Distributed Containment Control Research Articles

Robust Distributed Containment Control with Adaptive Performance and Collision Avoidance for Multi-Agent Systems

This paper deals with the containment control problem for multi-agent systems. The objective is to develop a distributed control scheme that leads a sub-group of the agents, called followers, within the convex hull that is formed by the leaders, which operate autonomously. Towards this direction, we propose a twofold approach comprising the following: (i) a cyber layer, where the agents establish, through the communication network, a consensus on a reference trajectory that converges exponentially fast within the convex hull of the leaders and (ii) a physical layer, where each agent tracks the aforementioned trajectory while avoiding collisions with other members of the multi-agent team. The main contributions of this work lie in the robustness of the proposed framework in both the trajectory estimation and the tracking control tasks, as well as the guaranteed collision avoidance, despite the presence of dynamic leaders and bounded but unstructured disturbances. A simulation study of a multi-agent system composed of five followers and four leaders demonstrates the applicability of the proposed scheme and verifies its robustness against both external disturbances that act on the follower model and the dynamic motion of the leaders. A comparison with a related work is also included to outline the strong properties of the proposed approach.

Distributed Containment Control Strategy for the Dynamic Stabilization of Integrated Energy System With Multiple Virtual Leaders

Distributed Containment Control Strategy for the Dynamic Stabilization of Integrated Energy System With Multiple Virtual Leaders

Containment control of systems with constraints and bounded disturbances

AbstractThis article studies the distributed containment control of a second‐order discrete‐time multi‐agent system with convex constraints on positions, nonconvex constraints on velocities, bounded disturbances on static points and switching topologies. A distributed control algorithm with disturbance information and local information is proposed. It is proved that when the static points with disturbances and the joint graph have a directed spanning forest among each time interval, all agents are gradually driven to the neighborhood of a convex hull spanned by the static points, and an upper bound of the neighborhood is obtained. The most innovative point is to utilize a rigorous mathematical theory to deal with convex constraint error rather than a geometric explanation. Meanwhile, another control algorithm with static point information and local information is proposed to converge all agents to the convex hull in the absence of external disturbances. Additionally, a numerical example is conducted to illustrate this theory.

Fuzzy adaptive containment control for fractional‐order heterogeneous nonlinear multi‐agent systems with mixed time‐varying delays

SummaryThis study investigates the issue of containment control (CC) of multi‐agent systems (MASs) that are heterogeneous, nonlinear, and fractional‐order while taking practical scenarios into account, such as uncertainties, unknown nonlinearities, time‐varying state delays, and distributed time‐varying delays. A fully distributed adaptive observer is created for each follower in accordance with the communication topology information among agents. This observer is designed to estimate the convex combination information of the leaders. The approach utilizes interval type‐2 fuzzy set theory and adaptive methods to design a distributed containment control strategy that only uses the self‐information of the followers and neighbor nodes' information. Sufficient conditions for implementing containment control are given. A new Lyapunov‐Krasovskii functional (LKF) is constructed, and the stability of the system with feedback loop is proven using fractional‐order theory and inequality methods. Lastly, a simulation example is presented to illustrate the efficacy of the proposed approach.

Adaptive containment control of heterogeneous high‐order fully actuated multi‐agent systems

AbstractIn this article, the distributed containment control schemes are presented for a class of nonlinear heterogeneous high‐order fully actuated multi‐agent systems. First, for each follower, the reference trajectory generator is constructed by using the output information of the neighbor agents. Then, the distributed containment controllers are designed for the system with known nonlinear system function matrices and control gain matrices. Further, since the existence of modeling errors and other uncertain factors, the obtained system model is often not accurate enough, that is, the system function matrix and control gain matrix are actually unknown nonlinear matrices. To tackle these obstacles, we employ the radial basis function neural network method to approximate the unknown nonlinear system function matrices and skillfully construct the controllers combined with the adaptive technology to eliminate the effects of the unknown control gain matrices. The developed control strategies can guarantee that the containment control can be realized and the containment errors can be adjusted to arbitrary precision. In the end, the simulation results on the electromechanical system and robotic system demonstrate the availability and effectiveness of the provided schemes.

Fully distributed containment control of second-order nonlinear multi-agent systems using disturbance observer with directed graph

Fully distributed containment control of second-order nonlinear multi-agent systems using disturbance observer with directed graph

Event-Triggered Distributed Containment Control for Networked Hypersonic Flight Vehicles

This article tackles the distributed output-feedback containment control task for networked hypersonic flight vehicles (HFVs) in the presence of limited communication resources. Distinctive with the state-of-the-art control methodologies designed for single/multiple HFVs, the distinguishing features of our design lie in that: 1) a novel switching event-triggered information transmission mechanism embedded with an error-dependent monotonically decreasing power term is devised in such a way that the frequencies of data transmission among distinct HFVs can be significantly reduced, while at the same time maintaining desired consensus tracking errors; 2) a new set of error variables is delicately formulated such that the containment control task is realized in the sense that all follower HFVs are ensured to converge to a dynamic convex hull formed by leader HFVs; and 3) the priori knowledge of flight state variables is not required during the control design. To be precise, a high-gain observer is resorted to tackle the challenge that the attitude angles information is normally difficult to be obtained precisely in a practical hypersonic regime. Comparative simulation tests are finally carried out to validate the superiorities of the obtained theoretical findings.

Distributed Fault-Tolerant Containment Control Protocols for the Discrete-Time Multiagent Systems via Reinforcement Learning Method.

This article investigates the model-free fault-tolerant containment control problem for multiagent systems (MASs) with time-varying actuator faults. Depending on the relative state information of neighbors, a distributed containment control method based on reinforcement learning (RL) is adopted to achieve containment control objective without prior knowledge on the system dynamics. First, based on the information of agent itself and its neighbors, a containment error system is established. Then, the optimal containment control problem is transformed into an optimal regulation problem for the containment error system. Furthermore, the RL-based policy iteration method is employed to deal with the corresponding optimal regulation problem, and the nominal controller is proposed for the original fault-free system. Based on the nominal controller, a fault-tolerant controller is further developed to compensate for the influence of actuator faults on MAS. Meanwhile, the uniform boundedness of the containment errors can be guaranteed by using the presented control scheme. Finally, numerical simulations are given to show the effectiveness and advantages of the proposed method.

Fixed‐time disturbance observer based distributed cooperative containment control with fixed‐time anti‐saturation compensator for multi‐unmanned aerial vehicles

AbstractThis article proposes a fixed‐time backstepping distributed cooperative containment control scheme for multiple unmanned aerial vehicles (UAVs). A fixed‐time compensator is designed for the fixed‐wing UAVs actuator saturation problem. Based on this, an improved fixed‐time disturbance observer is proposed for the problem of the excessive initial peak. The problem of “complexity explosion” is solved by the fixed‐time differential filter. For the distributed containment control of multiple UAVs, a cooperative control architecture based on a fixed‐time anti‐saturation compensation system is proposed. The proposed algorithm can be shown practicable by using Lyapunov stability theory and graph theory. Simulation results are given to demonstrate the effectiveness of the proposed control scheme.

Adaptive NN-Based Event-Triggered Containment Control for Unknown Nonlinear Networked Systems.

This article systematically addresses the distributed event-triggered containment control issues for multiagent systems subjected to unknown nonlinearities and external disturbances over a directed communication topology. Novel composite distributed adaptive neural network (NN) event-triggering conditions and event-triggered controller are raised meanwhile. Furthermore, the designed event-triggered controller is updated in an aperiodic way at the moment of event sampling, which saves the computation, resources, and transmission load. On the basis of the NN-based adaptive control techniques and event-triggered control strategies, the uniform ultimate bounded containment control can be achieved. In addition, the Zeno behavior is proven to be excluded. Simulation is presented to testify the effectiveness and advantages of the presented distributed containment control scheme.

Containment Control With Different Constraints

This paper addresses a containment control problem for discrete-time multi-agent systems when position, velocity and input constraints coexist. A nonlinear distributed containment control algorithm is presented. The main difficulty is how to decouple the nonlinearities caused by the three kinds of constraints. To prove the convergence of the containment control problem, the distances from the followers to the convex hull spanned by the leaders are analyzed by removing the errors caused by the projection operators and the stochasticities of the equivalent system matrices are explored to show nonincreasing property of the maximum distance. It is shown that containment control can be achieved as long as the convex hull is contained in each position constraint set. Numerical simulations are given to illustrate the obtained theoretical results.

Model-Free Adaptive Containment Control for Unknown Multi-Input Multi-Output Nonlinear MASs With Output Saturation

In this work, a model-free adaptive containment control scheme is investigated for a class of multi-input multi-output nonlinear multiagent systems, where the agents’ dynamics are unknown with output saturation. Firstly, the dynamics of followers are transformed into a equivalently data model by using full form dynamic linearization technology. Secondly, the distributed containment control algorithm is proposed only using the input data and the saturated output data of followers and neighbors. Further, the boundedness of the containment error is proved by using the contraction mapping principle and mathematical induction method. It is shown that the developed scheme can ensure that the followers move into the convex hull composed of the leaders. Last, the effectiveness of the developed scheme can be verified through numerical simulations.

Parametric Dynamic Distributed Containment Control of Continuous-Time Linear Multi-Agent Systems with Specified Convergence Speed

This paper focuses on the distributed containment control of continuous-time linear multi-agent systems (MASs) with multiple leaders over fixed topology. A parametric dynamic compensated distributed control protocol is proposed in which both the information from the observer in the virtual layer and actual adjacent agents are employed. The necessary and sufficient conditions of the distributed containment control are derived based on the standard linear quadratic regulator (LQR). On this basis, the dominant poles are configured by using the modified linear quadratic regulator (MLQR) optimal control and Geršgorin's circle criterion, hence the containment control with specified convergence speed of the MAS is achieved. Another main advantage of the proposed design is, in the case of virtual layer failure, by adjusting parameters the dynamic control protocol reduces to static, and the convergence speed can still be specified through the dominant pole assignment method combined with inverse optimal control. Finally, typical numerical examples are presented to demonstrate the effectiveness of theoretical results.

Observer-Based Fully Distributed Containment Control for MASs Subject to DoS Attacks

The problem of the observer-based fully distributed containment control for multiagent systems (MASs) subject to denial-of-service (DoS) attacks is investigated in this article. First, a switched fully distributed control framework is established for a class of DoS attacks constrained by the attack duration. Then, a novel attack-resilient control scheme is developed to accomplish the containment control task. The major advantages of the devised control scheme are that any information of the whole network topology structure is not involved and only the information from neighbor agents is used. What is more, a novel observer-based attack compensator is devised to resist DoS attacks. Finally, a practical example of the mobile robot system is presented to testify the validity of the designed control scheme by a comparison.

Learning-Based Distributed Containment Control for HFV Swarms Under Event-Triggered Communication

This article proposes a learning-based distributed containment control protocol for a team of hypersonic flight vehicles (HFVs) composed by some leaders and some followers in the presence of switching event-triggered communication. In contrast with most existing results concerning HFVs, the crucial characteristics of our design lie in that all leader and follower HFVs are empowered with a distributed cooperative learning capability in the sense that neural networks weights are not required to be adapted all the time, in that all follower HFVs are retained in the convex hulls spanned by leader HFVs all the time, and in that the communication among distinct HFVs is conducted based on an event-triggered strategy that utilizes a switching threshold. More precisely, by utilizing the learned knowledge represented by constant neural networks, an experience-based distributed control protocol is further proposed without the need for online adaptation. Numerical simulations studies on a group of HFVs have been conducted to verify the effectiveness of the presented results.

Distributed containment control for multiple ocean bottom flying nodes with velocity error constraint and input saturation

This paper uses the directed communication topology to investigate the finite-time error constraint containment control for multiple Ocean Bottom Flying Node (OBFN) systems with thruster faults. The OBFN is a benthic Autonomous Underwater Vehicle (AUV), which has been used to explore submarine resources. The model uncertainties, velocity error constraint, external disturbances, and thruster faults of OBFNs motivate the design of containment controller. Moreover, some followers could obtain the states of leader OBFNs. We designed the command filter and the input signal is a hyperbolic tangent function. The virtual velocity error command is generated to follow the velocity error. Then the novel velocity error constraint distributed control algorithm is developed. Furthermore, for the problem of input saturation, by designing a stable anti-saturation compensator, an improved containment algorithm is proposed. It is proved that both the proposed approaches can converge the containment errors towards zero through Lyapunov theory in finite time, which means the followers can reach the convex hull formed by leaders in finite time. Finally, simulation results demonstrate the effectiveness of the two strategies.

Distributed Containment Control With Prescribed Accuracy for Nonstrict-Feedback Switched Nonlinear Multiagent Systems

Distributed containment control issue with prescribed accuracy is addressed in this article for nonstrict-feedback switched nonlinear multiagent systems with aperiodically time-varying parameters. First, a novel <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">congelation of variables</i> method is adopted to deal with time-varying parameters, which are fast-varying in an unknown compact set with only their radii known a priori. Further, by means of the Gaussian basis function property of the radial basis function neural network, the backstepping recursive design method can work normally for nonstrict-feedback systems. In order to handle the switched dynamics and obtain the desired prescribed performance, a common Lyapunov function is designed by incorporating a series of continuously differentiable switching functions. Then, under the proposed containment control scheme, containment control is achieved, and meanwhile, each containment error converges with a prescribed accuracy, which is given before the containment controller is implemented. Finally, two simulations are performed to validate the theoretical results.

Active disturbance rejection-based distributed containment control for stochastic nonlinear multiagent systems

ABSTRACT This paper investigates a distributed active disturbance rejection containment control problem for stochastic nonlinear multiagent systems under a directed topology. First, a class of nonlinear extended state observers predicated on the fractional power functions are proposed and extended state estimations are employed to compensate completely unknown stochastic terms and total disturbances in real time. Then the tracking differentiator is adopted to avoid the issue of computational burden caused by the repeated differentiation of virtual controllers. In light of the active disturbance rejection control technique, a distributed containment control scheme is put forward, which effectively deals with the problems of unknown nonlinearities and uncertain dynamics. Moreover, it is proved that containment errors of all followers converge to a small neighbourhood of the origin via the stochastic Lyapunov theory. Finally, the effectiveness of the proposed control method is verified by simulation results.

Distributed Containment Control for Human-in-the-Loop MASs With Unknown Time-Varying Parameters

This paper considers the distributed containment control problem for human-in-the-loop (HiTL) multiagent systems (MASs) subject to unknown time-varying parameters and input saturation. A smooth function containing positive integrable time-varying function is embedded in the controller to compensate for the negative effects of unknown time-varying parameters and uncertain disturbances. Meanwhile, an auxiliary system with the same order as the considered system is skillfully introduced into the backstepping control method to overcome the problem of input saturation. By constructing an adaptive command filter with error compensation mechanism, the problems of the computation burden and filtering errors are solved simultaneously. Moreover, the output signals of followers can converge into the convex hull spanned by multiple dynamic leaders which are controlled by a human operator. Based on the Lyapunov stability theory, it is shown that the containment errors can asymptotically converge into the prescribed bounds. Finally, two simulation examples evaluate the effectiveness of the presented control scheme.

Projection-Based Containment Control of Multiple Nonlinear Systems With Switching Topologies

This article addresses the distributed containment control problem of nonlinear multiagent systems with directed jointly connected switching topologies. It is assumed that the dynamics of agents are unknown nonlinear pure-feedback forms. The novel adaptive containment-control laws are designed to solve the case without considering the formation among leaders first and then the case of leaders’ formation. Different from the existing results, a condition of average dwell time is given by using the smooth parameter projection. Uniformly ultimate boundedness of the closed-loop system is analyzed in detail. Simulations show the feasibility and effectiveness of the proposed scheme.