Containment Control Of Multi-agent Systems Research Articles

H∞ Containment Control of Multi-agent Systems with Random Communication Time-varying Delay

This paper investigates the H∞ containment control problem of multi-agent systems with random communication time-delay. The information exchanges between the agents are supposed to be randomly delayed, characterized by a Bernoulli distribution sequence. And a neighbor-based protocol with random communication delay is proposed. As external perturbation exits broadly in many practical systems, the paper deals with it by using H∞ control theory. By applying stochastic technique, Lyapunov analysis and the free-weighting matrices technique, theoretical results show that the followers will ultimately converge to the convex hull spanned by the leaders in the mean square sense with a prescribed H∞ performance index. Finally, a numerical example is given to demonstrate the validity of the theoretical results.

High order robust fast finite time containment control for multi-agent systems

This paper studies the problem of robust containment with trivial sensitivity to both initial conditions and communication topology for multi-agent systems. In this way, based on the homogeneity property of the dynamic systems, a new nonlinear high order sliding surface for containment problem is proposed. This sliding surface has a fast finite time dynamics which causes remarkably reduction of containment sensitivity to the multi-agent initial conditions and communication topology. Accordingly, a high order fast finite time containment control (HOFFT-CC) protocol is established and the containment of multiple agents to a convex hull is realized. The proposed framework solves the fast containment problem for high order dynamics that are subjected to the external disturbance and furthermore, for both directed and undirected graph topology. Moreover, because of decoupling the agents’ dynamics and converting the multi-agent problem to some single agent problems, the structure of the proposed method is simpler and more straightforward in comparison with previous works. The finite time stability of the closed loop multi-agent systems based on the homogeneity theory and Lyapunov theorem, is analyzed and proved. The proof is produced throughout the negative degree homogeneity property of the closed loop dynamics along with asymptotical stability. In addition, simulation for a general third order multi-agent system in a two-dimensional space is accomplished and the results demonstrate the trivial sensitivity of containment to both initial conditions and communication topology.

Dynamic Intermittent Feedback Design for $H_{\infty}$ Containment Control on a Directed Graph

This article develops a novel distributed intermittent control framework with the ultimate goal of reducing the communication burden in containment control of multiagent systems communicating via a directed graph. Agents are assumed to be under disturbance and communicate on a directed graph. Both static and dynamic intermittent protocols are proposed. Intermittent H∞ containment control design is considered to attenuate the effect of the disturbance and the game algebraic Riccati equation (GARE) is employed to design the coupling and feedback gains for both static and dynamic intermittent feedback. A novel scheme is then used to unify continuous, static, and dynamic intermittent containment protocols. Finally, simulation results verify the efficacy of the proposed approach.

Containment Control of Multi-agent Systems with Time-delays over Heterogeneous Networks

Containment Control of Multi-agent Systems with Time-delays over Heterogeneous Networks

Sampled-data leader-following consensus of nonlinear multi-agent systems subject to impulsive perturbations

In this paper, the sampled-data leader-following consensus is investigated for a class of nonlinear multi-agent systems, where all agents are influenced by impulsive perturbations emerging from the input channels. Using the algebraic graph theory, the leader-following consensus problem of the multi-agent system is transformed into the stability problem of a constructed error system. By the Lyapunov functional method and the impulsive system theory, sufficient conditions for leader-following consensus of the underlying multi-agent systems are given. The proposed results are then extended to the containment control of multi-agent systems with multiple leaders. Finally, two numerical examples are presented to show the validity of the proposed results.

High-order bipartite containment control in multi-agent systems over time-varying cooperation-competition networks

This paper examines the problem of bipartite containment control in high-order multi-agent systems, in which time-varying cooperation-competition networks are utilized to simulate the interactions among agents. Suppose there are two subgroups of followers, in which the followers in the same subgroup cooperate with each other and the followers belonging to different subgroups compete with each other. It is further assumed that the leaders cooperate with the followers in one subgroup and compete with the followers in another subgroup. Under these assumptions, it is shown that the followers who cooperate with the leaders will gradually enter the entity convex hull composed of the leaders, while the followers who compete with the leaders will enter the virtual convex hull opposite to the entity convex hull. In addition, this study also finds that that all followers kept moving without stopping when they entered the convex hulls. The authenticity of these discoveries is confirmed by a simulation example.

Controllable containment control of multi-agent systems based on hierarchical clustering

ABSTRACT In the practical application, such as military, logistics or drone control, in order to meet the mission needs, the scale of multi-agent systems is constantly expanding, and the number of leaders required to implement control is increasing. In containment control, it has some difficulties in forming convex hulls by traditional control methods to achieve ideal control purposes. We propose a method that is more suitable and effective for large-scale networks to achieve containment control here. In this paper, a controllable containment control algorithm based on hierarchical clustering for multi-agent systems is proposed by combining the topology optimisation theory and complex network controllability theory. First, the multi-agent network is divided into several communities according to the hierarchical clustering algorithm. Then the maximum matching algorithm of bipartite graph is used to determine the minimum leader set satisfying the network controllability. Second, the corresponding control protocols are designed for the agents, and a position adjustment control force is introduced to adjust the motion of individuals that are located outside the convex hull in the process of containment among the communities. Therefore, when achieving and maintaining the controllable containment control within the community, the controllable containment control among the communities can be achieved effectively through the proposed algorithm. Finally, some simulation examples are presented to demonstrate the effectiveness of the theoretical results.

Optimal Containment Control of Unknown Heterogeneous Systems With Active Leaders

This brief presents a partially model-free solution to the distributed containment control of multiagent systems using off-policy reinforcement learning (RL). The followers are assumed to be heterogeneous with different dynamics, and the leaders are assumed to be active in the sense that their control inputs can be nonzero. Optimality is explicitly imposed in solving the containment problem to not only drive the agents’ states into a convex hull of the leaders’ states but also minimize their transient responses. Inhomogeneous algebraic Riccati equations (AREs) are derived to solve the optimal containment control with active leaders. The resulting control protocol for each agent depends on its own state and an estimation of an interior point inside the convex hull spanned by the leaders. This estimation is provided by designing a distributed observer for a trajectory inside the convex hull of active leaders. Only the knowledge of the leaders’ dynamics is required by the observer. An off-policy RL algorithm is developed to solve the inhomogeneous AREs online in real time without requiring any knowledge of the followers’ dynamics. Finally, a simulation example is presented to show the effectiveness of the presented algorithm.

Distributed containment control of multi‐agent systems under asynchronous switching and stochastic disturbances

Distributed containment control of multi-agent systems with asynchronous switching and stochastic disturbances under a time-invariant directed graph is studied. Since both the process of identifying an active subsystem and that of applying a matched controller to the corresponding subsystem need to consume time, the controller switching usually lags behind the subsystem switching. In order to show that the controllers are still effective to tolerate some time delay, a multiple Lyapunov function is selected to present stability conditions. By employing stochastic stabilisation theory and matrix transformation, the problem of containment control is transformed to that of stability analysis of the closed-loop system and exponential stabilisation in mean square sense is achieved. Finally, two simulation examples are given to verify the effectiveness of the proposed results.

Containment control of directed networks with time-varying nonlinear multi-agents using minimum number of leaders

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.

Necessary and sufficient conditions for containment control of multi-agent systems with time delay

In this paper, the containment control problem for the discrete-time multi-agent systems with first-order dynamics is discussed. We first provide the necessary and sufficient condition for containment control without time-delay which is related to the value of the step-size and the structure of the interaction topology through the iterative method. Further, time-delay is taken into account making use of z−transformation and Routh Criterion. Finally, numerical simulations are provided to explain the influence of different step-sizes on stability of the multi-agent systems and testify the obtained results.

Adaptive Distributed Observer Approach for Cooperative Containment Control of Nonidentical Networks

This paper addresses the containment control problem of nonidentical networks with external disturbance via adaptive distributed observer method. We first present a formulation for containment error, which ensures all the followers’ outputs converge to the convex hull spanned by the leaders’ reference outputs. Then by using an adaptive distributed observer, the leaders’ system matrices and the states of convex hull are both estimated. Furthermore, a novel global regulate equation is designed to restrain the external disturbance, and the problem of containment control for multiagent systems is solved by a dynamic output feedback approach. Finally, some simulation results are given to illustrate the validity of the theoretical results.

Containment control of multi-agent systems via a disturbance observer-based approach

This paper deals with the containment control problem for multi-agent systems with exogenous disturbances. A disturbance observer-based control approach is employed to estimate the disturbances generated by an exogenous system. Consequently, distributed disturbance observer-based containment control protocols are proposed by using the state feedback control and the output feedback control, respectively. Furthermore, with the help of algebraic graph theory and Lyapunov stability theory, sufficient conditions are established to ensure that multi-agent systems with exogenous disturbances can achieve containment control via the disturbance observer-based approach. Finally, the effectiveness of our theoretical results is verified by providing numerical simulation examples.

Containment Control of Multi-agent Systems with Uniform Quantization

In this paper, the problem of containment control is investigated for a class of multi-agent systems with second-order integrator dynamics. A directed graph is considered, and a pair of matrix norm and vector norm is designed. Accounting for the limitation of the finite bandwidth channels, quantized communication topology based on the encoding–decoding strategy is designed, in which the quantizers only have finite quantization levels and it is independent of the initial state of agents. Moreover, the quantizer and controller are jointly designed only using the estimated value of the neighbors’ state information to ensure the system stability with less communication resource. The relationship between the quantization levels and sampling interval is established to guarantee that all the quantizers are not saturated, and thus ensure the asymptotic stability of the system. And a vector norm induced by a constructed matrix norm is applied to reduce the lower boundary of the communication data rate which is free from the dimension and number of agents. Finally, simulation examples are given to show the effectiveness of the new designed techniques.

Containment Control of Multi-Agent Systems With General Noise Based on Hierarchical Topology Reconfiguration

In this paper, the containment control problem of the second-order multi-agent systems (MASs) with general noise over directed topology is investigated. General noise, which may be the mixture of colored and white noise, is introduced to model the perturbation of MASs. Since constructing an anti-perturbed distributed controller for concerned MASs is difficult, we attend to use the perturbation tolerant character of the convex hull spanned by multiple leaders in the containment control problems of MASs. To this end, the hierarchical topology structure of MASs is used, which can largely reduce the communication loads and computational complexity. It is shown that the MASs are noise-to-state stable and the state of the MASs has an asymptotic gain in the mean square based on random differential equations (RDEs) theorem framework. Moreover, the relative hierarchical topology reconfiguration algorithm is given based on which the system can withstand stronger noise and all followers gradually converge to the convex hull formed by the leaders of the respective level. Finally, the numerical simulation is carried out to substantiate the feasibility of the proposed control theory.

Event-Triggered Containment Control of Multi-Agent Systems With High-Order Dynamics and Input Delay

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.

Distributed Containment Control of Multi-agent Systems with General Linear Dynamics and Time-delays

Containment control problems for high-order linear time-invariant multi-agent systems with fixed communication time-delays are investigated. Based on Lyapunov-Krasovskii functional method and the linear matrix inequality (LMI) method, sufcient conditions on the communication digraph, the feedback gains, and the allowed upper bound of the delays to ensure containment control of the multi-agent systems under the different containment control algorithms are given. Finally, numerical simulations are presented to demonstrate theoretical results.

Distributed Containment Control for Multi-agent Systems in Pure-feedback Form under Switching Topologies

The distributed containment control problem is investigated for nonlinear multi-agent systems in pure-feedback form subjected to switching directed communication topologies. Based on command filtered back-stepping technology and singular-perturbation theorem, a containment controller is addressed to guarantee that the followers’ outputs can converge to the convex hull spanned by multi-dynamic leaders, and the containment tracking errors between leaders and followers is semi-global practical exponential stable in the closed-loop system. A nonlinear anti-tangent filter is adopted to estimate the virtual control, avoiding the analytical deduction inherent in traditional back-stepping method and overcoming the ?circular construction problem? in non-affine pure-feedback systems. Differing from the existing back-stepping method, the proposed control scheme only requires leaders’ output signals and their first derivative signals, does not need the prior knowledge of their nth order derivative signals. The stability analysis is completed via the singular perturbation theory, revealing some novel features of the underlying back-stepping method. Finally, two simulation examples are provided to illustrate the effectiveness of the control scheme.

Event-based containment control for multi-agent systems with packet dropouts

ABSTRACTThis paper is concerned with the event-triggered containment control for stochastic multi-agent systems subject to packet dropouts. The adopted event-triggered protocol is with absolutely triggered conditions catering for the requirement of real-time to an extreme. In light of such a protocol, a novel definition of containment control in mean-square sense, named as χ-containment, is proposed to better describe the tracking dynamics of followers. Based on relative measurement outputs, the purpose of this paper is to design an output-feedback controller such that all followers converge into the convex hull spanned by leaders. First, with the help of the property of the Laplacian matrix, the containment control problem is transformed to an easily setting step by step. Then, sufficient conditions with the form of matrix inequalities are derived to guarantee the desired χ-containment which depends on the initial values and the event-triggered thresholds. By introducing a free matrix combined with an orthogonal basis of the null space of control matrix, the controller gain can be obtained by solving a set of linear matrix inequalities. Finally, a simulation example is given to verify the effectiveness of the designed control protocol.

Model-free optimal containment control of multi-agent systems based on actor-critic framework

Abstract This paper deals with the model-free optimal containment control problem for a class of linear multi-agent systems (MASs). In the existing results concerning containment control of MASs, the dynamics of the MASs is required to be completely known. Differently, in this paper, we propose a new distributed self-learning control scheme based on action dependent heuristic dynamic programming (ADHDP) to achieve containment control, where the model of MASs is no longer needed. The containment control problem is first transformed into a regulation problem on the dynamics of the designed local containment error. The policy iteration method based on the designed state-action value function (also called the Q-function) is introduced to deal with such a regulation problem. The convergence analysis of this policy iteration method is also given. Neural network (NN) based actor-critic framework is adopted to approximate the optimal Q-functions and the optimal control policies for facilitating the implementation of the proposed method. It shows that the approximated control policies achieve the containment control and satisfy the global Nash equilibrium. Finally, the simulation results are provided to demonstrate the effectiveness of the developed approach.