Consensus for multi-agent systems with inherent nonlinear dynamics under directed topologies

This paper studies fixed-time consensus of second-order leader-following multi-agent systems with inherent nonlinear dynamics. Firstly, a new fixed-time consensus protocol is designed to solve the tracking problem of the second-order nonlinear systems. By using Lyapunov theory and graph theory, we choose a different Lyapunov function candidate to verify the theoretical results. Then we consider the second-order multi-agent systems with multiple leaders and propose a new protocol to solve the fixed-time containment control problem. Finally, two numerical examples are proposed to demonstrate the effectiveness of the proposed fixed-time protocols.

This letter focuses on the problem of leader-following consensus of second-order Multi-Agent Systems (MAS) with switching topology and partial aperiodic sampled data. MAS are subject to various constraints related to information exchange among the agents. It is considered that each agent in the network is able to measure its position only and cannot measure either its velocity or acceleration (input). Moreover, the position information is sent to the neighbors at aperiodic and asynchronous sampling rates. At last, a switching communication topology among the agents is considered. An observer-based control protocol is proposed to achieve leader-following consensus for MAS with above mentioned constraints. Using an Average Dwell Time (ADT) approach, sufficient conditions are derived through Lyapunov-based stability analysis to ensure the leader-following consensus. Numerical examples are also included to show the effectiveness of the proposed scheme.

In this paper, a distributed protocol based on only relative position information is proposed for consensus of second-order multi-agent systems with inherent nonlinear dynamics and communication time delay. Compared with previous works, the distinguished feature of the paper lies in the directed interaction topology that is switching according to average dwell time (ADT) switching signals. Under the proposed protocol, we not only present sufficient conditions for ensuring consensus, but also explicitly give the lower bound of ADT for admissible switching signals. Numerical examples are provided to illustrate the performance of the proposed consensus algorithm.

In this manuscript, the stability and consensus problem of the leader-following multi-agent system is studied. The state information of the leader is only available to the dynamics of all the followers, while the communication among the agents occurs at sampling instant. The innovative part of this paper is to reach the consensus and attain the stability for prescribed MASs with interval time varying delay using impulsive control in the presence of leader. The interaction between the agent is illustrated by an undirected graph. A class of distributed impulsive protocol relying on sampling information is suggested to reach the leader following consensus. The consensus is critically relying on the sampling period, control gains. By performing the similar procedures, the consensus problem of multi-agent system is converted to stability problem of the error system. By utilizing the stability theory of impulsive systems, algebraic graph theory, sufficient conditions are derived to guarantee the leader-following consensus of the multi-agent system. Terminally, a numerical example is given to show an efficacy of this presented approach and the sureness of theoretical analysis.

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.

As a new area of research, consensus problems for multi-agent systems have been studied extensively in the literature. It is usually assumed that all agents share a common one-dimensional state space. The authors of this study concentrate on the consensus problems of multi-agent systems in the framework of high-dimensional state space. As a basis for the analysis, a general model is first introduced by presenting two typical examples along with some necessary and sufficient conditions for the system to solve a consensus problem. Then the structures of consensus functions are investigated and some algebraic characterisations are given. Finally, a class of switched multi-agent systems are discussed and some sufficient conditions for the possession of the consensus property are provided. Several examples to illustrate the effectiveness of theoretical results are given.

In this paper, high order consensus problem of multi-agent systems with non-identical unknown nonlinear dynamics following an unknown and nonlinear leader is investigated in networks with fixed and switching topologies. By parameterizations of unknown nonlinear dynamics of agents in the system, neighbor-based adaptive consensus algorithms are proposed by incorporating consensus errors in addition to relative position feedback. Base on algebraic graph theory, Lyapunov theory, Riccati inequalities and PE condition, analysis of stability and parameter convergence of the proposed algorithm are conducted. Finally, a simulation in switching networks is worked out to illustrate the effectiveness of the theoretical results.

<abstract><p>This article considers a consensus problem of multiagent systems with double integrator dynamics under nonuniform sampling. In the considered problem, the maximum sampling time can be selected arbitrarily. Moreover, the communication graph can change to any possible topology as long as its associated graph Laplacian has eigenvalues in an arbitrarily selected region. Existence of a controller that ensures consensus in this setting is shown when the changing topology graphs are undirected and have a spanning tree. Also, explicit bounds for controller parameters are given. A sufficient condition is given to solve the consensus problem based on making the closed loop system matrix a contraction using a particular coordinate system for general linear dynamics. It is shown that the given condition immediately generalizes to changing topology in the case of undirected topology graphs. This condition is applied to double integrator dynamics to obtain explicit bounds on the controller.</p></abstract>

This paper deals with the consensus problem of the second-order multi-agent systems based on linear system theory. By a system transformation, the consensus problem is converted to the stability problem of a linear system. The second-order systems considered include the systems with both the fixed topology and the Markov switching topology. Necessary and sufficient conditions of consensus or mean square consensus are obtained. The results are extended to the cases of the uncertain transition probability rates and time-delay, respectively. Finally, a simulation example is given to show the effectiveness of the presented results.

Consensus conditions for heterogeneous multi-agent sampled-data control systems with nonlinearities and inter-agent communication delay.

This article is aimed at solving leader-following consensus problem with an event-based sliding mode controller. The proposed control technique is partitioned into two parts – a finite time consensus problem and an event-based control mechanism. Leader-following heterogeneous multi-agents of first order having inherent nonlinear dynamics have been analysed to demonstrate efficacy and robustness of the proposed controller. In the first part, states of the follower agents have been attempted to be kept in consistence with those of the virtual leader using sliding mode control. In the second part, an event-based implementation of the control law has been incorporated to minimise the computational load on, and energy expenditure of the computational device equipped with the agents, while ensuring that the desired closed-loop performance of the system is not compromised. The advantage of using such a scheme, i.e. an event-based sliding mode controller, lies in the robustness capabilities of sliding mode controller and reduced computational expense of event-based mechanism. Numerical simulations and mathematical foundations ascertain the effectuality of the controller proposed herein.

With the development of swarm intelligence in last decades, consensus problem of multi-agent systems has been attracting much attention. To reveal the inherent mechanism of leader-following consensus in multi-agent systems with stochastic dynamics, PI control protocols are designed in this paper. Owing to the stochastic analysis techniques, algebraic graph theory, and constructing appropriate Lyapunov function, it is proved that the leader-following consensus of nonlinear stochastic dynamical multi-agent systems can be reached in mean square. Sufficient condition are deduced to select the PI control protocol parameters. Finally, the theoretical results are demonstrated through a simulation example.

The group consensus problem for fractional-order multiagent systems is investigated in this paper. With the help of double-tree-form transformations, the group consensus problem of fractional-order multiagent systems is proved to be equivalent to the asymptotical stability problem of reduced-order error systems. A class of distributed control protocols and some simple LMI sufficient conditions as well as necessary and sufficient conditions are proposed in this paper to solve the group consensus problem for fractional multiagent systems. Moreover, pinning control strategy has been taken into consideration. It is shown that the system converges more rapidly when the designed pinning protocols are adopted. In addition, the case of fractional system with switching topologies is also discussed and some corresponding sufficient conditions are obtained. Finally, some simulation results are presented to illustrate the theoretical results.

This paper mainly investigates the second-order group consensus for multi-agent systems with or without time-varying delays based on using the second-order neighbours' information. For the case without time-delays, it is shown that the sufficient conditions in form of Kronecker product can be obtained to achieve the given group consensus if the two subnetworks G <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , G <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> of virtual network G are balanced couple. The error system is adopted to solve the group consensus problems for multi-agent systems with time-varying delays. The ultimate results are worked out by Lyapunov functions. Finally, some illustrate examples are proved to demonstrate the effectiveness of the theoretical findings.

This paper focuses on the consensus problem in a decentralized multi-agent system with switching communication topologies. Consensus of agents can be reached for centralized dynamically switching topologies when the union of all topologies forms a spanning tree graph. In case of decentralized control, the topology must form a strongly connected graph to reach consensus. A new algorithm, which uses “back-stepping” of agents, is proposed in this work which assures consensus whenever the topology is not strongly connected. The algorithm ensures that when an agent reaches a position where if loses communication with others and the topology is no more a strongly connected graph, it back-tracks and take a different path to reach consensus. Simulation results show that after introducing back-stepping, each of the agent's path is chosen to ensure that communication with other agents is maintained and they come to a consensus in minimum possible time.