Containment Control Of Multi-agent Systems Research Articles

Neuro‐adaptive distributed output‐feedback containment control for multiagent systems with nonstrict‐feedback nonlinear dynamics and input constraints

AbstractIn this article, distributed adaptive controllers are designed for containment control of multiagent systems (MASs) with high‐order nonlinear dynamics in nonstrict‐feedback form. To broaden the application horizon, the agents' dynamics are considered heterogeneous, and the control saturation is taken into account. Moreover, the agents' dynamics, as well as their full state information, are assumed unknown. An adaptive observer is designed in the first step for each agent to estimate the agents' states using available output measurements. An adaptive backstepping controller is then integrated with the observer to solve the containment control problem. The computational complexity of the controller is reduced by adopting the command filtered adaptive backstepping approach to the containment control of MASs. The effect of the input saturation is also compensated by employing an auxiliary system throughout the design procedure. The proposed control approach guarantees that the states of all agents are cooperatively semiglobally uniformly ultimately bounded and containment errors converge to a small neighborhood of the origin. Finally, the effectiveness of the presented control algorithm is confirmed by a simulation example.

PI-based Containment Control for Multi-agent Systems with Input Saturations

PI-based Containment Control for Multi-agent Systems with Input Saturations

Cooperative Adaptive Containment Control With Parameter Convergence via Cooperative Finite-Time Excitation

This article addresses the problem of cooperative adaptive containment control for multiagent systems, which specifies the objective of jointly achieving containment control and accurate adaptive learning/identification of unknown system parameters. We consider a class of linear uncertain multiagent systems with multiple leaders subject to bounded unmeasurable inputs and multiple followers subject to unknown system dynamics. A novel cooperative adaptive containment control architecture is proposed, which consists of a discontinuous nonlinear state-feedback control law and a filter-based cooperative adaptation law. This new control architecture is compelling in the sense that exponential convergence of both containment tracking errors to zero and adaptation parameters to their true values can be achieved simultaneously under a mild cooperative finite-time excitation condition. This condition significantly relaxes existing ones (e.g., persistent excitation and finite-time excitation) for parameter identification in adaptive control systems. Effectiveness of the proposed approach has been demonstrated through both rigorous analysis and a case study.

Output Containment Control of Heterogeneous Linear Multiagent Systems With Unbounded Distributed Transmission Delays.

In this article, the output containment control problem of heterogeneous linear multiagent systems (MASs) with unbounded distributed transmission delays is considered. A key technical lemma is first established to show that the distributed observers under unbounded distributed transmission delays can be utilized to estimate the convex combination of the states of multiple leaders. Then, a novel distributed output feedback control law is proposed based on those distributed observers. It is shown that under our proposed control law, the output of each follower converges to the convex hull spanned by the outputs of the leaders. In addition, our results include relevant results on output containment control of MASs with bounded distributed or constant transmission delays as special cases. Finally, the effectiveness of the proposed control law is demonstrated by a simulation example.

Observer-Based Event-Triggered Fuzzy Adaptive Bipartite Containment Control of Multiagent Systems With Input Quantization

This article studies the bipartite containment control problem for nonlinear multiagent systems (MASs) with input quantization over a signed digraph. The design objective is to provide an appropriate distributed protocol such that the followers converge to a convex hull containing each leader's trajectory as well as its opposite trajectory different in sign. Based on a nonlinear decomposition approach of input quantization, an event-triggered control scheme is developed via backstepping technique. A fuzzy observer is constructed to estimate unmeasurable states. Moreover, the bipartite containment control scheme for nonlinear MASs is designed. It is demonstrated that all signals in the closed-loop system are semiglobally uniformly ultimately bounded and Zeno behavior is excluded. Finally, a simulation example is given to verify the validity of the designed method.

Containment control for multi-agent systems with fractional Brownian motion

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.

Non-Fragile Disturbance Observer-Based Containment Control of Multi-Agent Systems Over Switching Topologies

In this paper, the non-fragile containment control problem for linear multi-agent systems (MASs) with exogenous disturbance is investigated. The communication links among agents are constructed by a set of arbitrarily fast switching and directed topologies. First, there always exist uncertainties in the controller and observer gain matrices, a new class of distributed non-fragile disturbance observer-based controller is proposed to address such a problem with disturbance rejection under switching topologies. By making use of matrix transformation and Lyapunov theory, the containment control problem of MASs is converted into the asymptotic stability analysis problem of some containment error dynamics. Second, the corresponding non-fragile containment control problem of inherent nonlinear case with exogenous disturbance under switching topologies is further studied. Finally, two simulation examples are given to investigate the effectiveness of the proposed control strategy.

Containment Control of Multi-Agent Systems over Directed Graphs: A Delay Robustness Perspective

Containment Control of Multi-Agent Systems over Directed Graphs: A Delay Robustness Perspective

Distributed non-fragile containment control of nonlinear multi-agent systems with time-varying delays

ABSTRACT Distributed containment control for multi-agent systems with time delay is investigated, where the communication topology is directed. Different from the existing literature which mainly focuses on general linear dynamics with time delay, containment control of nonlinear dynamics is discussed with the help of a new follower-based time-varying delays control protocol. Furthermore, there always exist uncertainties in the controller and observer gain matrices, a novel class of non-fragile containment control with time delay is addressed for the first time, which can be more applicable and more significant to real physical systems. By making use of the convex analysis, algebraic graph theory, matrix transformation and Lyapunov theory, it is derived that the obtained results are cast as feasible linear matrix inequalities and the states of the followers finally converge to the convex hull formed by the leaders. Finally, two simulation examples of nine-agents topology are presented to verify the validity of obtained theoretical analysis.

Cooperative Bipartite Containment Control for Multiagent Systems Based on Adaptive Distributed Observer.

The cooperative bipartite containment control problem of linear multiagent systems is investigated based on the adaptive distributed observer in this article. The graph among the agents is structurally balanced. A novel distributed error term is designed to guarantee that some outputs of the followers converge to the convex hull spanned by the leaders, and the other followers' outputs converge to the symmetric convex hull. The matrices of the exosystems are not available for each follower. A general method is presented to verify the validity of a novel distributed adaptive observer rather than the previous approach. In other words, the definition of the M -matrix is not necessary in our result. Based on the distributed adaptive observer, an output-feedback control protocol is designed to solve the bipartite containment control problem. Finally, a numerical simulation is given to illustrate the effectiveness of the theoretical results.

Adaptive Fuzzy Containment Control for Multiagent Systems With State Constraints Using Unified Transformation Functions

In this article, the finite-time containment control problem of the nonlinear multiagent systems (MAS) is investigated, in which the follower agents are subjected to full state constraints. The fuzzy logic system is employed to approximate the uncertain dynamic of the nonlinear MAS. A new nonlinear transformation function (NTF) is proposed, which serves as a unified tool for coping with the systems subjected to state constraints and no constraint. By combing the variable transformation with the proposed NTF, the original systems with state constraints are converted into the equivalent free-constrained systems. Moreover, as long as the boundedness of the states in transformed systems is guaranteed, the states of the original MAS do not transgress the preassigned boundaries. Based on the finite-time stability theory, the adaptive fuzzy control scheme is constructed for the transformed systems. It is proved that the outputs of all the followers are driven to converge to the convex hull spanned by the leaders in a finite time, and all the signals in the closed-loop systems are bounded in sense of mean square. The full state constraints for the followers are not violated all the time. Especially, the control structure does not need to change even there is no constraint imposes on the state. Finally, simulation examples are given to verify the effectiveness of the proposed finite-time control scheme.

Output feedback containment control of multi-agent systems with semi-Markovian switching topologies and input-bounded leaders

This paper investigates the containment control problem of multi-agent systems with semi-Markovian switching topologies. Different from the related works, this paper considers a more general case that the control inputs of leaders are nonzero, the sojourn time distributions of the semi-Markovian switching topologies are mode transition-dependent, and the states of agents are not measurable. Reduced-order observer-based control protocols are proposed, respectively, for two cases that the transition rates are completely known and partially unknown, which ensures that the containment of the multi-agent systems can be achieved in the mean square sense. Finally, simulation examples are given to illustrate the validity of the theoretical results.

Distributed H∞ containment control of multiagent systems over switching topologies with communication time delay

SummaryIn this study, we consider the problem of distributed H∞ containment control for multiagent systems over switching communication topologies. There exists a constant time‐delay and the energy‐bounded communication disturbances in the information transmission process, which are considered. Using the relative output, we develop an observer‐based containment control scheme such that the followers asymptotically converge to the convex hull formed by the leaders with a guaranteed H∞ performance level. By constructing a Lyapunov functional and using the inequality technique, sufficient conditions for the existence of such dynamic controllers are obtained in terms of linear matrix inequalities. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed control protocol.

Pull-Based Event-Triggered Containment Control for Multiagent Systems With Active Leaders via Aperiodic Sampled-Data Transmission

In this article, the containment control problem of multiagent systems (MASs) with active leaders under a directed communication graph is addressed. A novel pull-based event-triggered protocol combined with aperiodic sampled-data mechanism is first presented, where each agent merely updates controller at its own triggering instants. Under the proposed control protocols, the information is only exchanged and calculated at the aperiodic sampling instants, therefore, it can reduce communication congestion and save computing resources. Furthermore, the Zeno behavior is naturally excluded because the trigger instants are in the set of aperiodic sampled instants. By virtue of the algebraic graph theory and Lyapunov stability analysis, it is shown that the active leaders can reach their desired states predefined arbitrarily and all followers are driven to the convex hull formed by the leaders. Finally, an illustrative example is given to validate the theoretical results and emphasize the advantages of the proposed protocols.

Containment control of multi-agent systems with nonvanishing disturbance via topology reconfiguration

Containment control of multi-agent systems with nonvanishing disturbance via topology reconfiguration

Distributed containment control of multi-agent systems with velocity and acceleration saturations

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.

Sampled-data containment control for double-integrator agents with dynamic leaders with nonzero inputs

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.

Stabilizability and Bipartite Containment Control of Multi-Agent Systems Over Signed Directed Graphs

This paper investigates the stabilizability and bipartite containment control problem of general linear multi-agent systems over signed directed graphs, where the negative edges indicate the antagonistic interactions between agents. By employing the proposed bipartite containment control protocols over signed directed graphs, and combining the linear system stabilization theory and the signed Laplacian matrix, the necessary condition for the stabilization of multi-agent systems with multiple leaders is discussed. According to this necessary condition, a leader-follower matching method is presented to establish leader-follower multi-agent system networks. Based on the leader-follower topology established above and the designed state feedback gain, the stability of multi-agent systems is proved by using the system error and the algebraic Riccati equation. It is shown that the followers can gradually converge into the convex hull spanned by the states and the sign-inverted states of leaders, and the bipartite containment control of multi-agent systems can be realized. The simulation results verify the feasibility of the theoretical analysis.

Distributed Functional Observer-based Event-triggered Containment Control of Multi-agent Systems

This paper studies the containment control problem of linear multi-agent systems (MASs) with a directed graph, where the states of the followers will asymptotically converge to the convex hull formed by those of the leaders. By introducing the functional observer, a novel distributed event-triggered control strategy is presented to schedule communications between agents, which depends on the relative input and output measurements with its neighbors. Furthermore, the minimum inter-event time is guaranteed to be strictly positive. An example is presented to illustrate the feasibility and efficiency of the theoretic results.

Distributed adaptive containment control for a class of discrete-time nonlinear multi-agent systems with uncertainties

A distributed adaptive containment control scheme is developed for a class of discrete-time multi-agent systems (MASs) under directed graphs. Each agent's model is described by nonlinear dynamics with unknown parameters that are nonlinearly coupled with the states. To deal with the uncertainties, a criterion function with weighted factor is adopted. By minimising the criterion function, a projection algorithm for each agent is designed to estimate the unknown parameters. Using the estimated parameters, an adaptive controller with only local information is designed for each agent to achieve containment control of MASs. Under the proposed distributed adaptive containment control scheme, it is guaranteed that all the leaders can finally track their reference signals and all the states of followers asymptotically converge to the convex hull formed by leaders (i.e. the convex hull formed by the reference signals). Finally, two simulation examples are given to illustrate the effectiveness of the proposed scheme.