Tracking Consensus for Second-Order Multi-Agent Systems with Nonlinear Dynamics in Noisy Environments

This paper investigates the leader-following tracking consensus problem for second-order multi-agent systems with time delays and nonlinear dynamics in noisy environments on the conditions of fixed and switching directed topologies. Based on a novel velocity decomposition technique and stochastic analysis, a measurement-based distributed tracking control protocol is proposed, under which all agents can track the leader in mean square. Simulation results are also given to illustrate the effectiveness of the proposed protocol.     

Distance-based formation tracking control of multi-agent systems with double-integrator dynamics

This paper addresses the distance-based formation tracking problem for a double-integrator modeled multi-agent system(MAS) in the presence of a moving leader in d-dimensional space. Under the assumption that the state of leader can be obtained over fixed graphs, a distributed distance-based control protocol is designed for each double-integrator follower agent. The protocol consists of three terms: a gradient function term, a velocity consensus term, and a leader tracking term.Different shape stabilizing functions proposed in the literature can be applied to the gradient function term. The proposed controller allows all agents to both achieve the desired shape and reach the same velocity with moving leader by controlling the distances and velocity. Finally, we analyze the local asymptotic stability of the equilibrium set with center manifold theory. We validate the effectiveness of our approach through two examples.     

Leader-following formation control of multi-agent networks based on distributed observers

To investigate the leader-following formation control, in this paper we present the design problem of control protocols and distributed observers under which the agents can achieve and maintain the desired formation from any initial states, while the velocity converges to that of the virtual leader whose velocity cannot be measured by agents in real time. The two cases of switching topologies without communication delay and fixed topology with time-varying communication delay are both considered for multi-agent networks. By using the Lyapunov stability theory, the issue of stability is analysed for multi-agent systems with switching topologies. Then, by considering the time-varying communication delay, the sufficient condition is proposed for the multi-agent systems with fixed topology. Finally, two numerical examples are given to illustrate the effectiveness of the proposed leader-following formation control protocols.     

Containment consensus with measurement noises and time-varying communication delays

In this paper,we consider the containment consensus control problem for multi-agent systems with measurement noises and time-varying communication delays under directed networks.By using stochastic analysis tools and algebraic graph theory,we prove that the followers can converge to the convex hull spanned by the leaders in the sense of mean square if the allowed upper bound of the time-varying delays satisfies a certain sufficient condition.Moreover,the time-varying delays are asymmetric for each follower agent,and the time-delay-dependent consensus condition is derived.Finally,numerical simulations are provided to illustrate the effectiveness of the obtained theoretical results.     

Rigidity based formation tracking for multi-agent networks

This paper considers the formation tracking problem under a rigidity framework, where the target formation is specified as a minimally and infinitesimally rigid formation and the desired velocity of the group is available to only a subset of the agents. The following two cases are considered: the desired velocity is constant, and the desired velocity is timevarying. In the first case, a distributed linear estimator is constructed for each agent to estimate the desired velocity. The velocity estimation and a formation acquisition term are employed to design the control inputs for the agents, where the rigidity matrix plays a central role. In the second case, a distributed non-smooth estimator is constructed to estimate the time-varying velocity, which is shown to converge in a finite time. Theoretical analysis shows that the formation tracking problem can be solved under the proposed control algorithms and estimators. Simulation results are also provided to show the validity of the derived results.     

Periodically intermittent controlling complex dynamical networks with time-varying delays to a desired orbit

This Letter investigates the problem of synchronization in complex dynamical networks with time-varying delays. A periodically intermittent control scheme is proposed to achieve global exponential synchronization for a general complex network with both time-varying delays dynamical nodes and time-varying delays coupling. It is shown that the sates of the general complex network with both time-varying delays dynamical nodes and time-varying delays coupling can globally exponentially synchronize with a desired orbit under the designed intermittent controllers. Moreover, a typical network consisting of the time-delayed Chua oscillator with nearest-neighbor unidirectional time-varying delays coupling is given as an example to verify the effectiveness of the proposed control methodology.     

Flocking of Multi-agent Systems Following Virtual Leader with Time-Varying Velocity

We consider the collective dynamics for a multi-agent system with a virtual leader. The velocity of the leader is time-varying and the interconnection topology of position network is switching based on the distances between agents. To track the leader in flocking, a neighbour-based local piecewise smooth controller is proposed for each agent. Using the control method, all agent velocities asymptotically approach the desired velocity while collisions can be avoided between agents. Some simulation results are provided to demonstrate the theoretical results.     

Consensus of multiple autonomous underwater vehicles with double independent Markovian switching topologies and timevarying delays

A new method in which the consensus algorithm is used to solve the coordinate control problems of leaderless multiple autonomous underwater vehicles(multi-AUVs) with double independent Markovian switching communication topologies and time-varying delays among the underwater sensors is investigated.This is accomplished by first dividing the communication topology into two different switching parts,i.e.,velocity and position,to reduce the data capacity per data package sent between the multi-AUVs in the ocean.Then,the state feedback linearization is used to simplify and rewrite the complex nonlinear and coupled mathematical model of the AUVs into a double-integrator dynamic model.Consequently,coordinate control of the multi-AUVs is regarded as an approximating consensus problem with various time-varying delays and velocity and position topologies.Considering these factors,sufficient conditions of consensus control are proposed and analyzed and the stability of the multi-AUVs is proven by Lyapunov-Krasovskii theorem.Finally,simulation results that validate the theoretical results are presented.     

Leader-following consensus problem with a varying-velocity leader and time-varying delays

In this paper, we study a leader-following consensus problem for a multi-agent system with a varying-velocity leader and time-varying delays. Here, the interaction graph among the followers is switching and balanced. At first, we propose a neighbor-based rule for every agent to track a leader whose states may not be measured. In addition, we consider the convergence analysis of this multi-agent system under two different conditions: the connection between the followers and the leader is time-invariant and time-varying. For the first case, a novel decomposition method is introduced to facilitate the convergence analysis. By utilizing a Lyapunov–Krasovskii functional, we obtain sufficient conditions for uniformly ultimately boundedness of the tracking errors. Finally, two simulations are also presented to illustrate our theoretical results.     

Chaotic system optimal tracking using data-based synchronous method with unknown dynamics and disturbances

We develop an optimal tracking control method for chaotic system with unknown dynamics and disturbances. The method allows the optimal cost function and the corresponding tracking control to update synchronously. According to the tracking error and the reference dynamics, the augmented system is constructed. Then the optimal tracking control problem is defined. The policy iteration(PI) is introduced to solve the min-max optimization problem. The off-policy adaptive dynamic programming(ADP) algorithm is then proposed to find the solution of the tracking Hamilton–Jacobi–Isaacs(HJI) equation online only using measured data and without any knowledge about the system dynamics. Critic neural network(CNN), action neural network(ANN), and disturbance neural network(DNN) are used to approximate the cost function, control, and disturbance. The weights of these networks compose the augmented weight matrix, and the uniformly ultimately bounded(UUB) of which is proven. The convergence of the tracking error system is also proven. Two examples are given to show the effectiveness of the proposed synchronous solution method for the chaotic system tracking problem.     

Coordinated Control of Multi-Agent Systems with a Varying-Velocity Leader and Input Saturation

In this paper, we investigate a leader-following tracking problem for multi-agent systems with bounded inputs. We propose a distributed bounded protocol for each follower to track a leader whose states may not be completely measured. We theoretically prove that each agent can follow the leader with estimable track errors. Finally, some numerical simulations are presented to illustrate our theoretical results.     

Stochastic bounded consensus tracking of leader–follower multi-agent systems with measurement noises based on sampled-data with small sampling delay

This paper is concerned with the stochastic bounded consensus tracking problems of leader–follower multi-agent systems, where the control input of an agent can only use the information measured at the sampling instants from its neighborhood agents or a virtual leader with a time-varying reference state, the measurements are corrupted by random noises, and the signal sampling process induces a small sampling delay. The augmented matrix method, probability limit theory and algebra graph theory are employed to derive the necessary and sufficient conditions guaranteeing mean square bounded consensus tracking. It turns out that the convergence of the proposed protocol simultaneously depends on the constant feedback gains, the network topology, the sampling period and the sampling delay, and that the static consensus tracking error depends on not only the above-mentioned factors, but also the noise intensity, the number of agents and the upper bound of the changing rate of the virtual leader’s state. The obtained results cover no sampling delay as a special case. Simulations are provided to demonstrate the effectiveness of the theoretical results.     

Finite-time consensus of second-order leader-following multi-agent systems without velocity measurements

This Letter investigates the finite-time consensus problems of second-order multi-agent systems in the presence of one and multiple leaders under a directed graph. Specifically, we propose two bounded control laws, which are independent of velocity information, to deal with the finite-time consensus tracking problem with one leader and the finite-time containment control problem with multiple leaders, respectively. With the aid of homogeneous theory, some sufficient conditions are established for the achievement of the finite-time tracking control problem of second-order multi-agent systems. Numerical examples are finally provided to illustrate the theoretical results.     

时变不确定时滞连续系统的鲁棒H∞保成本控制

针对一类同时具有状态时滞和输入时滞的时变不确定连续系统,研究了H_∞保成本状态反馈控制器的设计,假定其中的时变不确定性项是范数有界的,但不需要满足匹配条件.通过构造广义Lyapunov函数和线性矩阵不等式(LMI)方法,给出了系统可H_∞鲁棒镇定同时满足保性能指标的一个充分条件,仅通过求解一个相应的线性矩阵不等式,就可得到鲁棒H_∞保性能控制器使得闭环系统的一个保成本函数对所有允许的不确定参数有上界,并经过迭代,通过求解凸优化问题得到最优鲁棒H_∞保性能控制器.最后用示例说明了该方法的有效性. 关键词： 连续系统 时滞 H_∞鲁棒控制')" href="#">H_∞鲁棒控制 保成本控制     

Synchronization stability of general complex dynamical networks with time-varying delays

The synchronization problem of some general complex dynamical networks with time-varying delays is investigated. Both time-varying delays in the network couplings and time-varying delays in the dynamical nodes are considered. The novel delay-dependent criteria in terms of linear matrix inequalities (LMI) are derived based on free-weighting matrices technique and appropriate Lyapunov functional proposed recently. Numerical examples are given to illustrate the effectiveness and advantage of the proposed synchronization criteria.     

Robust Trajectory Tracking Control for Continuous-Time Nonlinear Systems with State Constraints and Uncertain Disturbances

In this paper, a robust trajectory tracking control method with state constraints and uncertain disturbances on the ground of adaptive dynamic programming (ADP) is proposed for nonlinear systems. Firstly, the augmented system consists of the tracking error and the reference trajectory, and the tracking control problems with uncertain disturbances is described as the problem of robust control adjustment. In addition, considering the nominal system of the augmented system, the guaranteed cost tracking control problem is transformed into the optimal control problem by using the discount coefficient in the nominal system. A new safe Hamilton–Jacobi–Bellman (HJB) equation is proposed by combining the cost function with the control barrier function (CBF), so that the behavior of violating the safety regulations for the system states will be punished. In order to solve the new safe HJB equation, a critic neural network (NN) is used to approximate the solution of the safe HJB equation. According to the Lyapunov stability theory, in the case of state constraints and uncertain disturbances, the system states and the parameters of the critic neural network are guaranteed to be uniformly ultimately bounded (UUB). At the end of this paper, the feasibility of the proposed method is verified by a simulation example.     

Passivity analysis for uncertain neural networks with discrete and distributed time-varying delays

In this Letter, the passivity problem of uncertain neural networks with discrete and distributed time-varying delays is investigated. New delay-dependent conditions for this problem are obtained by using a novel Lyapunov functional together with the linear matrix inequality (LMI) approach. Numerical examples are given to show the effectiveness of our theoretical results.     

Robust stability results for uncertain stochastic neural networks with discrete interval and distributed time-varying delays

This Letter is concerned with stability analysis problem for uncertain stochastic neural networks with discrete interval and distributed time-varying delays. The parameter uncertainties are assumed to be norm bounded and the delay is assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the Lyapunov-Krasovskii functional and stochastic stability theory, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities. Some stability criteria are formulated by means of the feasibility of a linear matrix inequality (LMI) and by introducing some free-weighting matrices. Finally, two numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI conditions.     

Adaptive Q-S (lag, anticipated, and complete) time-varying synchronization and parameters identification of uncertain delayed neural networks

In this paper, a new type of generalized Q-S (lag, anticipated, and complete) time-varying synchronization is defined. Adaptive Q-S (lag, anticipated, and complete) time-varying synchronization and parameters identification of uncertain delayed neural networks have been considered, where the delays are multiple time-varying delays. A novel control method is given by using the Lyapunov functional method. With this new and effective method, parameters identification and Q-S (lag, anticipated, and complete) time-varying synchronization can be achieved simultaneously. Simulation results are given to justify the theoretical analysis in this paper.     

Robust adaptive synchronization for a general class of uncertain chaotic systems with application to Chua's circuit

The synchronization problem for a general class of uncertain chaotic systems is addressed. The underlying systems may be perturbed by unknown time-varying parameters, unstructured uncertainties, and external disturbances. Meanwhile, the time-varying parameters and disturbances are neither required to be periodic nor to have known bounds. Assuming the disturbances are L(2) signals, an adaptive control incorporated with H(∞) control technique is employed to construct a robust adaptive synchronization algorithm. Then, removing such assumption, a novel adaptive-based method is developed to achieve the goal of synchronization. In order to demonstrate the effectiveness of the proposed algorithms, such methods are applied to solve the synchronization problem of uncertain chaotic Chua's circuits.