Consensus Of Nonlinear Multi-agent Systems Research Articles

Consensus of Nonlinear Multi-Agent Systems with an Arbitrary Communication Delay

Consensus of Nonlinear Multi-Agent Systems with an Arbitrary Communication Delay

Observer-based consensus for nonlinear multi-agent systems with intermittent communication

The article studies a consensus control problem for second-order nonlinear multi-agent systems with a leader where the velocity of the active leader cannot be obtained in real time. Under the common assumption that the multiple agents can communicate with their neighbors only during a sequence of discontinuous time intervals, a new neighbour-based consensus control protocol based on observers is developed for each agent. With the help of multiple Lyapunov function technology, some sufficient conditions are derived such that the follower agents can track the leader and keep pace with the leader at the same time under fixed topology. Moreover, the similar results are given under the switching topology. Finally, numerical examples are presented for illustration.

Sampled-data leader-following consensus for nonlinear multi-agent systems with Markovian switching topologies and communication delay

This paper is concerned with sampled-data leader-following consensus of nonlinear multi-agent systems with random switching network topologies and communication delay. By modeling the switching of network topologies by a Markov process and considering the effect of communication delay, a new sampled-data consensus control protocol with variable sampling period is proposed. With this protocol, the leader-following consensus problem is equivalently converted to the stability of a class of Markovian jump systems with a time-varying delay. Then, by employing Lyapunov–Krosovskii functional method and the weak infinitesimal operation, a new delay-dependent stability criterion is derived, which ensures that the leader-following consensus can be globally exponentially achieved in mean-square sense. Based on this criterion, the switching consensus controller gains are obtained by solving a set of linear matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness of the design method.

Consensus of nonlinear multi-agent systems with observer-based protocols

This paper is concerned with distributed pinning consensus problem for a class of nonlinear multi-agent system with observer-based protocols. Two types of state observers including local observer and distributed pinning observer are proposed for the single nonlinear agent with the first one designed by the local output information and the second one designed via the relative output information of its neighboring agents. According to the state information observed, a distributed pinning observer-based protocol is proposed for the leader-following consensus of the multi-agent system. Furthermore, two multi-step algorithms are presented to construct the observer gains and the protocol parameters for the proposed protocols respectively. It is shown that under the condition that the pinning joint communication topology contains a directed spanning tree, the sufficient criteria established can not only ensure the observation error to be globally asymptotically stable, but also guarantee the consensus of the multi-agent system to be solved asymptotically. Finally, two numerical examples are provided to demonstrate the effectiveness of the observer-based protocols.

Second-order consensus of nonlinear multi-agent systems with restricted switching topology and time delay

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.

Consensus of nonlinear multi-agent systems with self and communication time delays: A unified framework

In this paper, we study the consensus problem of multi-agent systems with parametric uncertainties on directed graph communication topologies containing a spanning tree. The challenge lies in that the input–output property of a strictly proper system transfer function involving self and communication delays and the extremum of a delay-involved transfer function are both unclear. By establishing a new input–output property of the delay-involved strictly proper transfer function and applying a constructive approach in frequency domain, we obtain the extremum of the delay-involved transfer function, upon which, we establish a unified framework to resolve the consensus problem of multi-agent systems with parametric uncertainties and time delays, and the terminal convergence point value is achieved. Based upon Lyapunov stability theory and frequency domain input–output analysis, we demonstrate that the proposed unified consensus control framework ensures scaled weighted average consensus with the integral action of the synchronization signal vector. Simulation results are provided to demonstrate the effectiveness of the proposed consensus scheme.

Leader‐following consensus of non‐linear multi‐agent systems with jointly connected topology

The leader-following consensus of non-linear multi-agent systems is investigated in this study. The authors further study this problem without the assumption that the topology among followers is connected or fixed. Based on a representative general non-linear model, they address such a leader-following consensus issue from a new perspective and then obtain several basic criteria for the consensus of the non-linear multi-agent system. Simultaneously, the simplified conditions of its corresponding linear multi-agent systems for achieving consensus are derived. Finally, numerical examples are presented to verify the theoretical analysis.

Fuzzy Modelling and Consensus of Nonlinear Multiagent Systems With Variable Structure

The consensus problem of multiagent nonlinear systems (MANNs) with variable structure is discussed in this paper. T-S fuzzy models are first presented to describe MANNs with variable structure. The nodes of each T-S fuzzy model are rearranged so that the global fuzzy model is decomposed into independent and small-scale fuzzy models. It is shown that the consensus of the global fuzzy model is equivalent to that of its corresponding small-scale fuzzy models in which the continuous and sampled controllers are applied. Sufficient conditions are derived to ensure the consensus of the controlled fuzzy models. Finally, simulation results are given to illustrate the effectiveness of the proposed criteria.

Robust homogenization and consensus of nonlinear multi-agent systems

In this paper, we consider consensus of a group of heterogeneous agents with nonlinear dynamics in the presence of system uncertainties. It requires that all agent states reach an agreement which is governed by specified reference dynamics. However, the reference dynamics do not generate a specific reference trajectory for feedback regulation for any agent. For this purpose, the proposed controller integrates two fundamental actions, homogenization and consensus, concurrently. On one hand, it asymptotically regulates each individual (heterogeneous, nonlinear, and uncertain) agent dynamics to the common reference dynamics using a robust homogenization technique; on the other hand, it aligns agent trajectories, asymptotically governed by the common reference dynamics, to consensus through network cooperation. The effectiveness of the controller is verified in the rigorous proof and numerical simulation.

Eigenvalue Based Approach for Global Consensus in Multiagent Systems with Nonlinear Dynamics

This paper addresses the global consensus of nonlinear multiagent systems with asymmetrically coupled identical agents. By employing a Lyapunov function and graph theory, a sufficient condition is presented for the global exponential consensus of the multiagent system. The analytical result shows that, for a weakly connected communication graph, the algebraic connectivity of a redefined symmetric matrix associated with the directed graph is used to evaluate the global consensus of the multiagent system with nonlinear dynamics under the common linear consensus protocol. The presented condition is quite simple and easily verified, which can be effectively used to design consensus protocols of various weighted and directed communications. A numerical simulation is also given to show the effectiveness of the analytical result.

Consensus for nonlinear multi-agent systems with sampled data

This paper deals with the consensus problems of multi-agent systems with nonlinear dynamics and sampled data information. The control input of each agent is based on the information of its neighbors at discrete sampling instants rather than the whole continuous process. An input delay approach is utilized to transform the sampling data into the time-varying delayed data. A novel time-dependent Lyapunov functional consisting of the continuous term and the discontinuous term is proposed. Tools like matrix theory, algebraic graph theory, relaxed matrix approach, and convex analysis technique are utilized to derive the sufficient conditions. The estimated upper bound of the sampling interval can be obtained by the proposed conditions. Then, the necessary and sufficient conditions for consensus in systems with linear dynamics are presented. It is shown that the consensus conditions depend on the parameters of the sampling interval, spectra of the Laplacian matrix, and coupling strength. The effectiveness of the proposed design method is demonstrated by the simulation examples.

Adaptive Third-Order Leader-Following Consensus of Nonlinear Multi-agent Systems with Perturbations

We investigate the third-order leader-following consensus problem of nonlinear multi-agent systems in undirected network topologies. Based on graph theory and Lyapunov stability theory, the adaptive control method is employed to achieve leader-following consensus in an undirected network of agents with nonlinear third-order dynamics against the perturbations. Simulation examples validate the correctness of the results and show that the control gains have a great influence on the convergence performance of errors for a short time.

Second-order leader-following consensus of nonlinear multi-agent systems via pinning control

Without assuming that the interaction diagraph is strongly connected or contains a directed spanning tree, this paper studies the second-order leader-following consensus problem of nonlinear multi-agent systems with general network topologies. Based on graph theory, matrix theory, and LaSalle’s invariance principle, a pinning control algorithm is proposed to achieve leader-following consensus in a network of agents with nonlinear second-order dynamics. Furthermore, a pinning consensus protocol is developed for coupled double-integrators with a constant reference velocity. In particular, this paper addresses what kind of agents and how many agents should be pinned, and establishes some sufficient conditions to guarantee that all agents asymptotically follow the virtual leader. Numerical simulations are given to verify the theoretical analysis.