Bipartite time-varying formation group containment control for multi-agent systems based on multi-layer network and semi-signed directed graph

Observer-based distributed adaptive fault-tolerant containment control of multi-agent systems with general linear dynamics

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.

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.

Formation control for nonlinear multi-agent systems by robust output regulation

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

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.

This paper investigates the containment control problem for multi-agent systems based on the broadcast gossip algorithm, in which only one agent wakes up in the light of the asynchronous time model at each time and sends its information, and one part of the remaining agents get the message to update their states while the other part keep the states unchanged. We equivalently transform the algorithm into a mathematical model with the matrix-vector form, then conduct a detailed theoretical analysis for the mathematical model by utilizing tools including graph theory and stochastic matrix. Then, we establish a necessary and sufficient algebraic graph condition to ensure that every follower gradually enters the convex hull spanned by the leaders. Finally, we give a numerical example to argument the validity of theoretical result.

Containment control of heterogeneous multi-agent systems

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.

This paper investigates the event-based prescribed performance fuzzy adaptive containment control problem for multi-agent systems with unknown control direction and sensor faults. In the proposed control strategy, the tracking error can converge to the prescribed boundary by designing a performance function. An adaptive faults compensation scheme is introduced to handle sensor faults. In addition, the technology of Nussbaum-type function is employed to cope with the difficulty of unknown control gains. Moreover, by utilizing the Lyapunov stability theory, it is proven that the developed control method can ensure all the signals of closed-loop system are semi-globally uniformly ultimately bounded. Finally, the effectiveness of the developed strategy is verified by some simulation results.KeywordsMulti-agent systemsEvent-triggered containment controlPrescribed performance controlUnknown control directionSensor faults

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.

Disturbances can significantly impact the dynamic performance and stability of a system, making them a key focus in stability analysis. However, direct measurement of disturbances is often challenging due to technological and cost limitations. These disturbances introduce uncertainties that complicate multi-agent coordination, particularly in formation control tasks. Consequently, designing effective control strategies for multi-agent systems becomes both challenging and crucial. This paper addresses the affine transformation formation control problem of multi-agent systems in the presence of unknown disturbances. We begin by using a state-space model to describe agent dynamics and employing an unknown input observer to estimate both the state and the unknown disturbances. Based on these estimates, we redesign the control law to ensure that tracking errors converge to an adjustable residual set. This distributed control approach allows agents to operate without global information, thereby reducing communication requirements. Finally, a simulation example demonstrates the feasibility and effectiveness of the proposed control law.

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.

This article investigates the iterative learning control problem for a class of nonlinear heterogeneous multi-agent systems. The main contribution of this article is to apply iterative learning control algorithm to the multi-agent systems with multiple leaders, and solve the containment control problem of multi-agent systems in the sense of iterative learning control stability. Based on the framework of communication topologies, distributed iterative learning controllers are designed. And when the iterative learning control laws are applied to the systems, the containment errors between the followers’ states and the convex hull spanned by the leaders’ states over a finite-time interval are bounded, and furthermore, the containment errors can converge to zero as the iteration index approaches to infinity in the absence of initial errors. A simulation example is finally constructed to verify the effectiveness of the theoretical method.

This paper studies the containment control issue of multi-agent systems with time delay. By adopting continuous-time and sampled-data-based control protocols, we establish some necessary and sufficient containment control criteria for multi-agent systems with time delay. For the continuous-time case, our results show that both topology structure and time delay play an important role in the containment control of multi-agent systems, no matter whether the leaders are stationary (first-order system) or dynamic with constant velocity and time-varying position (second-order system). Furthermore, the maximum value of time delay to guarantee the achievement of containment control is given by the Hopf bifurcation theory. Moreover, we extend the results to the sampled-data case. Finally, numerical simulations are given to illustrate our main results.