Consensus for heterogeneous networked multi-agent systems with switching topology and time-varying delays

A cooperative actuator fault accommodation strategy for a team of linear time-invariant (LTI) multi-agent systems with a switching topology and directed communication network graph is studied in this paper. The faults could occur in more than one agent simultaneously and the fault severity is not needed to be precisely estimated. The proposed fault accommodation strategy is performed in two levels: the agent level fault recovery (ALFR) and the team level fault recovery (TLFR). Whenever a fault is detected, the recovery strategy is to locally recover faulty agents based on inaccurate estimates of the faults in the first step and to reconfigure the weights of the information flow graph in the second step. The proposed strategy is based on the sub-optimal solution of a bi-linear matrix inequality (BMI) and guarantees the consensus achievement of the team. The stability properties of the proposed controller and the recovery strategy are investigated based on Lyapunov analysis. The effectiveness of our proposed consensus algorithm is illustrated by performing numerical simulations for a team of ten agents and the performance of our strategy is compared with the centralized and decentralized fault recovery approaches in the literature.

In this paper, we are concerned with the problem of containment control for a class of nonlinear multi-agent system. The local dynamics under consideration is governed by a nonlinear system with time delays and white Gaussian noise. The multi-agent system consists of both leaders and followers, and the containment control protocol proposed is an interaction between the leaders and followers characterised by time-varying delays and switching topology. Under a certain assumption on the connectivity of the whole network, by constructing a Lyapunov–Krasovskii functional, and using the average dwell time approach and some new analytical techniques, the sufficient conditions are established to ensure that each follower converges in mean square to the convex hull spanned by the leaders. A numerical example is presented to illustrate the effectiveness of the theoretical results.

In this paper, we mainly focus on developing a new paradigm motivated by investigating the consensus problem of networked Lagrangian systems with unknown time-varying delay and switching topologies. We propose a class of dynamic feedback by adding differentiators to accommodate the discontinuity and uncertainty resulting from time-varying delay and switching topologies, yielding arbitrary times differentiable reference velocities. Using these reference velocities, we develop delay/topology-independent adaptive controllers with arbitrary times differentiable control torques for networked Lagrangian systems. This specific practice motivates the formulation of a new paradigm, referred to as forwardstepping, for handling discontinuity, time-varying uncertainty, and unavailable state measurement in control systems.

Nonlinear Multi-Agent System Consensus with Time-Varying Delays

Consensusability of multi-agent systems with time-varying communication delay

The problem of intelligent L2-L∞ consensus design for leader-followers multiagent systems (MASs) under switching topologies is investigated based on switched control theory and fuzzy deep Q learning. It is supposed that the communication topologies are time-varying, and the model of MASs under switching topologies is constructed based on switched systems. By employing linear transformation, the problem of consensus of MASs is converted into the issue of L2-L∞ control. The consensus protocol is composed of the dynamics-based protocol and learning-based protocol, where the robust control theory and deep Q learning are applied for the two parts to guarantee the prescribed performance and improve the transient performance. The multiple Lyapunov function (MLF) method and mode-dependent average dwell time (MDADT) method are combined to give the scheduling interval, which ensures stability and prescribed attenuation performance. The sufficient existing conditions of consensus protocol are given, and the solutions of the dynamics-based protocol are derived based on linear matrix inequalities (LMIs). Then, the online design of the learning-based protocol is formulated as a Markov decision process, where the fuzzy deep Q learning is utilized to compensate for the uncertainties and achieve optimal performance. The variation of the learning-based protocol is modeled as the external compensation on the dynamics-based protocol. Therefore, the convergence of the proposed protocol can be guaranteed by employing the nonfragile control theory. In the end, a numerical example is given to validate the effectiveness and superiority of the proposed method.

Admissible consensus problems for high-order linear time-invariant descriptor multi-agent systems with switching topologies are dealt with. Firstly, by the state projection on the consensus subspace and the complement consensus subspace, admissible consensus problems are converted into admissible problems of a reduced-order switching subsystem, and an explicit expression of the consensus function is presented based on the First Equivalent Form. Secondly, a necessary and sufficient condition for admissible consensualization is proposed, which can guarantee the scalability of descriptor multi-agent systems since it is independent of the number of agents. Finally, numerical simulations are presented to illustrate theoretical results.

This paper investigates an observer-based control strategy for networked multi-agent systems with general linear dynamics and time-varying communication delays in a sampling setting. The communication topology is assumed to be directed fixed. Different from a traditional observer-based controller for a single system, the objects that need to be observed here are the state differences between an agent and its neighbours. Using a system transformation method, some equivalent conditions concerning the consensus of multi-agent systems are established. Moreover, we prove that both the connection weights and the communication topology play an important role in the study of multi-agent systems, and establish a linear matrix inequality based observer design method.

Distributed adaptive time-varying formation for multi-agent systems with general high-order linear time-invariant dynamics

Time-varying group formation-tracking control for general linear multi-agent systems with switching topologies and varying time delays is studied in this paper. Due to the deferent effects in coordinated problem, the agents in group formation-tracking are divided into two roles, leaders and followers, respectively. The followers are allowed to achieve the expected subgroup formation and, in the meantime, tracking the trajectory of the leaders in each group. Firstly, utilizing the neighboring information, the observers is proposed for each follower to estimate the leader’s state in the subgroup. Based on the transformed of the estimated error and Lyapunov theory, the effectiveness of the proposed observer is proven. Secondly, by incorporating the state observer in the formation-tracking protocol, the novel controller is put forward to solve the group formation-tracking problem under the influence of both time-varying delays and switching networks. Then, an algorithm to determine the gain matrix is presented, and the convergence the of group formation error is also demonstrated. Finally, a numerical simulation result is given to verify the practical of the theoretical results.

We consider multi-agent systems with time-varying delays and switching interconnection topologies. By constructing a suitable Lyapunov—Krasovskii functional and using the reciprocally convex approach, new delay-dependent consensus criteria for the systems are established in terms of linear matrix inequalities (LMIs), which can be easily solved by using various effective optimization algorithms. Two numerical examples are given to illustrate the effectiveness of the proposed methods.

This paper investigates the consensus problem for multiagent systems with time-varying delays. The bounded delays can be arbitrarily fast time-varying. The communication topology is assumed to be undirected and fixed. With general linear dynamics under average state feedback protocols, the consensus problem is then transformed into the robust control problem. Further, sufficient frequency domain criteria are established in terms of small gain theorem by analyzing the delay dependent gains for both continuous-time and discrete-time systems. The controller synthesis problems can be solved by applying the frequency domain design methods. Numerical examples are demonstrated to verify the effectiveness of the proposed approaches.

This paper studies the consensus problem of heterogeneous linear multiagent systems with arbitrarily large constant, time-varying, or distributed communication delays. Novel distributed dynamic controllers are proposed for such multiagent systems with fixed and switching directed communication topologies, respectively. It is shown that the controlled heterogeneous linear multiagent system can reach consensus for arbitrarily large constant, time-varying, and distributed communication delays under some sufficient conditions. Simulation examples are provided to demonstrate the effectiveness of the proposed controllers.

This article considers the controllability problem for multi-agent systems. In particular, the structural controllability of multi-agent systems under switching topologies is investigated. The structural controllability of multi-agent systems is a generalisation of the traditional controllability concept for dynamical systems, and purely based on the communication topologies among agents. The main contributions of this article are graph-theoretic characterisations of the structural controllability for multi-agent systems. It turns out that the multi-agent system with switching topology is structurally controllable if and only if the union graph 𝒢 of the underlying communication topologies is connected (single leader) or leader–follower connected (multi-leader). Finally, this article concludes with several illustrative examples and discussions of the results and future work.

The paper studies the consensus problem of heterogeneous multi-agent systems with time-delay, both a constant and time-varying delay are considered. For the heterogeneous multi-agent systems composed of the first-order agents and second-order agents, a novel PI-like protocol is designed to guarantee all the agents can reach consensus asymptotically by using Lyapunov stability theory, graph theory and matrix theory. The communication topology is assumed to have a directed spanning tree. An example with simulation is presented to illustrate the effectiveness of the proposed results.