Distributed control of uncertain multiagent systems for tracking a leader with unknown fractional‐order dynamics

This paper proposes distributed adaptive cooperative control algorithms for second‐order agents to track a leader with unknown dynamics. The models of the followers and the leader are composed of uncertain nonlinear components. The order of the leader's dynamics is unknown and can be fractional. Only the single output information is shared among neighbored agents. To simplify the control design, linearly parameterized neural networks are used to approximate the unknown functions. We first present an adaptive control for leaderless consensus and then extend the method to the tracking problem. Thorough theoretical proofs as well as numerical simulation are included to verify the results. Compared with relevant literature, the new approach applies to a larger variety of systems because (i) knowledge about the structure of leader's model is unnecessary; (ii) the unknown functions in different agents' dynamics can be diverse and arbitrary, in other words, the algorithms apply to heterogeneous agents; (iii) the results can be simply used without parameter calculations.     

有向图中网络Euler-Lagrange系统的自适应协调跟踪

基于一致性理论, 在有向图中研究网络 Euler-Lagrange 系统的协调跟踪控制. 所有跟随智能体的动力学模型均为 Euler-Lagrange 方程. 在仅有部分跟随智能体能获取领航智能体信息的情形下, 同时考虑系统模型的参数不确定性, 设计分布式自适应控制律实现所有跟随智能体对领航智能体的跟踪. 针对领航智能体的运动状态, 考虑以下两种情形: 1) 领航智能体为固定点; 2) 领航智能体为动态点. 对第一种情形, 设计的控制律使得所有跟随智能体渐近交会于固定点; 对第二种情形, 首先对每个跟随智能体设计分布式连续估计器, 然后提出了分布式自适应控制律. 当每个跟随智能体均能获取领航智能体的加速度信息时, 设计的控制律能实现对领航智能体的渐近跟踪, 当跟随智能体不能获取领航智能体的加速度信息时, 跟踪误差是有界的. 最后通过仿真分析验证设计的控制算法是合理有效的.     

Distributed consensus tracking of multi-agent systems with nonlinear dynamics under a reference leader

This paper investigates the distributed consensus tracking problem for multi-agent systems with Lipschitz-type dynamics under a reference leader. It is assumed that the leader state information is only available to a subset of followers, while the bounded reference input of the leader’s is unavailable to any follower. To achieve consensus tracking, a class of discontinuous protocols based on the relative information between the neighbouring agents are proposed. Furthermore, as extensions of the former result, the robust and adaptive consensus tracking problems are studied for the case where there exist parameter uncertainties and external disturbances in the network. Finally, the effectiveness of the theoretical result is demonstrated through a network of single-link manipulators.     

Adaptive tracking control of leader–follower systems with unknown dynamics and partial measurements

In this paper, a decentralized adaptive tracking control is developed for a second-order leader–follower system with unknown dynamics and relative position measurements. Linearly parameterized models are used to describe the unknown dynamics of a self-active leader and all followers. A new distributed system is obtained by using the relative position and velocity measurements as the state variables. By only using the relative position measurements, a dynamic output–feedback tracking control together with decentralized adaptive laws is designed for each follower. At the same time, the stability of the tracking error system and the parameter convergence are analyzed with the help of a common Lyapunov function method. Some simulation results are presented to validate the proposed adaptive tracking control.     

Adaptive output feedback consensus tracking for linear multi-agent systems with unknown dynamics

In this paper, the consensus tracking problem with unknown dynamics in the leader for the linear multi-agent systems is addressed. Based on the relative output information among the agents, decentralised adaptive consensus protocols with static coupling gains are designed to guarantee that the consensus tracking errors converge to a small neighbourhood around the origin and all the signals in the closed-loop dynamics are uniformly ultimately bounded. Moreover, the result is extended to the case with dynamic coupling gains which are independent of the eigenvalues of the Laplacian matrix. Both of the protocols with static and dynamic coupling gains are designed by using the relative outputs, which are more practical than the state-feedback ones. Finally, the theoretical results are verified through an example.     

Adaptive Leader‐Following Consensus for Uncertain Nonlinear Multi‐Agent Systems

This paper is concerned with the adaptive leader‐following consensus for first‐ and second‐order uncertain nonlinear multi‐agent systems (NMASs) with single‐ and double‐integrator leader, respectively. Remarkably, the control coefficients of the followers need not belong to any known finite interval, which makes the systems in question essentially different from those in the related works. Moreover, parameterized unknowns exist in the nonlinearities of the followers, and unknown control input is imposed on the leader, which make the problems difficult to solve. To compensate for these uncertainties/unknowns, the leader‐following consensus protocols are constructed by employing adaptive technique for the first‐order and the second‐order NMASs. Under the designed adaptive consensus protocols and the connected graph, the leader‐following consensus is achieved. Finally, two examples are given to show the effectiveness of the proposed leader‐following consensus protocols.     

Adaptive neural control for multiagent systems with asymmetric time‐varying state constraints and input saturation

This article investigates the leader‐follower consensus problem of a class of non‐strict‐feedback nonlinear multiagent systems with asymmetric time‐varying state constraints (ATVSC) and input saturation, and an adaptive neural control scheme is developed. By introducing the distributed sliding‐mode estimator, each follower can obtain the estimation of leader's trajectory and track it directly. Then, with the help of time‐varying asymmetric barrier Lyapunov function and radial basis function neural networks, the controller is designed based on backstepping technique. Furthermore, the mean‐value theorem and Nussbaum function are utilized to address the problems of input saturation and unknown control direction. Moreover, the number of adaptive laws is equal to that of the followers, which reduces the computational complexity. It is proved that the leader‐follower consensus tracking control is achieved without violating the ATVSC, and all closed‐loop signals are semiglobally uniformly ultimately bounded. Finally, the simulation results are provided to verify the effectiveness of the control scheme.     

Distributed Adaptive Output Consensus of Unknown Heterogeneous Non-Minimum Phase Multi-Agent Systems

This article addresses the leader-following output consensus problem of heterogeneous linear multi-agent systems with unknown agent parameters under directed graphs.The dynamics of followers are allowed to be non-minimum phase with unknown arbitrary individual relative degrees.This is contrary to many existing works on distributed adaptive control schemes where agent dynamics are required to be minimum phase and often of the same relative degree.A distributed adaptive pole placement control sche...     

Prescribed performance global stable adaptive neural dynamic surface consensus tracking control of stochastic multi-agent systems with hysteresis inputs and nonlinear dynamics

This paper focuses on the leader-following consensus control problem of stochastic multi-agent systems with hysteresis inputs and nonlinear dynamics. A leader-following consensus scheme is presented for stochastic multi-agent systems directions under directed graphs, which can achieve predefined synchronisation error bounds. By mainly activating an auxiliary robust control component for pulling back the transient escaped from the neural active region, a multi-switching robust neuro adaptive controller in the neural approximation domain, which can achieve globally uniformly ultimately bounded tracking stability of multi-agent systems recently. A specific Nussbaum-type function is introduced to solve the problem of unknown control directions. Using a dynamic surface control technique, distributed consensus controllers are developed to guarantee that the outputs of all followers synchronise with that of the leader with prescribed performance. Based on Lyapunov stability theory, it is proved that all signals in closed-loop systems are uniformly ultimately bounded and all the follower agents can keep consensus with the leader. Two simulation examples are provided to illustrate the effectiveness and advantage of the proposed control scheme.     

Distributed finite-time consensus tracking for nonlinear multi-agent systems with a time-varying reference state

This paper investigates the consensus tracking problem for nonlinear multi-agent systems with a time-varying reference state. The consensus reference is taken as a virtual leader, whose output is only its position information that is available to only a subset of a group of followers. The dynamics of each follower consists of two terms: nonlinear inherent dynamics and a simple communication protocol relying only on the position of its neighbours. In this paper, the consensus tracking problem is respectively considered under fixed and switching communication topologies. Some corresponding sufficient conditions are obtained to guarantee the states of followers can converge to the state of the virtual leader in finite time. Rigorous proofs are given by using graph theory, matrix theory, and Lyapunov theory. Simulations are presented to illustrate the theoretical analysis.     

Observer-based prescribed-time consensus control for heterogeneous multi-agent systems under directed graphs

This work studies the prescribed-time robust consensus tracking problem of heterogeneous multi-agent systems over directed graphs. Aiming at multi-agent systems with a static leader and only matched disturbances, a distributed observer-based consensus algorithm is developed, to ensure that the tracking errors converge to zero accurately in prescribed time. For the case of multi-agent systems with a dynamic leader and mismatched/matched disturbances, an adaptive strategy based on a distributed observer and a disturbance observer is designed by the dynamic damping reciprocal technology. Such strategy can avoid the numerical singularity, adapt to the situation that the upper bounds of the disturbances are unknown, and assure that the tracking errors converge to an adjustable neighborhood of zero within prescribed time. Finally, simulations are given to verify the effectiveness of the proposed control strategies.     

Adaptive robust consensus tracking for nonlinear second‐order multi‐agent systems with heterogeneous uncertainties

This paper addresses the consensus tracking problem for a class of heterogeneous nonlinear second‐order multi‐agent systems with parametric uncertainties, unmodeled dynamics, and bounded external disturbances. By linearly parameterizing the control input of the leader, two distributed adaptive robust consensus tracking control protocols with dynamic and fixed coupling gains are constructed based on the relative information from neighboring agents. The global tracking errors are shown to be guaranteed to exponentially converge to a ball with a constant radius at a prescribed rate of convergence under external disturbances. Finally, a numerical example is provided to verify the theoretical results. Copyright © 2017 John Wiley & Sons, Ltd.     

Finite‐time consensus tracking for harmonic oscillators using both state feedback control and output feedback control

This paper investigates the distributed finite‐time consensus‐tracking problem for coupled harmonic oscillators. The objective is to guarantee a team of followers modeled by harmonic oscillators to track a dynamic virtual leader in finite time. Only a subset of followers can access the information of the virtual leader, and the interactions between followers are assumed to be local. We consider two cases: (i) The followers can obtain the relative states between their neighbors and their own; and (ii) Only relative outputs between neighboring agents are available. In the former case, a distributed consensus protocol is adopted to achieve the finite‐time consensus tracking. In the latter case, we propose a novel observer‐based dynamic protocol to guarantee the consensus tracking in finite time. Simulation examples are finally presented to verify the theoretical analysis. Copyright © 2012 John Wiley & Sons, Ltd.     

Cooperative Adaptive Fuzzy Output Feedback Control for Synchronization of Nonlinear Multi‐Agent Systems in the Presence of Input Saturation

This paper considers the leader‐following synchronization problem of nonlinear multi‐agent systems with unmeasurable states in the presence of input saturation. Each follower is governed by a class of strict‐feedback systems with unknown nonlinearities and the information of the leader can be accessed by only a small fraction of followers. An auxiliary system is introduced and its states are used to design the cooperative controllers for counteracting the effect of input saturation. By using fuzzy logic systems to approximate the unknown nonlinearities, local adaptive fuzzy observers are designed to estimate the unmeasurable states. Dynamic surface control (DSC) is employed to design distributed adaptive fuzzy output feedback controllers. The developed controllers guarantee that the outputs of all followers synchronize to that of the leader under directed communication graphs. Based on Lyapunov stability theory, it is proved that all signals in the closed‐loop systems are semiglobally uniformly ultimately bounded (SGUUB), and the tracking error converges to a small neighborhood of the origin. An example is provided to show the effectiveness of the proposed control approach.     

Adaptive iterative learning control for coordination of second‐order multi‐agent systems

In this paper, an efficient framework is proposed to the consensus and formation control of distributed multi‐agent systems with second‐order dynamics and unknown time‐varying parameters, by means of an adaptive iterative learning control approach. Under the assumption that the acceleration of the leader is unknown to any follower agents, a new adaptive auxiliary control and the distributed adaptive iterative learning protocols are designed. Then, all follower agents track the leader uniformly on [0,T] for consensus problem and keep the desired distance from the leader and achieve velocity consensus uniformly on [0,T] for the formation problem, respectively. The distributed multi‐agent coordinations performance is analyzed based on the Lyapunov stability theory. Finally, simulation examples are given to illustrate the effectiveness of the proposed protocols in this paper.Copyright © 2013 John Wiley & Sons, Ltd.     

Fully distributed consensus for fuzzy multiagent systems with jointly connected topology

This paper investigates the problem of fully distributed consensus for polynomial fuzzy multiagent systems (MASs) under jointly connected topologies. First, a polynomial fuzzy modeling method is presented to characterize the error dynamics that is constructed by one leader and multiple followers. Then, using the relative state information and the agents' dynamics, a distributed adaptive protocol is designed to guarantee that MASs under jointly connected topologies can achieve consensus in a fully distributed fashion. Utilizing the Lyapunov technique, a relaxed sufficient criterion is proposed to ensure consensus for fuzzy MASs under jointly connected topologies. Moreover, the adaptive coupling weights between neighboring agents can converge to certain values. The derived condition is transformed into a sum-of-squares form, which can be solved numerically. We provide an example to illustrate the proposed distributed adaptive consensus technique's validity.     

Adaptive Fixed-Time Control of Nonlinear MASs With Actuator Faults

The adaptive fixed-time consensus problem for a class of nonlinear multi-agent systems(MASs) with actuator faults is considered in this paper. To approximate the unknown nonlinear functions in MASs, radial basis function neural networks are used. In addition, the first order sliding mode differentiator is utilized to solve the “explosion of complexity” problem,and a filter error compensation method is proposed to ensure the convergence of filter error in fixed time. With the help of the Nussbaum...     

Task-space fully distributed tracking control of networked uncertain robotic manipulators without velocity measurements

This paper investigates the task-space synchronised tracking problem of uncertain networked manipulators interconnected on directed graphs, where the dynamic leader is available to only a subset of followers and followers have only local interaction. A fully distributed tracking controller is proposed, which is composed of a distributed desired trajectory estimator, a joint-space velocity observer and an adaptive cooperative control algorithm. Specifically, the proposed controller allows each manipulator to track the dynamic leader solely using local task-space position measurements. Besides, in the presence of both dynamic and kinematic uncertainties, the adaptive cooperative control algorithm indeed improves the system's robustness. Furthermore, it is strictly proved that the proposed control scheme ensures that both task-space position and velocity tracking errors converge to zero as time tends to infinity. In the end, simulation results are provided to demonstrate the effectiveness of the proposed controller.     

Distributed adaptive tracking control for high-order multi-agent systems with unknown dynamics

In this paper, we investigate the adaptive tracking problem of high-order multi-agent systems with unknown parameters and unknown nonlinear functions. Under the assumption that the leader is the root of a spanning tree, a distributed adaptive controller with tuning function is constructed recursively based on backstepping design method. The designed controller can guarantee that the tracking errors and the parameter errors eventually converge to an arbitrarily small compact set by choosing design parameters. A simulation example demonstrates the effectiveness of the design scheme.     

Distributed leader‐follower consensus for a class of semilinear second‐order multiagent systems using time scale theory

The problem of distributed leader‐follower consensus for second‐order linear multiagent systems with unknown nonlinear inherent dynamics is investigated in this paper. It is assumed that the dynamic of each agent is described by a semilinear second‐order dynamic equation on an arbitrary time scale. Using calculus on time scales and direct Lyapunov's method, some sufficient conditions are derived to ensure that the tracking errors exponentially converge to zero. Some numerical results show the effectiveness of the proposed scheme.