanced graphs

In this paper, we consider a collective tracking problem of a multi-agent system which has a varying-velocity leader and evolves on balanced information topologies. First, we propose a coordination-variable-based control strategy for every agent to track the leader whose state may not be measured. Moreover, from a collective behavior perspective, a new decomposition method is utilized to decompose the resulting closed-loop system into two subsystems, and a novel measure also is introduced to characterize collective tracking performance of the system. Finally, we prove that the proposed control strategy can not only estimate the tracking errors but also increase the introduced measure to improve collective tracking performance even under the case of balanced information topologies. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society