Distributed Disturbance Observer-Based Containment Control of Multi-Agent Systems with Event-Triggered Communications

This paper studies the containment control problem of linear multi-agent systems (MASs) subject to external disturbances, where the communication graph is a directed graph with the followers being undirected connections. In order to save communication costs and energy consumption, a distributed disturbance observer-based event-triggered controller is employed based on the relative outputs of neighboring followers. Compared with conventional controllers, our observer-based controller utilizes the relative outputs of neighboring followers at the same triggered instant. Furthermore, it is shown that Zeno behavior can be avoided. Finally, the validity of our proposed methodology is demonstrated by a simulation example.

This paper considers the containment control of linear multi-agent system with weakly connected information topology. By defining the node-induced strongly connected subgraph as strong component, the agents contained in strong components with zero in-degree are called leaders and the others are called followers. Then, a sufficient and necessary condition is proposed for all agents to achieve containment by employing an observer-based protocol, where all followers finally converge to the convex hull formed by leaders and each strong component of leaders asymptotically achieve consensus. Since the number of leader agents in each strong component are always larger than one, the proposed scheme is more robust for the malfunction of leaders. Further, two LMIs are given to design the observer-based protocol. Numerical examples are included to illustrate the validity of the proposed results.

This paper addresses the critical problem of secure containment control for fractional-order heterogeneous and nonlinear multi-agent systems (MASs) subjected to both mixed time-varying delays and malicious false data injection. Such issues are highly relevant in modern networked control systems where data integrity and robustness are increasingly threatened. Within a leader–follower framework, the attacker injects unknown, time-varying, and deceptive signals that can compromise consensus and system stability. To counteract this, we propose a novel distributed observer and adaptive fuzzy-based feedback controller design for each agent. The observer accurately estimates the agents’ states despite false data, while the controller ensures convergence and robustness under heterogeneous dynamics and delays. Stability of the closed-loop system is rigorously analyzed using a Lyapunov–Krasovskii functional tailored to fractional-order systems. Finally, simulation results demonstrate the effectiveness and resilience of the proposed control strategy against adversarial attacks.

Containment control of heterogeneous multi-agent systems

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.

ABSTRACTThe event-based broadcasting containment control problem for both first-order and second-order multi-agent systems under directed topology is investigated. Based on certain event, each agent decides when to transmit its current states to its neighbours and the agents’ distributed control algorithms are based on these sampled state measurements, which can significantly decrease the number of the controllers’ updates. All the agents are divided into two groups, namely, the leaders and the followers. The formation control is introduced. The leaders exchange their information to converge to a formation. The followers utilise the information from both their leader neighbours and their follower neighbours and are driven to the convex hull of the leaders using the proposed control algorithms. Numerical simulations are provided to illustrate the effectiveness of the obtained theoretical results.

This paper focuses on the problem of the event-triggered adaptive containment control for a class of nonlinear multiagent systems (MASs) with prescribed performance and immeasurable states. First, the radial basis function neural networks (RBFNNs) are adopted to approximate the uncertain smooth nonlinear function, and the neural network-based state observer is designed to estimate the unmeasurable state. Besides, to reduce the control resource consumption and get a better balance between the system performance and network constraints, the switching threshold-based event-triggered control strategy is introduced. Based on this, the novel distributed containment controller is designed by utilizing the adaptive backstepping technique and the dynamic surface control (DSC) technique to guarantee that the output of each follower converges to the convex hull formed by multileader. Moreover, the containment errors can be converged to the prescribed boundary and all signals in closed-loop system are semi-global uniformly ultimately bounded (SGUUB) as well. Finally, the simulation examples are carried out to illustrate the efficiency of the proposed controller.

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.

This paper investigates the distributed containment control problem for multi-agent systems with general linear dynamics under a directed graph. A new observer based on the relative outputs of neighboring agents is developed to estimate the relative states of neighbors which avoid designing the observer for the leaders in the existing literature. A matrix transformation is introduced to eliminate the coupling terms resulting from the simultaneous design of the observer and the controller gains. Then a sufficient condition on the existence of the observer-based controllers is presented in terms of strict linear matrix inequalities. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed design method.

In this paper, the bipartite containment control problem of multi-agent systems (MASs) with unknown disturbances is studied. At first, a signed undirected graph is used to describe the Cooperative-Antagonistic interaction among the agents. Different from some conventional results of convergence in the infinite time domain, the control protocol proposed in this paper achieves the fixed-time convergence, and applies the fixed-time control and bipartite consensus to the containment control, making the proposed control protocol more practical. In addition, this paper also considers the existence of external disturbances and a novel fixed-time bipartite containment control protocol is proposed to eliminate them. Then, the stability analysis under the control protocol is completed by using the Lyapunov theory and mathematical theorem. Finally, the effectiveness of the proposed control scheme is verified by some simulation examples.

Sampled-data based containment control of continuous-time multi-agent systems with switching topology and time-delays

This study applies a design method called linear quadratic regulator to tackle the containment control problem of discrete-time linear multi-agent systems over directed graphs. By solving an algebraic Riccati equation, the study establishes both necessary and sufficient conditions required to achieve consensus. The researchers introduce an innovative distributed control law for information transmission between leaders and followers. This control law allows the following agents to move within the convex hull formed by the navigation agent, and effectively enables them to converge quickly and then follow again by introducing position error adjustment parameters. The effectiveness of the proposed algorithms is demonstrated through a simulation example.

We investigate the fixed-time containment control (FCC) problem of multi-agent systems (MASs) under discontinuous communication. A saturation function is used in the controller to achieve the containment control in MASs. One difference from using a symbolic function is that it avoids the differential calculation process for discontinuous functions, which further ensures the continuity of the control input. Considering the discontinuous communication, a dynamic variable is constructed, which is always non-negative between any two communications of the agent. Based on the designed variable, the dynamic event-triggered algorithm is proposed to achieve FCC, which can effectively reduce controller updating. In addition, we further design a new event-triggered algorithm to achieve FCC, called the team-trigger mechanism, which combines the self-triggering technique with the proposed dynamic event trigger mechanism. It has faster convergence than the proposed dynamic event triggering technique and achieves the tradeoff between communication cost, convergence time and number of triggers in MASs. Finally, Zeno behavior is excluded and the validity of the proposed theory is confirmed by simulation.

A novel method of disturbance observer-based integral backstepping control is proposed for the two-tank liquid level system with external disturbances. The problem of external disturbances can be settled in this paper. Firstly, the mathematical model of the two-tank liquid level system is established based on fluid mechanics and principle of mass conservation. Secondly, an integral backstepping control strategy is designed in order to ensure liquid level tracking performance by making the tracking errors converge to zero in finite time. Thirdly, a disturbance observer is designed for the two-tank liquid level system with external disturbances. Finally, the validity of the proposed method is verified by simulation and experiment. By doing so, the simulation and experimental results prove that the scheme of disturbance observer-based integral backstepping control strategy can suppress external disturbances more effective than the disturbance observer-based sliding mode control method and has better dynamic and steady performance of the two-tank liquid level system.

Containment control of singular heterogeneous multi-agent systems