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Abstract: Distributed finite-time attitude containment control for multiple rigid bodies is addressed in this paper. When there exist multiple stationary leaders, we propose a model-independent control law to guarantee that the attitudes of the followers converge to the stationary convex hull formed by those of the leaders in finite time by using both the one-hop and two-hop neighbors’ information. We also discuss the special case of a single stationary leader and propose a control law using only the one-hop neighbors’ information to guarantee cooperative attitude regulation in finite time. When there exist multiple dynamic leaders, a distributed sliding-mode estimator and a non-singular sliding surface were given to guarantee that the attitudes and angular velocities of the followers converge, respectively, to the dynamic convex hull formed by those of the leaders in finite time. We also explicitly show the finite settling time. [Copyright &y& Elsevier]

In this paper, a finite-time containment robust control scheme is proposed for autonomous surface vehicle with input saturation constraint. Firstly, to achieve finite-time containment control, a saturated distributed equivalent control algorithm is proposed based on the position and velocity measurements of neighbors and a part of leaders; In light of the tools from algebraic graph theory and homogeneous theory, it is theoretically proven that all the follower will converge to the convex hull formed by the virtual leaders in finite-time; Then, in order to suppress the influence of external disturbance, a nonlinear integral sliding mode surface based on equivalent control law is designed. Combined with finite-time Lyapunov stability theory, a finite-time cooperative control law is proposed, which makes the system tend to sliding surface in finite-time from any initial state; Finally, simulation results are presented to verify the effectiveness of the proposed control scheme. • A novel finite-time containment control scheme is proposed for autonomous surface vehicles by using homogeneous theory. • By using a saturated function, the amplitude of the proposed control scheme can be limited. • To suppress the disturbance, a nonlinear integral sliding mode surface based on equivalent control law is designed. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of containment control strategy for a fleet of follower underactuated surface vessels (USVs) for avoiding obstacles safely and efficiently if the leader USVs are well equipped with high precision sensors. Therefore, within in this framework, we present a constructive method to design totally new prescribed-time performances for formation containment control problem for multiple underactuated surface vehicles (USVs) with unavailable velocity information, uncertainties and subject to inputs and outputs constraints, under directed communication graphs. First, in order to reconstruct the unavailable velocity information as well as to estimate unknown USVs dynamics, induced by unmodeled dynamics, and environmental disturbances, a fuzzy-adaptive observer is designed for the state estimation using only global position information and local measurement of the USVs orientation angle. Next, relying on the backstepping method with anti-windup compensators, new robust output feedback distributed controllers for the follower USVs are designed. Unlike some existing results, based on the use of a speed function, the devised controllers are able to drive the USVs to a neighborhood of the convex hull formed by the leaders in a given finite time at a controllable rate of convergence that can be prescribed by the user. Furthermore, to address the containment error constraints requirement, a universal barrier function approach with a new state transformation is introduced to deal with such constraints. It is shown that all the signals are bounded by an arbitrarily positive constant after a prescribed time. The benefits of the proposed control scheme are validated through computer simulations. • Flocking of multiple UAVs in a narrow passage. • Adaptive based Fuzzy-logic containment control. • Prescribed-time performances for containment control of USVs. • Constrained maneuvering Output with Input saturations. • Output-Feedback for containment control of USVs. [ABSTRACT FROM AUTHOR]

This paper introduces a distributed containment control strategy for multiple unmanned surface vehicles (USVs) under the unknown external disturbances. The communication network of the USVs is a fixed, directed topology and only a part of the follower USVs can read the states of leader USVs. To guarantee the transient and steady-state performance of the system, the tracking errors are converted into new error functions. By utilizing the disturbance observer, the external disturbances are effectively estimated. According to the new group of errors, a distributed containment controller is proposed with the estimated external disturbances. Furthermore, using graph theory and Lyapunov approach, it is proved that all variables of the multiple USV systems are bounded and the tracking errors can be confined within the specified performance ranges. Finally, simulation results illustrate the effectiveness of the designed distributed containment controller., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2021 ISA. Published by Elsevier Ltd. All rights reserved.)

This study investigates the containment problem of networked underactuated unmanned surface vehicles (USVs) guided by multiple virtual leaders using an event-triggering control mechanism. Each USV is subject to external disturbance and internal model uncertainties. First, a finite-time observer is introduced to identify the model uncertainties and the unmeasured USV velocities. Then, a guidance law is designed to generate a series of virtual reference points for each USV so that these points are contained within the convex hull spanned by the virtual leaders. Meanwhile, the path update law for each virtual leader is proposed. Next, to steer the USVs towards the corresponding reference points, an event-triggered-based control law is developed for each USV using the observed data, in which the event-triggering technique is applied in the channel of sensor-to-controller to reduce communication burden while ensuring the similar control performance with the continuous mechanism. Besides, a first-order filter is introduced to provide the derivatives of the virtual control laws. Finally, stability analysis shows that the closed-loop system is finite-time stable and all error signals converge to a small bound within finite time. Comparative simulations are provided to show the effectiveness of the proposed event-triggered containment control method. [Display omitted] • The proposed method can indirectly calculate the control laws for underactuated USVs. • A novel event-triggering mechanism is applied in the sensor-to-controller channel of each USV. • The proposed triggering threshold is related to system states, and is time-varying. • The event-triggered closed-loop containment control system is finite-time stable. [ABSTRACT FROM AUTHOR]

• The dynamics of all agents in multi-agent systems are modeled by the R-L fractional differential equation. • A novel iterative relationship is found during the convergence analysis. • Sufficient conditions for general first-order fractional discrete-time multi-agent systems achieving containment control are given. • Sufficient conditions for second-order fractional discrete-time multi-agent systems with nonconvex constraints achieving containment control are given. This paper is devoted to the containment control problem of fractional discrete-time multi-agent systems (FDTMASs) with nonconvex velocity and control input constraints. First, distributed containment controllers with nonlinear projection algorithms are proposed for all followers. Then, some sufficient conditions are deduced during the convergence analysis of the closed-loop systems. By using Lyapunov stability theory and properties of fractional calculus, it proved that the containment control of the systems could be achieved with the distributed containment controller. Finally, some numerical examples are given to show the correctness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

The paper deals with topology-induced containment output feedback for ensuring multi-consensus of homogeneous linear systems evolving over a weakly connected communication digraph. Starting from the extension of a recent characterization of multi-consensus, a decentralized static feedback enforcing multi-consensus is designed based on a suitable network-induced decomposition; a neighborhood state-observer is proposed for completing the design. The results are finally illustrated over a simple simulated example. [ABSTRACT FROM AUTHOR]

This paper investigates the containment control problem for multi-agent systems (MASs) with multiple leaders which have non-zero control inputs. Agents' tracking errors are described by a linear system with an external disturbance. The containment control problem is then solved by applying a distributed observer-based output feedback controller. Anti-windup (AW) compensation is designed by convex conditions, to improve the performance in the presence of actuator saturation. Finally, simulations are presented to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The coordination control of multi-agent systems (MASs) with stochastic noise has been widely studied. But it is still unclear when the stochastic noise is the fractional Brownian motion (fBm), which has the character of memorability. In this paper, we investigate the containment control problem of MASs with fBm over a directed communication network. Firstly, we design several state observers to estimate the states of the followers. Then, based on the estimation information, we design a novel control function for each follower. With the aid of the properties of analytic semigroup and fixed point theorem, we prove that the MASs can achieve the mean-square containment control or quasi-containment control. Finally, we provide simulation examples to demonstrate the effectiveness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we study a containment control problem for second-order multi-agent systems in the presence of convex position constraints and switching graphs. A distributed algorithm with a nonlinear projection operator is proposed to guarantee that each agent eventually converges into the convex hull spanned by some given multiple static points, while the position of each agent is kept lying in a given closed set. It is proved that all agents ultimately converge into the convex hull while each agent remains in its constraint set as long as there exists a directed path from the static points to the agents in the union of the graphs in each bounded time interval. Finally, a numerical example is given to illustrate the obtained theoretical results. [ABSTRACT FROM AUTHOR]

This paper studies the problem of distributed containment control for multi-agent systems modeled by double integrators. A new class of rotation-free distributed containment controllers with successive saturated loops is proposed for the challenging situation where the velocity and acceleration of each agent are required to stay within their desired ranges. It is proved that the objective of containment control is achievable if the parameters of the controllers satisfy a mild condition. Moreover, the desired ranges of the accelerations and the velocities are allowed to be very small, and the interconnection topology is allowed to be directed and switched. [ABSTRACT FROM AUTHOR]

A practical event-triggered design method is developed for cooperative robust containment control problem of multi-agent systems with multiple leaders. The multi-agent systems discussed in this paper are essentially heterogeneous, and each follower is modeled by a integrator with the external disturbance. A containment error also has been expressed to ensure all the outputs of followers converge to the convex hull spanned by the outputs of the leaders. For the case that the undirected communication graph among followers is connected, a distributed containment compensator is designed based on the local state information of neighboring agents. Furthermore, a distributed output feedback controller is designed to solve the event-triggered containment control problem of the continuous-time multi-agent systems. Finally, a numerical example is given to verify the effectiveness of the main results. [ABSTRACT FROM AUTHOR]

The objective of containment control in multi-agent systems is to design control algorithms for the followers to converge to the convex hull spanned by the leaders. Sampled-data based containment control algorithms are suitable for the cases where the power supply and sensing capacity are limited, due to their low-cost and energy-saving features resulting from discrete sensing and interactions. In addition, sampled-data control has advantages in performance, price and generality. On the other hand, when the agents have double-integrator dynamics and the leaders are dynamic with nonzero inputs, the existing algorithms are not directly applicable in a sampled-data setting. To this end, this paper proposes a sampled-data based containment control algorithm for a group of double-integrator agents with dynamic leaders with nonzero inputs under directed communication networks. By applying the proposed control algorithm, the followers converge to the convex hull spanned by the dynamic leaders with bounded position and velocity containment control errors, and the ultimate bound of the overall containment error is proportional to the sampling period. A numerical simulation is presented to illustrate the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper presents an estimator-based minimal learning parameter (EMLP) neuroadaptive dynamic surface containment control design capable of guaranteeing transient and steady-state behavior for multiple quadrotors with uncertainties, such that the followers can be driven into the convex hull constituted by multiple dynamic leaders with prescribed bounded errors. To facilitate the control design, the quadrotor dynamics is decomposed into translational and rotational subsystems. For each subsystem, in order to enable smooth and rapid learning of unknown system uncertainties and reduce the computational load in traditional neural network (NN), the estimation errors, instead of tracking errors, are used to regulate NN weights and only one NN learning parameter is required for adaptive neural approximation with the aid of MLP, which is more feasible for real-time implementation. Additionally, dynamic surface control (DSC) technique is introduced in control design to extract the time derivative of virtual control laws, and thus the issue of "explosion of complexity" can be circumvented. As an extension, prescribed performance function and error transformation technique are utilized to address the preselected containment synchronization error constraints problem. Finally, the stability analysis is established to prove that all error signals are uniformly ultimately bounded (UUB). Simulation results illustrate the effectiveness and superiority of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This paper studies containment control for second-order multi-agent systems via intermittent sampled position data communication. For the proposed protocols with and without time delay, some necessary and sufficient conditions are obtained to achieve containment by means of discussing the relationship between the network structure and some system parameters, and the final states of all followers are identified by the initial values of the leaders and the topology structure. Finally, several numerical simulations are given to verify the correctness of the theoretical results. [ABSTRACT FROM AUTHOR]

The problem of prescribed-time containment control of unmanned underwater vehicles (UUVs) with faults and uncertainties is considered. Different from both regular finite-time control and fixed-time control, the proposed prescribed-time control strategy is built upon a novel coordinate transformation function and the block decomposition technique, resulting in the followers being able to move into the convex hull spanned by the leaders in prespecifiable convergence time. Moreover, intermediate variables and the control input terms are also shown to remain uniformly bounded at the prescribed-time. To reduce the magnitude of the bounds, a novel fixed-time observer for the fault is proposed. Two numerical examples are provided to verify the effectiveness of the proposed prescribed-time control strategy. [ABSTRACT FROM AUTHOR]

This paper investigates the containment control problem for a class of partial differential multi-agent systems, which are governed by the parabolic equations (heat equations) or the second-order hyperbolic equations (wave equations). The distributed containment-based feedback control laws are obtained by constructing an appropriate Lyapunov functional, and under the action of the feedback control laws, the containment errors between the followers ′ states and the convex hull spanned by the leaders ′ states on an appropriate Sobolev space can converge to zero as time tends to infinity. Simulation examples are finally used to show the effectiveness of the theoretical analysis. • Put forward the containment control problem of partial differential MASs. • Apply the Lyapunov functional approach. • The partial differential MASs are governed by the most important PDEs. [ABSTRACT FROM AUTHOR]

In this paper, the problem of containment control with minimum number of leaders in arbitrary directed networks consisting of time-varying nonlinear multi-agents is investigated. Unlike the existing containment control problem with redundant leaders in special networks, we consider the problem with minimum number of leaders in arbitrary directed networks. We show that the problem of finding the minimum number of leaders can be converted into a minimum spanning tree problem by introducing a toll station connecting with each agent. By employing the developed Edmonds' algorithm, the minimum number of leaders is located at the roots of each tree in the obtained spanning forest. This situation allows us to achieve containment control in a distributed manner. On the basis of this situation, a distributed protocol is developed to address the containment control of multi-agent systems with time-varying nonlinear dynamics. Simulation results are provided to illustrate the efficiency of the proposed methodology. Our work makes it possible for studying and extending application of containment control problems in various complex networks. • We consider a containment control problem with minimum number of leaders in arbitrary directed networks consisting of time-varying nonlinear multi-agents. • We show that this problem can be formulated as a minimum spanning forest problem, and based on which a distributed containment control protocol is developed. • We uncover that the minimum number of leaders are found locating at the roots of each tree in the obtained spanning forest. This method differs from the existing containment control problem with redundant leaders in specific networks. [ABSTRACT FROM AUTHOR]

This paper studies the problem of distributed containment control for multi-agent systems with high-order dynamics and input delays. Two event-triggered control algorithms are proposed for multi-agent systems without and with input delay, respectively. The communication instants between two linked followers are determined by the event-triggering condition, and every follower can detect the event based on its own control input. For the followers, edge-based estimators are adopted to predict state differences to neighbors. Control inputs of the followers are calculated based on the predicted values of the state differences. To deal with the input delay, a delay comprehension approach is developed. It is proved that for arbitrarily large but bounded input delays, the followers can move into the convex hull spanned by the leaders asymptotically. Simulation results show the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of event-triggered containment control for second-order multi-agent systems with sampled position data. First, a distributed event-triggered containment control protocol is designed, which utilizes the sampled position data only and allows the event-triggering condition to be intermittently examined at constant sampling instants. Then, based on the algebraic graph theory and matrix theory, a sufficient condition on the communication topology, the controller gains, and the sampling period is derived so as to achieve containment control. Finally, a numerical example is provided to verify the theoretical results., (Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.)