Leader‐following consensus of multiple uncertain Euler‐Lagrange systems

A new adaptive distributed controller is developed for the leader‐following consensus problem of multiple uncertain Euler‐Lagrange systems. A distinct feature of our proposed approach as opposed to the existing ones is that it does not need the exchange of controller's state among the communication network. As a consequence, it not only makes the implementation of the controller much easier but also reduces the communication cost. The effectiveness of the main result is demonstrated by some exemplary applications to cooperative control of multiple two‐link robot arms.     

Leader‐following consensus with connectivity preservation of uncertain Euler–Lagrange multi‐agent systems

The leader‐following consensus problem for multiple Euler–Lagrange systems has been extensively studied for various scenarios. Under the assumption that the communication graph is jointly connected, one of our recent papers gave the solution for the case where the leader system can generate a combination of arbitrary step signal, arbitrary ramp signal, and arbitrary sinusoidal signals. In practice, it is desirable to enable the control law the capability of maintaining the connectivity of the communication graph, thus achieving the leader‐following consensus without assuming the connectivity of the communication graph. We call such a problem as leader‐following consensus with connectivity preservation. By combining the adaptive control technique and potential function technique, we will show that such a problem is solvable. By employing different potential functions, our approach may also lead to the solution of such problems as rendezvous, flocking and swarming. Copyright © 2017 John Wiley & Sons, Ltd.     

Leader‐following attitude consensus of multiple uncertain spacecraft systems subject to external disturbance

The attitude consensus problem of multiple rigid spacecraft systems is one of the key issues in spacecraft formation flying and has been extensively studied. In this paper, we further consider the leader‐following attitude consensus problem of multiple rigid uncertain spacecraft systems subject to a class of multi‐tone sinusoidal disturbances with arbitrarily unknown amplitudes, initial phases, frequencies, and constant biases. In contrast to the existing results, in order to achieve asymptotic reference tracking and disturbance rejection by smooth control, we have integrated the distributed observer approach with internal model and adaptive control techniques. Simulation results are shown to validate the effectiveness of the proposed control law. Copyright © 2016 John Wiley & Sons, Ltd.     

Observer‐based leader‐following consensus of uncertain nonlinear multi‐agent systems

In this paper, the leader‐following consensus problem of uncertain high‐order nonlinear multi‐agent systems on directed graph with a fixed topology is studied, where it is assumed that the relative states of a follower and its neighbors are immeasurable and only the relative outputs are available. Nonlinear adaptive observers are firstly proposed for each follower to estimate the states of it and its neighbors, and an observer‐based distributed adaptive control scheme is constructed to guarantee that all followers asymptotically synchronize to a leader with tracking errors being semi‐globally uniform ultimate bounded. On the basis of algebraic graph theory and Lyapunov theory, the closed‐loop system stability analysis is conducted. Finally, numerical simulations are presented to illustrate the effectiveness and potential of the proposed new design techniques. Copyright © 2017 John Wiley & Sons, Ltd.     

Leader‐following consensus for nonlinear agents with measurement feedback

The leader‐following consensus problem is investigated for large classes of nonlinear identical agents. Sufficient conditions are provided for achieving consensus via state and measurement feedback laws based on a local (ie, among neighbors) information exchange. The leader's trajectories are assumed bounded without knowledge of the containing compact set and the agents' trajectories possibly unbounded under the action of a bounded input. Generalizations to heterogeneous agents and robustness are also discussed.     

Distributed event‐triggered tracking control with a dynamic leader for multiple Euler‐Lagrange systems under directed networks

The distributed tracking control for multiple Euler‐Lagrange systems with a dynamic leader is investigated in this article via the event‐triggered approach. Only a portion of followers have access to the leader, and the communication topology among all agents is directed that contains a directed spanning tree rooted at the leader. The case that the leader's generalized velocity is constant is first considered, and a distributed event‐based control law is developed by using a velocity estimator. When the leader's generalized velocity is time‐varying, novel distributed continuous estimators are proposed to avoid the undesirable chattering effect while guaranteeing that the estimate errors converge to zeros. With the designed distributed estimators, another distributed event‐based control protocol is provided. Controller update frequency and resource consumption in our work can be reduced by applying the aforementioned two distributed control laws, and the tracking errors can converge to zeros. In addition, it is rigorously proved that no agent exhibits Zeno behavior. Finally, the effectiveness of the proposed distributed event‐based control laws is elucidated by a number of simulation examples.     

Model‐independent consensus control of Euler‐Lagrange agents with interconnecting delays

In this paper, we introduce, for the first time, a proportional‐integral‐derivative controller to solve the consensus problem for networked Euler‐Lagrange agents. The proposed control scheme solves both the leaderless and the leader‐follower consensus problems without requiring the exact knowledge of any part of the agent model. Contrary to the previous studies in the literature, we do not require either to cancel any part of the agent model, which renders robust our approach, nor employ discontinuous controllers. It is proven that both consensus problems are solved globally and asymptotically and the presence of bounded time‐varying communicating delays is considered.     

Finite‐time consensus of Euler‐Lagrange agents without velocity measurements via energy shaping

Motivated by the energy‐shaping framework and the properties of homogeneous systems, this paper deals with the problem of achieving consensus of multiple Euler‐Lagrange (EL) systems using the energy shaping plus damping injection principles of passivity‐based control. We propose a method to derive a novel family of decentralized controllers that is capable of solving the leaderless and the leader‐follower consensus problems in finite‐time in networks of fully actuated EL systems without employing velocity measurements. As in the energy‐shaping methodology, the controller is another EL system and the plant‐controller interconnection is the gradient of a suitable defined potential function. The potential energy and dissipation functions, of the controller, are provided with some homogeneous properties in order to achieve finite‐time convergence. This paper provides several simulations that corroborate the performance of different controllers.     

Tracking control of uncertain Euler–Lagrange systems with finite‐time convergence

A unified solution is presented to the tracking control problem of Euler–Lagrange systems with finite‐time convergence. A reconstruction module is designed to estimate the overall of unmodeled dynamics, disturbance, actuator misalignment, and multiple actuator faults. That reconstruction is accomplished in finite time with zero error. A nonsingular terminal sliding mode controller is then synthesized, and the resultant closed‐loop system is also shown to be finite‐time stable with the reference trajectory followed in finite time. Unlike most sliding mode control methods to handle system uncertainties, the designed control has less conservativeness and stronger fault tolerant capability. A rigid spacecraft system is used to demonstrate the effectiveness and potential of the proposed scheme. Copyright © 2014 John Wiley & Sons, Ltd.     

Distributed Adaptive Event‐Triggered Control for Leader‐Following Consensus of Multi‐Agent Systems

This paper studies the leader‐following consensus problem for Lipschitz nonlinear multi‐agent systems using novel event‐triggered controllers. A distributed adaptive law is introduced for the event‐based control strategy design such that the proposed controllers are independent of system parameters and only use the relative states of neighboring agents, and hence are fully distributed. Due to the introduction of an event‐triggered control scheme, the controller of the agent is only triggered at it's own event times, and thus reduces the amount of communication between controller and actuator and lowers the frequency of controller updates in practice. Based on a quadratic Lyapunov function, the event condition which uses only neighbor information and local computation at trigger instants is established. Infinite triggers within a finite time are also verified to be impossible. The effectiveness of the theoretical results are illustrated through simulation examples.     

Integral sliding mode control for Euler‐Lagrange systems with input saturation

This paper investigates the robust control for the Euler‐Lagrange (EL) system with input saturation by using the integral sliding mode control and adaptive control. An integral sliding mode surface that is suitable for solving the problem of the input constraint is given based on the saturation function. By using the integral sliding mode surface, two robust antisaturation controllers are designed for the EL system with external disturbances. The first controller can deal with the external disturbances with known bounds, whereas the second one can compensate the external disturbances with unknown bounds by using the adaptive control. Finally, the effectiveness of the proposed controllers is demonstrated by strict theoretical analysis and numerical simulations.     

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.     

Distributed formation‐containment control with Euler‐Lagrange systems subject to input saturation and communication delays

This paper is concerned with the problem of formation‐containment on networked systems, with interconnected systems modeled by the Euler‐Lagrange equation with bounded inputs and time‐varying delays on the communication channels. The main results are the design of control algorithms and sufficient conditions to ensure the convergence of the network. The control algorithms are designed as distributed dynamic controllers, in such a way that the number of neighbors of each agent is decoupled from the bound of the control inputs. That is, in the proposed approach the amplitude of the input signal does not directly increase with the number of neighbors of each agent. The proposed sufficient conditions for the asymptotic convergence follow from the Lyapunov‐Krasovskii theory and are formulated in the linear matrix inequalities framework. The conditions rely only on the upper bound of delays and on a subset of the controller parameters, but they do not depend on the model of each agent, which makes it suitable for networks with agents governed by distinct dynamics. In order to illustrate the effectiveness of the proposed method we present numerical examples and compare with similar approaches existing in the literature.     

Distributed model‐independent consensus of Euler–Lagrange agents on directed networks

This paper proposes a distributed model‐independent algorithm to achieve leaderless consensus on a directed network where each fully‐actuated agent has self‐dynamics described by Euler–Lagrange equations of motion. Specifically, we aim to achieve consensus of the generalised coordinates with zero generalised velocity. We show that on a strongly connected graph, a model‐independent algorithm can achieve the consensus objective at an exponential rate if an upper bound on the initial conditions is known a priori. By model‐independent, we mean that each agent can execute the algorithm with no knowledge of the equations describing the self‐dynamics of any agent. For design of the control laws which achieve consensus, a control gain scalar and a control gain matrix are required to satisfy several inequalities involving bounds on the matrices of the agent dynamic model, bounds on the Laplacian matrix describing the network topology and the set of initial conditions; design of the algorithm therefore requires some knowledge on the bounds of the agent dynamical parameters. Because only bounds are required, the proposed algorithm offers robustness to uncertainty in the parameters of the multiagent system. We systematically show that additional relative velocity information improves the performance of the controller. Numerical simulations are provided to show the effectiveness of the algorithm. Copyright © 2016 John Wiley & Sons, Ltd.     

Event‐based distributed robust synchronization control for multiple Euler‐Lagrange systems without relative velocity measurements

This paper focuses on the event‐based distributed robust leaderless synchronization control for multiple Euler‐Lagrange systems with directed communication topology that contains a directed spanning tree. Update frequency of the system is reduced by taking advantages of the event‐triggered approach, which can help extend the service life of the controller. Robust control theory is employed to guarantee the synchronization stability of the networked Euler‐Lagrange systems when unmodeled dynamics occur. The cost on the distributed synchronization protocol design can be saved due to the relaxation of the requirement on relative velocity measurements. Furthermore, our results are more practical because unknown disturbance is taken into consideration. In addition, it can be rigorously analyzed that each agent can exclude the undesired Zeno behavior. Some simulation examples are provided in the end to demonstrate the effectiveness of the proposed event‐based distributed robust control algorithm.     

Cooperative controller design for synchronization of networked uncertain Euler–Lagrange systems

This paper addresses the synchronization problems with/without a dynamic leader for a team of distributed Lagrange systems on digraph. A systematic way to design and analyze the distributed control algorithms is presented. The contributions of the paper are twofold. First, the adaptive coordination control protocols are proposed for synchronization of networked uncertain Lagrange systems with/without tracking. This protocol can guarantee synchronization in finite time. Second, the design of the distributed tracking controller for the networked dynamic systems is proposed by using Lyapunov methods. The development is suitable for the general digraph communication topologies. Simulation examples are included to demonstrate the effectiveness of the proposed algorithms. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

Event-triggered finite-time consensus of multiple Euler Lagrange systems under Markovian switching topologies

Finite-time consensus problem for multiple Euler Lagrange systems under Markovian switching topologies is investigated through an event-triggered control protocol. First, instead of the general stochastic topology, the graph of the entire system is governed by some Markov chains to the edge set, which can recover the traditional Markovian switching topologies in line with the practical communication environment. Then, by utilising an integral sliding-mode control strategy, rigorous analysis of finite-time consensus is performed through the graph theory and Lyapunov stability theory. An event-triggered communication law is delicately carried out for each agent, and Zeno behaviour of triggering time sequences is excluded absolutely. Finally, several simulation results on six two-link manipulators are given to verify the effectiveness of the designed control strategy.     

A Saturating Extension of an Output Feedback Controller for Internally Damped Euler‐Lagrange Systems

In this research, a novel extension of the passivity‐based output feedback trajectory tracking controller is developed for internally damped Euler‐Lagrange systems with input saturation. Compared with the previous output feedback controllers, this new design of a combined adaptive controller‐observer system will reduce the risk of actuator saturation effectively via generalized saturation functions. Semi‐global uniform ultimate boundedness stability of the tracking errors and state estimation errors is guaranteed by Lyapunov stability analysis. An application of the proposed saturated output feedback controller is the stabilization of a nonholonomic wheeled mobile robot with saturated actuators towards desired trajectories. Simulation results are provided to illustrate the efficiency of the proposed controller in dealing with the actuator saturation.     

Consensus analysis for leader‐following multi‐agent systems with second‐order individual dynamics and arbitrary sampling

This paper performs a consensus analysis of leader‐following multi‐agent systems with multiple double integrators in the framework of sampled‐data control. Both single‐leader and multiple‐leader scenarios are considered under the assumption of networks with detectable position‐like state information. The coordination tasks are accomplished by a given protocol with the robustness against the change of sampling periods. The sampling periods can be chosen to be of an arbitrary fixed length or large time‐varying length. Under the proposed protocol, we achieve two objectives: (i) in the single leader‐subgroup case, all followers reach an agreement with leaders on states asymptotically and (ii) in the multiple leader‐subgroup case, each follower converges to some convex combination of the final states of all leaders. It is shown that the final state configuration of the convex combination is uniquely determined by the underlying interaction topology, which can be any weakly connected graph. Compared with the existing results on leader‐following networks, the consensus problem and the containment problem are solved in a unified framework with large sampling periods. Some numerical experiments are conducted to illustrate the dynamic behavior of all agents with this protocol. Copyright © 2017 John Wiley & Sons, Ltd.