Distributed Containment Control Research Articles

Guaranteed performance design for distributed bounded containment control of networked uncertain underactuated surface vessels

This paper presents a predefined performance design approach for distributed containment control of networked heterogeneous underactuated surface vessels (USVs) under a directed graph topology. It is assumed that the position information of multiple dynamic leaders is informed to only a subset of the followers consisting of USVs and all nonlinearities and external forces in each USV follower are unknown. The local control law for each USV follower is recursively designed using the predefined performance design technique where auxiliary variables are presented to deal with underactuated constraints in the predefined performance design framework and the approach angles capable of the tracking of both straight and curved line are employed. Compared with the existing literature on the control of multiple ocean vehicles with uncertainties, the proposed distributed control methodology is simply designed without using any function approximators and adaptive techniques to estimate uncertainties or their bounds. It is shown that the distributed containment errors are preserved within the predefined bounds of transient and steady-state performance in the Lyapunov sense.

Observer-based event-triggered containment control of multi-agent systems with time delay

ABSTRACTThis paper studies the containment control of general linear multi-agent systems with or without time delay. The observer-based event-triggered control schemes will be considered. For the conventional distributed containment control protocol, we will not update the relative state continuously, i.e. the relative state will be updated by some events which happen intermittently. A completely decentralised event trigger will be designed for leader–follower systems. Under the proposed protocol, if we design some appropriate feedback gain matrices, all followers will asymptotically converge to the convex hull spanned by the dynamic leaders. Numerical simulations are also provided and the results show highly consistent with the theoretical results.

Containment Control of Single-Integrator Network With Limited Communication Data Rate

This technical note investigates distributed containment control for a single-integrator continuous-time multi-agent system with a limited communication data rate. Network topology is a directed communication graph. The containment control with quantized communication for each follower is designed using only its neighbour's quantized information so that all followers move into the convex hull spanned by the leaders. Necessary and sufficient criteria which guarantee achievement of containment consensus are given if the communication data rates are unfixed or fixed. Under a given bound on communication data rate, an algorithm is established to achieve the containment consensus. Finally, all the theoretical results are illustrated by numerical simulations.

Containment Control for First-Order Multi-Agent Systems with Time-Varying Delays and Uncertain Topologies**Supported by the National Natural Science Foundation of China under Grant Nos. 61273152, 61304052, 51407088, the Science Foundation of Education Office of Shandong Province of China under Grant Nos. ZR2011FM07, BS2015DX018

Containment control of first-order multi-agent systems with uncertain topologies and communication time-delays is studied. Suppose system topologies are dynamically changed, a containment control algorithm with time-varying delays is presented. The stability of the control algorithm is studied under the assumption that communication topologies are jointly-connected, and constraint condition of distributed containment control for delayed multi-agent systems is derived with the aid of Lyapunov-Krasovskii function. Simulation results are provided to prove the correctness and effectiveness of the conclusion.

Recordando al Dr. Ramon Balius i Juli (1928-2016), médico del deporte y humanista

This paper studies a discrete-time formation containment tracking control problem of a linear heterogeneous multi-unmanned system under the leader-follower formation with switching directed topology and unknown external disturbance. To solve the containment tracking control of the heterogeneous multi-unmanned system with switching directed topology, distributed containment control strategies are presented in this paper. First, according to practical situation, the discrete-time heterogeneous multi-unmanned system composed of unmanned aerial vehicles and unmanned ground vehicle is given. Then, by using switching directed topology, the distributed state feedback control strategies are proposed for the leaders and followers. An l2−l∞ performance index is introduced to guarantee the tracking performance of the heterogeneous multi-unmanned system under the unknown energy-bounded disturbance. The controller gains of the leaders and followers are solved by a set of linear matrix inequalities (LMIs). Finally, simulation results demonstrate the effectiveness of the designed control strategies.

A low-complexity design for distributed containment control of networked pure-feedback systems and its application to fault-tolerant control

Summary This paper addresses a low-complexity distributed containment control problem and its extension to fault-tolerant control for networked nonlinear pure-feedback systems under a directed graph. The multiple dynamic leaders are neighbors of only a subset of the followers described by completely non-affine multi-input multi-output pure-feedback dynamics. It is assumed that all followers' nonlinearities are heterogeneous and unknown. The proposed containment controller is implemented by using only error surfaces integrated by performance bounding functions and does not require any differential equations for compensating uncertainties and faults. Thus, compared with the previous containment control approaches for multi-agent systems with unknown non-affine nonlinearities, the distributed containment control structure is simplified. In addition, it is shown that the proposed control scheme can be applied to the fault-tolerant containment control problem in the presence of unexpected system and actuator faults, without reconstructing any control structure. It is shown from Lyapunov stability theorem that all followers nearly converge to the dynamic convex hull spanned by the dynamic leaders and the containment control errors are preserved within certain given predefined bounds. Copyright © 2016 John Wiley & Sons, Ltd.

Containment of Higher-Order Multi-Leader Multi-Agent Systems: A Dynamic Output Approach

This technical note addresses the distributed containment control problem for a linear multi-leader multi-agent system with a directed communication topology. A new class of distributed observer-type containment protocols based only on the relative output measurements of the neighboring agents is proposed, removing the impractical assumption in some of the existing approaches that the observers embedded in the multiple dynamic agents have to share information with their neighbors. Under the mild assumption that, for each follower, there exists at least one leader having a directed path to that follower, some sufficient conditions are derived to guarantee the states of the followers to asymptotically converge to a convex hull formed by those of the dynamic leaders. Finally, some numerical simulations on containment of a multi-vehicle system are given to verify the effectiveness of the theoretical results.

Distributed containment control of fractional-order uncertain multi-agent systems

This paper investigates the containment control problem of uncertain linear multi-agent systems, where the dynamics of each agent is described by a fractional-order differential equation. Based on the stability theory of fractional-order systems and matrix theory, some sufficient conditions are presented to ensure that the states of the followers can asymptotically converge to the convex hull formed by those of the leaders, and the feedback matrix of the proposed protocol is also determined according to linear matrix inequalities. Two simulation examples are provided to demonstrate the effectiveness of the theoretical results.

Containment control of multi-agent systems with fixed time-delays in fixed directed networks

Containment control of multi-agent system with time-delays is a meaningful topic with considerable realistic significance in the research of multi-agent systems. This paper investigates the distributed containment control of a group of mobile autonomous agents with multiple stationary or dynamic leaders, when considering the fixed time-delay under fixed directed network topologies. In the case of studying the multi-agent delayed system with continuous-time, Laplace transform and final value theorem are employed. Specifically some sufficient conditions are obtained which can ensure the containment of the first-order multi-agent systems. Moreover, an effective control protocol is designed for the first-order discrete-time systems with fixed time-delays. Finally, simulation examples are given to verify the effectiveness of the theoretical results and conclusions.

Distributed reference model based containment control of second-order multi-agent systems

This paper addresses the distributed containment control problem in a group of agents governed by second-order sampled-data dynamics with directed network topologies. Based on the assumption on the communication topology between agents, a distributed reference model based containment controller is adopted to drive the followers to the convex hull spanned by leaders. By studying the performance of the reference models connected in a distributed network and discussing the limiting behavior of agents by treating the effects of error states of reference models as disturbances in a tracking problem, it can be proved that the containment control problem can be solved by the proposed controller with appropriate sample period and control parameters. Finally, numerical examples are used to illustrate our theoretical results.

Distributed containment control for bounded unknown second-order nonlinear multi-agent systems with dynamic leaders

This paper investigates distributed containment control problems for second-order nonlinear multi-agent systems with dynamic leaders. In the presence of bounded unknown nonlinearity, a distributed control algorithm based on High-frequency Feedback Robust Control is proposed. Under this algorithm, a sufficient condition is proposed to ensure that all the followers will converge to the dynamic convex hull formed by dynamic leaders and the containment error can be ultimately bounded for the directed graph where at least one leader has a directed path to each follower and the communication among the followers are undirected. Numerical simulations are also presented to illustrate the effectiveness of the theoretical results.

Distributed containment control with predefined performance of high‐order multi‐agent systems with unknown heterogeneous non‐linearities

This study presents a predefined performance design approach for the distributed containment control of heterogeneous non-linear strict-feedback systems with multiple dynamic leaders under a directed graph topology where the leaders are neighbours of only a subset of the followers. It is assumed that all followers’ non-linearities unmatched in the control input are unknown. The performance bounds, which characterise the convergence rate and maximum overshoot of control errors, are incorporated into the control error vectors, in order to ensure the predefined transient and steady-state performance of containment control errors. On the basis of these error vectors, the authors design a simple distributed containment control system without employing any function approximators to estimate unknown non-linearities and calculating the repeated derivatives of virtual controllers. It is shown from Lyapunov stability theorem that all followers nearly converge to the dynamic convex hull spanned by the dynamic leaders and the containment control errors are preserved within certain given predefined bounds.

Distributed Containment Control for Nonlinear Multi‐Agent Systems with Time‐Delayed Protocol

AbstractIn this paper, the containment control problem is considered for nonlinear multi‐agent systems with directed communication topology. Under the guidance of designed distributed communication protocols with/without previous state information, the followers are expected to converge to a dynamic convex hull spanned by multiple leaders. Two multi‐step algorithms are proposed to construct the corresponding protocols, the state feedback protocol and the delay‐coupled protocol, under which the containment control can be achieved asymptotically. Furthermore, it is found that the delay‐coupled protocol is rather sensitive to time delays. That is, real‐time tracking will become impossible by only using long‐dated previous state information. Finally, a numerical example is given to demonstrate the applicability and efficiency of the proposed schemes.

Distributed containment control of second‐order multiagent systems with input delays under general protocols

This article addresses the distributed containment control problem in a group of agents governed by second‐order dynamics with directed network topologies. Considering there are multiple leaders, we study a general second‐order containment controller which can realize several different consensus modes by adjusting control gains. A necessary and sufficient condition on the control gains of the general containment controller is provided. Moreover, the delay sensitivity of the closed‐loop multiagent system under the general containment controller is studied; the maximal upper bound of the constant delays is obtained. Finally, several numerical examples are used to illustrate the theoretical results. © 2015 Wiley Periodicals, Inc. Complexity 21: 112–120, 2016

Distributed Containment Control with Dynamic Leaders Based on Binocular Vision

In this paper, we study the distributed containment control problem for multi-robot system with dynamic leaders in the presence of parametric uncertainties. The binocular vision system is used as the sensing device to provide real-time status information for the followers, so flrstly, a new binocular visual model for dynamic target is established. Then RBF neural networks are employed to approximate the unknown nonlinear functions in the system model of followers, and the approximated values are introduced into the designed sliding mode controllers to make compensation. Finally, simulation results are presented to show the validity of the proposed control strategy.

Distributed containment control and state observer design for multi-agent robotic system

Aiming at the distributed containment control problem for multi-agent robotic system with stationary leaders, a position-sensorless control strategy is proposed based on binocular visual servo and feedback dissipative Hamilton theory. Firstly, the topological relationship among the robots is built by using directed graph, which makes each follower determine its neighbour robots. Secondly, a binocular visual servo model is established, so as to describe the dynamic information of the tracking target point for each follower through the neighbour robots' image information. Thirdly, the distributed containment controllers are designed based on the pre-feedback control strategy and feedback dissipative Hamilton theory; furthermore, in the case that each follower is not equipped with internal position sensor, the full-order state observers are developed by using the 'expansion + feedback' method, and then realise the position-sensorless control. Finally, a simulation is carried out on multiple two degrees-of-freedom (DOF) robots, and results show the validity of the proposed control strategy.

Distributed containment control for uncertain nonlinear multi-agent systems in non-affine pure-feedback form under switching topologies

This paper considers the containment control problem of uncertain nonlinear multi-agent systems with multiple dynamic leaders under switching directed topologies. The followers are governed by a class of non-affine pure-feedback systems with arbitrary uncertainty. Implicit function and mean value theorems are employed to overcome the difficulty in controlling the non-affine pure-feedback systems and fuzzy logic systems are utilized to approximate the unknown nonlinear functions. Distributed adaptive containment controllers are proposed to guarantee that the outputs of all followers converge to the convex hull spanned by the multiple dynamic leaders. In addition, by incorporating the distributed dynamic surface control (DSC) technique, the developed containment controllers are able to eliminate the problem of “explosion of complexity” inherent in backstepping design. Based on Lyapunov stability theory, it is proved that all signals in the closed-loop systems are cooperatively semiglobally uniformly ultimately bounded (CSUUB), and the containment errors converge to a small neighborhood of the origin. An example is provided to show the effectiveness of the control approach.

Necessary and sufficient conditions for distributed containment control of multi‐agent systems without velocity measurement

This study investigates the distributed containment control for second-order multi-agent systems with multiple stationary or dynamic leaders based on only position information. Based on stability and algebraic graph theories, some necessary and sufficient conditions are obtained. Firstly, when the leaders are stationary, a necessary and sufficient condition is given to guarantee that all followers will ultimately converge to the stationary convex hull spanned by the stationary leaders for arbitrary initial states. The containment control protocol is designed based on a distributed filter, which is used for estimating the neighbours’ velocities of each follower. Secondly, when each leader is dynamic with constant velocity, using sampled current and outdated position data, a necessary and sufficient condition is obtained to drive the followers into the dynamic convex hull spanned by the dynamic leaders. Finally, some numerical simulations are presented to illustrate the proposed theories.

Distributed Containment Control for Multiple Unknown Second-Order Nonlinear Systems With Application to Networked Lagrangian Systems

In this paper, we consider the distributed containment control problem for multiagent systems with unknown nonlinear dynamics. More specifically, we focus on multiple second-order nonlinear systems and networked Lagrangian systems. We first study the distributed containment control problem for multiple second-order nonlinear systems with multiple dynamic leaders in the presence of unknown nonlinearities and external disturbances under a general directed graph that characterizes the interaction among the leaders and the followers. A distributed adaptive control algorithm with an adaptive gain design based on the approximation capability of neural networks is proposed. We present a necessary and sufficient condition on the directed graph such that the containment error can be reduced as small as desired. As a byproduct, the leaderless consensus problem is solved with asymptotical convergence. Because relative velocity measurements between neighbors are generally more difficult to obtain than relative position measurements, we then propose a distributed containment control algorithm without using neighbors' velocity information. A two-step Lyapunov-based method is used to study the convergence of the closed-loop system. Next, we apply the ideas to deal with the containment control problem for networked unknown Lagrangian systems under a general directed graph. All the proposed algorithms are distributed and can be implemented using only local measurements in the absence of communication. Finally, simulation examples are provided to show the effectiveness of the proposed control algorithms.

Distributed impulsive containment control for second-order multi-agent systems with multiple leaders

This paper considers the problem of distributed containment control for second-order multi-agent systems via impulsive control, here both multiple stationary and dynamic leader cases under a directed network topology that characterizes the interaction among the leaders and the followers are addressed. Two distributed impulsive containment control protocols for such system are proposed, where each agent only exchanges position information with its neighbors and updates its velocity state in the form of an abrupt jumps setting. For the stationary leader case, a necessary and sufficient condition is presented to achieve the containment control task, while for the dynamical leader case, a sufficient criterion is derived to regulate all followers to access the dynamic convex hull formed by the dynamic leaders. Finally, numerical examples are given to illustrate the theoretical results.