Leader-following consensus of multi-agent systems under fixed and switching topologies ☆

Distributed consensus tracking is addressed in this paper for multi-agent systems with Lipschitz-type node dynamics. The main contribution of this work is solving the consensus tracking problem without the assumption that the topology among followers is strongly connected and fixed. By using tools from M-matrix theory, a class of consensus tracking protocols based only on the relative states among neighboring agents is designed. By appropriately constructing Lyapunov function, it is proved that consensus tracking in the closed-loop multi-agent systems with a fixed topology having a directed spanning tree can be achieved if the feedback gain matrix and the coupling strength are suitably selected. Furthermore, with the assumption that each possible topology contains a directed spanning tree, it is theoretically shown that consensus tracking under switching directed topologies can be achieved if the control parameters are suitably selected and the dwell time is larger than a positive threshold. The results are then extended to the case where the communication topology contains a directed spanning tree only frequently as the system evolves with time. Finally, some numerical simulations are given to verify the theoretical analysis.

Consensus Tracking of Multi-Agent Systems With Lipschitz-Type Node Dynamics and Switching Topologies

This paper addresses the fixed-time leader–follower consensus problem for high-order integrator multiagent systems subject to matched external disturbances. A new cascade control structure, based on a fixed-time distributed observer, is developed to achieve the fixed-time consensus tracking control. A simulation example is included to show the efficacy and the performance of the proposed control structure with respect to different initial conditions.

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Fixed-Time Consensus Tracking for Multiagent Systems With High-Order Integrator Dynamics

Multi-agent systems (MASs) have received tremendous attention from scholars in different disciplines, including computer science and civil engineering, as a means to solve complex problems by subdividing them into smaller tasks. The individual tasks are allocated to autonomous entities, known as agents. Each agent decides on a proper action to solve the task using multiple inputs, e.g., history of actions, interactions with its neighboring agents, and its goal. The MAS has found multiple applications, including modeling complex systems, smart grids, and computer networks. Despite their wide applicability, there are still a number of challenges faced by MAS, including coordination between agents, security, and task allocation. This survey provides a comprehensive discussion of all aspects of MAS, starting from definitions, features, applications, challenges, and communications to evaluation. A classification on MAS applications and challenges is provided along with references for further studies. We expect this paper to serve as an insightful and comprehensive resource on the MAS for researchers and practitioners in the area.

Multi-Agent Systems: A Survey

Fixed-time cooperative control is currently a hot research topic in multiagent systems since it can provide a guaranteed settling time, which does not depend on initial conditions. Compared with asymptotic cooperative control algorithms, fixed-time cooperative control algorithms can achieve better closed-loop performance and disturbance rejection properties. Different from finite-time control, fixed-time cooperative control produces the faster rate of convergence and provides an explicit estimation of the settling time independent of initial conditions, which is desirable for multiagent systems. This paper aims at presenting an overview of recent advances in fixed-time cooperative control of multiagent systems. Some fundamental concepts about finite- and fixed-time stability and stabilization are first recalled with insight understanding. Then, recent results in finite- and fixed-time cooperative control are reviewed in detail and categorized according to different agent dynamics. Finally, this paper raises several challenging issues that need to be addressed in the near future.

An Overview of Recent Advances in Fixed-Time Cooperative Control of Multiagent Systems

Resilient leader-following consensus in continuous double-integrator multi-agent systems is considered in this paper. To realize global objectives, all agents need to communicate with their neighbors, which can be vulnerable to malicious attacks. In spite of the presence of malicious agents, the benign ones aim to follow the leader. With regards to this, a resilient leader-following consensus protocol is presented. Under certain topology condition, the proposed protocol can guarantee that the resilient leader-follower consensus is achieved. Simulation results are finally given to demonstrate the validity of theoretical results.

Resilient Leader-Following Consensus of Continuous Second-order Multi-agent Systems With Malicious agents

In this paper, we investigate distributed fault detection (FD) problem for a group of heterogeneous agents with internal model controllers. In order to avoid utilizing solutions of complicated matrix equations in the fault detection (FD) module, we design a distributed internal model control law with a state estimator additionally, and design observers for the MAS closed-loop system formed by the designed control law to generate residuals to detect the faulty agent, where the observer feedback information just contains itself and its neighbors’ state and state estimate information, then the utilization of solutions of matrix equations is avoided. Finally, a numerical example is utilized to verify effectiveness of the proposed distributed FD scheme, where the faulty agent will be detected in time, and the designed control law will realize cooperative output regulation (COR) if no fault occurs.

Distributed Fault Detection for A Class of Heterogeneous Agents with Internal Model Controllers

The minimal-order problem of the dynamic output regulators of linear time-invariant systems is considered, and a lower bound for the minimal-order is given. Unlike in previous works, the lower bound presented is a simple function of the system dimension and ranks of the input and output matrices, computation involves neither a rank minimization problem nor a semi-definite programming problem. An example is given to illustrate the non-conservativeness of the lower bound.

On the minimal-order of dynamic output regulators

In this paper the tracking problem with reference tracking signals and input signals being written as the form of Fourier series is considered. A method of feedforward tracking control based on the frequency preserving property of stable linear system is proposed. A direct relationship between control input and reference output for linear system is given which can be expressed as the linear transformation of Fourier coefficients between them. A quadratic performance with combined constraints of tracking error and control input is presented and the equivalence between the optimal problem under this performance and the least mean square problem is established.

The feedforward tracking control for linear systems with quadratic performance

This paper investigates a fault-tolerant leaderless consensus problem for general linear multi-agent systems (MASs) under a strongly connected directed communication graph. The influences of the actuator bias faults and loss of actuator effectiveness faults on MASs are considered in this paper. The designed fully distributed adaptive fault-tolerant consensus protocols (FTCPs) can make all agents' states achieve consensus, asymptotically. Using the features of the loss of actuator effectiveness faults and the strongly connected graph, novel positive definite Lyapunov functions are constructed skillfully to analyse the validity of the proposed protocols. Finally, simulation examples are presented to demonstrate the effectiveness of the proposed protocols.

Fully Distributed Fault-Tolerant Leaderless Consensus of Multi-Agent Systems Under Directed Communication Graph

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