离散时间分数阶多自主体系统的时延一致性

复杂工作环境中,许多自然现象的个体动力学特性用整数阶方程不能描述,只能用非整数阶（分数阶）动力学来描述个体的运动行为. 本文假设多自主体系统内部连接组成有向加权网络,个体的动态特性应用分数阶动力学方程描述,个体之间数据传输存在通信时延. 应用分数阶系统的Laplace变换和频域理论,研究了离散时间的分数阶多自主体系统的渐近一致性. 应用Hermit-Biehler 定理,研究了具有样本时延的分数阶多自主体系统的运动一致性,得到保证系统稳定的时延的上界阈值. 最后应用一个实例对结论进行了验证.     

Observer‐predictor feedback for consensus of discrete‐time multiagent systems with both state and input delays

This article is concerned with the consensus problem for discrete‐time multiagent systems with both state and input delays. Single observer‐predictor‐based protocols and multiple observer‐predictors feedback protocols are simultaneously established to predict the future state such that the input delay that can be arbitrarily large yet bounded is completely compensated. It is shown that the consensus of the multiagent system can be achieved by the single/multiple observer‐predictors feedback protocol. Moreover, sufficient conditions guaranteeing the consensus of the multiagent system are provided in terms of the stability of some simple observer‐error systems, and the separation principle is discovered. Finally, a numerical example is worked out to illustrate the effectiveness of the proposed approaches.     

Adaptive consensus control for stochastic nonlinear multiagent systems with full state constraints

In this paper, the consensus tracking problem is investigated for stochastic nonlinear multiagent systems with full state constraints and time delays. The barrier Lyapunov functions proposed for single‐agent constrained systems are constructively extended to solve the consensus problem for multiagent systems with the full state constraints. Some Lyapunov‐Krasovskii functionals are introduced to compensate for state time delays, which are inherent in the complicated nonlinear systems. Based on the variable separation technique, the difficulty arising from the nonstrict‐feedback structure is overcome. Under a directed communication topology, the distributed neuroadaptive control protocols are proposed to guarantee that all the follower agents follow the trajectory of the leader agent and the full state constraints are not violated. The effectiveness of the proposed distributed adaptive control approach is verified via simulation examples.     

A new approach to consensus problems in discrete-time multiagent systems with time-delays

In this paper, consensus problems in discrete-time multiagent systems with time-invariant delays are considered. In order to characterize the structures of communication topologies, the concept of "pre-leader-follower" decomposition is introduced. Then, a necessary and sufficient condition for state consensus is established. By this method, consensus problems in networks with a single time-delay, as well as with multiple time-delays, are studied, and some necessary and sufficient conditions for solvability of consensus problems are obtained.     

Projective synchronization for fractional-order memristor-based neural networks with time delays

In this paper, the global projective synchronization for fractional-order memristor-based neural networks with multiple time delays is investigated via combining open loop control with the time-delayed feedback control. A comparison theorem for a class of fractional-order systems with multiple time delays is proposed. Based on the given comparison theorem and Lyapunov method, the synchronization conditions are derived under the framework of Filippov solution and differential inclusion theory. Several feedback control strategies are given to ensure the realization of complete synchronization, anti-synchronization and the stabilization for the fractional-order memristor-based neural networks with time delays. Finally, a numerical example is given to illustrate the effectiveness of the theoretical results.

     

具有定常输入的二阶多智能体系统的平均一致性滤波

本文考察了具有定常输入的二阶多智能体系统平均一致性滤波问题,提出了一种比例-积分一致性滤波算法。在定常输入和固定对称连通拓扑的前提下,根据Routh判据和Nyquist判据分别得到二阶多智能体系统在无时延和相同通信时延约束下渐近收敛一致的收敛条件,且多智能体系统最终一致性状态为定常输入的平均值。最后,通过由5个智能体组成的多智能体系统在连通拓扑结构下的数值仿真,验证了理论结果的正确性。     

Adaptive bipartite consensus control of high‐order multiagent systems on coopetition networks

In this paper, a bipartite consensus problem is considered for a high‐order multiagent system with cooperative‐competitive interactions and unknown time‐varying disturbances. A signed graph is used to describe the interaction network associated with the multiagent system. The unknown disturbances are expressed by linearly parameterized models, and distributed adaptive laws are designed to estimate the unknown parameters in the models. For the case that there is no exogenous reference system, a fully distributed adaptive control law is proposed to ensure that all the agents reach a bipartite consensus. For the other case that there exists an exogenous reference system, another fully distributed adaptive control law is also developed to ensure that all the agents achieve bipartite consensus on the state of the exogenous system. The stability of the closed‐loop multiagent systems with the 2 proposed adaptive control laws are analyzed under an assumption that the interaction network is structurally balanced. Moreover, the convergence of the parameter estimation errors is guaranteed with a persistent excitation condition. Finally, simulation examples are provided to demonstrate the effectiveness of the proposed adaptive bipartite consensus control laws for the concerned multiagent system.     

Containment control for second-order multi-agent systems with time-varying delays

This paper considers the containment control problem for second-order multi-agent systems with time-varying delays. Both the containment control problem with multiple stationary leaders and the problem with multiple dynamic leaders are investigated. Sufficient conditions on the communication digraph, the feedback gains, and the allowed upper bound of the delays to ensure containment control are given. In the case that the leaders are stationary, the Lyapunov–Razumikhin function method is used. In the case that the leaders are dynamic, the Lyapunov–Krasovskii functional method and the linear matrix inequality (LMI) method are jointly used. A novel discretized Lyapunov functional method is introduced to utilize the upper bound of the derivative of the delays no matter how large it is, which leads to a better result on the allowed upper bound of the delays to ensure containment control. Finally, numerical simulations are provided to illustrate the effectiveness of the obtained theoretical results.     

Distributed containment control for nonlinear multiagent systems in pure‐feedback form

In this paper, the problem of distributed containment control for pure‐feedback nonlinear multiagent systems under a directed graph topology is investigated. The dynamics of each agent are molded by high‐order nonaffine pure‐feedback form. Neural networks are employed to identify unknown nonlinear functions, and dynamic surface control technique is used to avoid the problem of explosion of complexity inherent in backstepping design procedure. The Frobenius norm of the ideal neural network weighting matrices is estimated, which is helpful to reduce the number of the adaptive tuning law and alleviate the networked communication burden. The proposed distributed containment controllers guarantee that all signals in the closed‐loop systems are cooperatively semiglobally uniformly ultimately bounded, and the outputs of followers are driven into a convex hull spanned by the multiple dynamic leaders. Finally, the effectiveness of the developed method is demonstrated by simulation examples.     

Fully distributed robust consensus control of multi-agent systems with heterogeneous unknown fractional-order dynamics

This paper investigates the robust consensus control problem of heterogeneous unknown nonlinear fractional-order multi-agent systems (FOMASs) without leader and with multiple leaders of bounded inputs. More specifically, FOMASs with nonidentical unknown coupling nonlinearities and external disturbances are considered in this paper, which takes the first-order MASs as its special case. Based on the σ-modification adaptive control technique, some class of discontinuous robust adaptive control protocols are proposed to solve the leaderless consensus problem and containment consensus problem, respectively. By means of the set-valued maps theory and by artfully choosing Lyapunov function, it is shown that the proposed consensus protocols are user friendly in that they are capable of compensating uncertain coupling nonlinearities, rejecting disturbances, rendering smaller control gains and thus requiring smaller amplitude on the control input while preserving global consensus convergence. All of the proposed robust adaptive consensus protocols are independent of any global and unknown information and thus are fully distributed. Some numerical simulations are provided to validate the correctness of the obtained results.     

Approximately adaptive neural cooperative control for nonlinear multiagent systems with performance guarantee

This paper studies the cooperative control problem for a class of multiagent dynamical systems with partially unknown nonlinear system dynamics. In particular, the control objective is to solve the state consensus problem for multiagent systems based on the minimisation of certain cost functions for individual agents. Under the assumption that there exist admissible cooperative controls for such class of multiagent systems, the formulated problem is solved through finding the optimal cooperative control using the approximate dynamic programming and reinforcement learning approach. With the aid of neural network parameterisation and online adaptive learning, our method renders a practically implementable approximately adaptive neural cooperative control for multiagent systems. Specifically, based on the Bellman's principle of optimality, the Hamilton–Jacobi–Bellman (HJB) equation for multiagent systems is first derived. We then propose an approximately adaptive policy iteration algorithm for multiagent cooperative control based on neural network approximation of the value functions. The convergence of the proposed algorithm is rigorously proved using the contraction mapping method. The simulation results are included to validate the effectiveness of the proposed algorithm.     

Distributed finite‐time containment control for multiple Euler‐Lagrange systems with communication delays

In this paper, distributed finite‐time containment control for multiple Euler‐Lagrange systems with communication delays and general disturbances is investigated under directed topology by using sliding‐mode control technique. We consider that the information of dynamic leaders can be obtained by only a portion of the followers. Firstly, a nonsingular fast terminal sliding surface is selected to achieve the finite‐time convergence for the error variables. Then, a distributed finite‐time containment control algorithm is proposed where the neural network is utilized to approximate the model uncertainties and external disturbances of the systems. Furthermore, considering that error constraint method can improve the performance of the systems, a distributed finite‐time containment control algorithm is developed by transforming the error variable into another form. It is demonstrated that the containment errors are bounded in finite time by using Lyapunov theory, graph theory, and finite‐time stability theory. Numerical simulations are provided to show the effectiveness of the proposed methods.     

Consensus of multiagent systems based on disturbance observer

The objectives of this work are the development and design of disturbance observers (DO’s) for a team of agents that accomplish consensus on agents’ states in the presence of exogenous disturbances. A pinning control strategy is designed for a part of agents of the multiagent systems without disturbances, and this pinning control can bring multiple agents’ states to reaching an expected consensus value. Under the effect of the disturbances, nonlinear disturbance observers are developed for disturbances generated by an exogenous system to estimate the disturbances. Asymptotical consensus of the multiagent systems with disturbances under the composite controller can be achieved. Finally, by applying an example of multiagent systems with switching topologies and exogenous disturbances, the design of the parameters of DO’s are illuminated.     

On system state equipartitioning and semistability in network dynamical systems with arbitrary time-delays

In many applications involving multiagent systems, groups of agents are required to agree on certain quantities of interest. In particular, it is important to develop consensus protocols for networks of dynamic agents with directed information flow, switching network topologies, and possible system time-delays. In this paper, we use compartmental dynamical system models to characterize dynamic algorithms for linear and nonlinear networks of dynamic agents in the presence of inter-agent communication delays that possess a continuum of semistable equilibria, that is, protocol algorithms that guarantee convergence to Lyapunov stable equilibria. In addition, we show that the steady-state distribution of the dynamic network is uniform, leading to system state equipartitioning or consensus. These results extend the results in the literature on consensus protocols for linear balanced networks to linear and nonlinear unbalanced networks with time-delays.     

Multiple asymptotical stability analysis for fractional-order neural networks with time delays

This paper formulates the multiple asymptotical stability for a general class of fractional-order neural networks with time delays. By exploiting the properties of upper bounded and lower bounded functions derived from the addressed fractional-order neural network model as well as the comparison principle for fractional-order calculus, a lot of sufficient conditions are obtained to guarantee the existence and multiple asymptotical stability of the equilibrium points for the fractional-order neural networks with time delays. It reveals that the results gained in this paper are applicable to analyses of both multiple asymptotical stability and global asymptotical stability. Besides, three numerical examples are presented to showcase the validity of the derived results.     

Adaptive‐impulsive consensus of multiagent systems

This paper studies the leader‐following consensus problem of multiagent nonlinear systems with uncertain parameters and control gain error. On the basis of the theory of impulsive differential equations, the adaptive control technique, and the Lyapunov stability theory, some novel adaptive‐impulsive consensus conditions are given to realize the consensus of a class of multiagent nonlinear systems. Compared with the existing investigations on the impulsive consensus of multiagent systems, the proposed impulsive control protocol with uncertain parameters and control gain error is more rigorous and effective in practical systems. Four numerical simulations are verified to confirm the effectiveness of the proposed methods.     

分数阶非线性多智能体系统的一致性研究

研究固定拓扑结构下的分数阶非线性多智能体系统协调控制的动力学模型问题。由于实际多智能体系统中,系统的状态变量难以全部测量,为了克服这一困难,利用状态观测器对系统状态进行重构并基于重构状态进行状态反馈。利用分数阶Lyapunov稳定性理论,证明了当反馈增益矩阵满足一定的线性矩阵不等式（LMI）条件时,系统中的智能体最终趋于所给定的目标状态。最后利用分数阶微积分的预估-校正算法进行数值仿真验证了理论分析的有效性和可行性。     

Fractional discrete-time consensus models for single- and double-summator dynamics

The leader–following consensus problem of fractional-order multi-agent discrete-time systems is considered. In the systems, interactions between opinions are defined like in Krause and Cucker–Smale models but the memory is included by taking the fractional-order discrete-time operator on the left-hand side of the nonlinear systems. In this paper, we investigate fractional-order models of opinions for the single- and double-summator dynamics of discrete-time by analytical methods as well as by computer simulations. The necessary and sufficient conditions for the leader–following consensus are formulated by proposing a consensus control law for tracking the virtual leader.     

Containment control of multi‐agent systems by exploiting the control inputs of neighbors

This paper studies the containment control problem for multi‐agent systems consisting of multiple leaders and followers connected as a network. The objective is to design control protocols so that the leaders will converge to a certain desired formation while the followers converge to the convex hull of the leaders. A novel protocol is proposed by exploiting the control input information of neighbors. Both continuous‐time and discrete‐time systems are considered. For continuous‐time systems, it is proved that the protocol is robust to any constant delays of the neighbors' control inputs. For discrete‐time systems, a sufficient condition on the feedback gain for the containment control is given in terms of the time delay and graph information. Some numerical examples are given to demonstrate the results. Copyright © 2013 John Wiley & Sons, Ltd.     

Consensus with a reference state for fractional-order multi-agent systems

This paper investigates consensus of fractional-order multi-agent systems (MASs) with a reference state. First, a consensus control law with a constant reference state is given using graph theory and stability analysis of fractional-order. Then, a general control law and a particular one for consensus of fractional-order MASs with a time-varying reference state are proposed. Next, the above control laws are extended to solve formation tracking problem. Finally, several simulations are presented to verify the effectiveness of the obtained results.