Non-identical Nonlinear Dynamics Research Articles

Novel Reference Trajectory-Based Finite-Time Consensus Protocols for Multiagent Systems With Non-Identical Nonlinear Dynamics

This paper investigates the finite-time consensus for second-order multiagent systems under directed networks, where each agent is described by a non-identical nonlinear system. By using the reference trajectory-based method, two novel protocols are developed for the leader-follower and leaderless cases, respectively. It is noted that the dynamical evolutions of each agent's state and the reference trajectory are coupled, and the information of reference trajectories is not allowed to transmit in the communication channels. By the developed protocols, the relative state errors among agents can converge to the origin (instead of a neighborhood of the origin) within a finite time, though there are unknown parameters in agents' dynamics. The nonlinear terms in agents' dynamics are not required to be bounded by known constants or functions, which invalidates many consensus schemes based on the sliding mode control. Using the graph theory, Lyapunov functional method and finite-time stability theory, sufficient conditions are established for the finite-time consensus of considered multiagent systems. Finally, simulation examples are given to validate the effectivity of the proposed protocols.

Adaptive event-triggered group consensus of multi-agent systems with non-identical nonlinear dynamics

The paper is concerned with mean-square group consensus for second-order multi-agent systems with non-identical dynamics, where the agents in the same group have the identical dynamics, the agents in the different groups have non-identical nonlinear dynamics. To reduce the update frequency of event-triggered controller, a novel adaptive dynamic event-triggered communication scheme is presented based on the local stochastic sampled information. The proposed event-triggered conditions of the position state and velocity state have be given separately owe to their state ranges may be different, which lead to the position state and velocity state with different event-triggered instants and release intervals. The event-triggered matrices and time-varying event-triggered parameters are introduced into event-triggered conditions, the given event-triggered conditions are detected only at discrete sampled times, which means Zeno behavior can be excluded. A novel distributed protocol is designed based on the neighboring agents information of the position state and velocity state at event-triggered instants. The group consensus issue can be transformed into the convergence problem of the augmented error system. Then some mean-square group consensus criteria can be derived with the help of tools from graph theory and matrix analysis, and the event-triggered matrices can be obtained by solving some linear matrix inequalities. Finally, two numerical examples are employed to show the validity and advantage of the proposed transmission scheme.

Distributed Error Estimation for Quasi-Synchronization of Heterogeneous Dynamical Networks

This article proposes a distributed error estimation approach to investigate the quasi-synchronization problem of heterogeneous dynamical networks with static and adaptive coupling laws under a directed communication topology. By introducing a pining control strategy, a novel class of distributed error estimation algorithms is proposed for solving the quasi-synchronization problem of heterogeneous dynamical networks with a static coupling law by exploring the local information among the neighboring nodes. By removing the assumption that the smallest real part of the nonzero eigenvalues of the Laplacian matrix associated with the communication graph must be known, we also address the case of the quasi-synchronization of heterogeneous dynamical networks with nonidentical nonlinear dynamics and an adaptive coupling law. It is proved, in the sense of Lyapunov function, that the distributed error estimation for the quasi-synchronization problem of heterogeneous dynamical networks with static and adaptive coupling laws will be achieved with a bounded synchronization error level. Finally, two examples are presented to demonstrate the effectiveness of the proposed approaches.

Distributed cooperative neural control of a class of nonlinear multi‐agent systems with unknown time‐varying control coefficient

SummaryThis article studies the leader–follower cooperative tracking problem of a class of multi‐agent systems with unknown nonlinear dynamics. As the load of the following agent may be changing throughout the whole work process, we consider the control coefficient of the following agent to be time‐varying and nonlinear instead of constant, which is more practical. All agents are connected by the directed communication graph with weighted topology. The followers can have unknown nonidentical nonlinear dynamics and external disturbances. The nonautonomous leader generates the reference trajectory for only part of the followers and others can only receive the information from their neighbors. To achieve the ultimate synchronization of all following agents to the leader, the novel cooperative adaptive control protocols are designed based on the neural approximation and adaptive updating mechanism. A novel singularity‐avoided adaptive updating law is proposed to estimate the control coefficient and compensate for the unknown dynamics online. Lyapunov theory is used to prove the ultimate boundedness of the synchronization tracking error. The correctness and effectiveness of the presented control scheme are demonstrated by two simulations in SISO and MIMO cases, respectively.

Asynchronous Quasi-Consensus of Heterogeneous Multiagent Systems With Nonuniform Input Delays

This paper analyzes the consensus problem in heterogenous nonlinear multiagent systems. The multiagent systems not only have nonidentical nonlinear dynamics for all agents, but also have different network topologies for position and velocity interactions. An asynchronous sampled-data control without any input delays is first proposed, the information of each agent is only sampled at its own sampling instants and need not be sampled at other sampling instants. Then, quasi-consensus in heterogenous multiagent systems is proved by Lyapunov stability theory. When asynchronous sampled-data control has nonuniform input delays, sufficient conditions for quasi-consensus in heterogenous multiagent systems are further obtained. The upper bound of quasi-consensus errors is estimated. Finally, numerical simulations are provided to verify the effectiveness of theoretical results.

Robust cooperative learning control for directed networks with nonlinear dynamics

This paper studies a class of robust cooperative learning control problems for directed networks of agents (a) with nonidentical nonlinear dynamics that do not satisfy a global Lipschitz condition and (b) in the presence of switching topologies, initial state shifts and external disturbances. All uncertainties are not only time-varying but also iteration-varying. It is shown that the relative formation of nonlinear agents achieved via cooperative learning can be guaranteed to converge to the desired formation exponentially fast as the number of iterations increases. A necessary and sufficient condition for exponential convergence of the cooperative learning process is that at each time step, the network topology graph of nonlinear agents can be rendered quasi-strongly connected through switching along the iteration axis. Simulation tests illustrate the effectiveness of our proposed cooperative learning results in refining arbitrary high precision relative formation of nonlinear agents.

Finite-time consensus of a leader-following multi-agent network with non-identical nonlinear dynamics and time-varying topologies

In this paper, the finite-time consensus of a leader-following multi-agent network with non-identical nonlinear dynamics and time-varying topologies is investigated. All the agents, especially the leaders, have non-identical and nonlinear dynamics. According to the algebraic graph theory, Lyapunov stability theory and Kronecker product, a control strategy strategy is established to guarantee the finite-time consensus of multi-agent network with multiple leaders. Furthermore, several numerical simulations illustrate the effectiveness and feasibility of the proposed method.

Adaptive cluster synchronization in directed networks with nonidentical nonlinear dynamics

In this article, the problem of cluster synchronization in the complex networks with nonidentical nonlinear dynamics is considered. By Lyapunov functional and M‐matrix theory, some sufficient conditions for cluster synchronization are obtained. Moreover, the least number of nodes which should be pinned is given. It is shown that when the root nodes of all the clusters are pinning‐controlled, cluster synchronization with adaptive coupling strength can be achieved. Different from the constraints of many literatures, the assumption is that each row sum for all diagonal submatrices of the Laplacian matrix is equal to zero. Finally, a numerical simulation in the network with three scale‐free subnetwork is provided to demonstrate the effectiveness of the theoretical results. © 2016 Wiley Periodicals, Inc. Complexity 21: 380–387, 2016

Distributed adaptive control for time-varying formation tracking of a class of networked nonlinear systems

ABSTRACTThis paper considers the time-varying formation problem of tracking a reference for a class of networked systems consisting of multiple nonlinear subsystems with unknown parameters and non-identical nonlinear dynamics. The communication status among the subsystems is represented by a directed graph. A portion of subsystems have no access to the information of reference. Distributed adaptive controllers are proposed by employing backstepping technique. It is proved that, with the proposed scheme, all the closed-loop signals are globally bounded and all the subsystems can track the reference while building and keeping the prescribed time-varying formation shape. Simulation results are given to illustrate the effectiveness of the proposed scheme.

Distributed adaptive neural network control for a class of heterogeneous nonlinear multi-agent systems subject to actuation failures

ABSTRACTIn this paper, the cooperative adaptive consensus tracking problem for heterogeneous nonlinear multi-agent systems on directed graph is addressed. Each follower is modelled as a general nonlinear system with the unknown and nonidentical nonlinear dynamics, disturbances and actuator failures. Cooperative fault tolerant neural network tracking controllers with online adaptive learning features are proposed to guarantee that all agents synchronise to the trajectory of one leader with bounded adjustable synchronisation errors. With the help of linear quadratic regulator-based optimal design, a graph-dependent Lyapunov proof provides error bounds that depend on the graph topology, one virtual matrix and some design parameters. Of particular interest is that if the control gain is selected appropriately, the proposed control scheme can be implemented in a unified framework no matter whether there are faults or not. Furthermore, the fault detection and isolation are not needed to implement. Finally, a simulation is given to verify the effectiveness of the proposed method.

Adaptive synchronization of coupled nonidentical chaotic systems with complex variables and stochastic perturbations

This paper considers asymptotic synchronization in an array of complex-variable chaotic systems, where node systems exhibit nonidentical nonlinear dynamics and subject to different stochastic perturbations. The effects of the differences among the node systems are overcome by designing a special adaptive discontinuous controller. By using Lyapunov stability theorem and stochastic properties, sufficient conditions are obtained to guarantee the synchronization. Finally, numerical simulations are given to show the effectiveness of the theoretical results.

Finite-time consensus for second-order stochastic multi-agent systems with nonlinear dynamics

In this study, the problem of finite-time consensus in probability for second-order stochastic multi-agent systems with non-identical nonlinear dynamics is investigated. Based on the stochastic finite-time stability theorems and adding a power integrator technique, we propose the distributed control algorithm for the stochastic multi-agent systems, which can guarantee all agents converge to consensus in finite time with probability one under an undirected graph. Two simulation examples are presented to demonstrate the effectiveness of the proposed methods.

Distributed node‐to‐node consensus of multi‐agent systems with stochastic sampling

SummaryThis paper is concerned with the mean square node‐to‐node consensus tracking problem for multi‐agent systems with nonidentical nonlinear dynamics and directed topologies. The randomly occurred uncertainties in the sampling devices may result in stochastically varied sampling periods, which lead to the investigation of node‐to‐node consensus problem under stochastic sampling. By employing the input‐delay method and discontinuous Lyapunov functional approach, it arrives at some sufficient conditions under which the state of each follower can track that of the corresponding leader asymptotically in the mean square sense. Finally, some numerical simulations are provided to verify the effectiveness of the theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.