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This accessible book provides an introduction to the analysis and design of dynamic multiagent networks. Such networks are of great interest in a wide range of areas in science and engineering, including: mobile sensor networks, distributed robotics such as formation flying and swarming, quantum networks, networked economics, biological synchronization, and social networks. Focusing on graph theoretic methods for the analysis and synthesis of dynamic multiagent networks, the book presents a powerful new formalism and set of tools for networked systems. The book's three sections look at foundations, multiagent networks, and networks as systems. The authors give an overview of important ideas from graph theory, followed by a detailed account of the agreement protocol and its various extensions, including the behavior of the protocol over undirected, directed, switching, and random networks. They cover topics such as formation control, coverage, distributed estimation, social networks, and games over networks. And they explore intriguing aspects of viewing networks as systems, by making these networks amenable to control-theoretic analysis and automatic synthesis, by monitoring their dynamic evolution, and by examining higher-order interaction models in terms of simplicial complexes and their applications. The book will interest graduate students working in systems and control, as well as in computer science and robotics. It will be a standard reference for researchers seeking a self-contained account of system-theoretic aspects of multiagent networks and their wide-ranging applications. This book has been adopted as a textbook at the following universities: University of Stuttgart, GermanyRoyal Institute of Technology, SwedenJohannes Kepler University, AustriaGeorgia Tech, USAUniversity of Washington, USAOhio University, USA

In this paper, the fixed-time consensus tracking control problem of multiagent systems (MASs) subject to unknown nonlinearities and performance constraints is investigated. Initially, an improved fixed-time performance function is designed, which enables the consensus tracking errors to converge to the preset region in fixed time, and alleviates the initial error conditions by setting the parameters appropriately. Moreover, the unknown nonlinearities of MASs are approximated by the radial basis function neural network (RBF NN). Subsequently, a fixed-time prescribed performance controller is designed, which excludes the fractional power of tracking error to prevent potential singularity problems existing in stability proof. Additionally, a fixed-time dynamic surface filter is formulated to eliminate the “explosion of complexity” issue, meanwhile, the filter errors are bounded in fixed time. Utilizing the Lyapunov stability theory, it can be guaranteed that all signals in MASs exhibit practically fixed-time stability, and the consensus errors all approach a small region centered on origin within the prescribed bounds. Finally, simulations are presented to verify the validity of the proposed control strategy.

This paper proposes a new continuous-time control method to address the problem of bipartite formation tracking for heterogeneous multiagent systems (HMASs) with uncertain follower models under switching and fixed topologies. First, to estimate the state information of the dynamically unknown leader, an objective trajectory system is constructed for the followers. Then, using the Lyapunov theorem, it is proved that under the studied conditions, the system states can achieve bipartite consensus with the leader’s state. Subsequently, based on the objective trajectory system, fuzzy logic system, and backstepping method, a control law is designed for the follower system with unknown nonlinear characteristics. The proposed method provides continuous control under switching topologies and ensures that the follower group tracks the leader in the desired formation. At the same time, the method imposes few restrictions on the dynamic characteristics of the follower system, making it widely applicable. At the end of the paper, numerical simulations demonstrate that the control objectives are achieved for HMASs with complex nonlinear characteristics under switching topologies.

A comprehensive guide to formation control of multi-agent systems using rigid graph theory This book is the first to provide a comprehensive and unified treatment of the subject of graph rigidity-based formation control of multi-agent systems.

This paper investigates the consensus of multiagent systems based on impulsive control with actuator faults. A typical fault that the actuator has partial loss of effectiveness (PLOE) with multiple modes is taken into consideration. Two main adaptive control schemes are designed to solve the tracking consensus problem with second-order nonlinear agent model. On the one hand, to estimate the PLOE mode, an asynchronous impulsive adaptive scheme using full system information is presented and the consensus proves to be achieved under sufficient conditions. On the other hand, by considering each agent as an input–output system, an impulsive adaptive scheme with extended observers is introduced with only output information available. The consensus first proves to be achieved by a method using time-varying linear matrix inequalities (LMIs) theoretically. However, it is difficult to obtain certain solutions of the time-varying LMIs for condition checking. Then, the feasibility analysis is made and an alternative scheme is proposed to deal with this issue instead. Numerical simulations are presented to support the theoretical results.

The consensus of higher-order nonlinear heterogeneous multiagent systems with matched and unmatched uncertainties is studied in this paper. The distributed observer-based controllers for multiagent systems are achieved using a fixed-time sliding mode controller based on the disturbance observer. For this purpose, the disturbance observers are designed for finite-time estimation of matched and unmatched uncertainties. Using the estimated values, the fixed-time distributed sliding mode controllers are designed and the consensus protocol is achieved. In this regard, a theorem is proved, which guarantees the fixed-time convergence of consensus errors. The effectiveness of the proposed distributed controllers has been validated through simulations for two robotic multiagent systems and a numerical example.

This study investigates a fully distributed event-triggered consensus control problem for nonlinear multiagent systems (MASs). Initially, a polynomial fuzzy model is adopted to describe the nonlinear error dynamics of leader-following MASs. Subsequently, an edge-based event-triggered mechanism is proposed to asynchronously transmit the agent’s state to its neighbors. Based on this mechanism, a novel asynchronous event-triggered control protocol is proposed to accomplish the consensus task. Meanwhile, the control protocol is fully distributed and uses only information about the neighboring agents and itself. Furthermore, sufficient conditions based on the sum-of-squares are obtained to achieve asymptotic consensus for the studied systems with a strictly dissipative performance by constructing an ε-dependent Lyapunov function. Finally, a chaotic circuit example is provided to illustrate the validity of the proposed scheme by comparisons.

This paper investigates distributed online optimization in a networked multiagent system, where each agent has its own private objective and constraint functions that vary over time. In many real‐world scenarios, computing the gradient of the cost function can be challenging, especially when agents have limited computational capabilities. Moreover, communication delays are common in practical networked systems due to various factors. This paper considers a unified framework for distributed online optimization that can handle bandit feedback and communication delays feedback simultaneously. A distributed primal‐dual algorithm is proposed that utilizes bandit feedback, in which the agents estimate the gradients of their objective and constraint functions by sampling the function values. An enlarged network model that incorporates the delayed information exchanged among the agents is introduced. Through theoretical analysis, it is shown that the proposed algorithm achieves sublinear upper bounds on both the dynamic regret and the constraint violation despite communication delays. Evolution of the time‐averaged dynamic regret and the time‐averaged constraint violation for resource allocation.

The adaptive fixed-time bipartite containment issue of p -normal multiagent systems (MASs) with unmodeled dynamics is investigated. In view of the structural characteristics of high-order systems, the technology of adding a power integrator is adopted which overcomes the difficulty caused by the high power of virtual control and real control items. In addition, to further optimize the rationality of resource utilization, an improved threshold strategy including saturation threshold, control input and decreasing function of errors is proposed. Based on practical fixed-time theory, a fixed-time containment control strategy is devised, which ensures that some followers converge to a convex hull spanned by leaders, others converge to the symmetric one spanned by leaders within fixed time. Finally, the effectiveness of the developed containment control scheme and the superiority of the improved threshold strategy are illustrated by comparison simulation results.

The issue of time-varying group formation tracking (TVGFT) control for heterogeneous nonlinear multiagent systems (MASs) with unknown dynamics is studied in the framework of high-order fully actuated system approaches. To achieve the desired TVGFT, two kinds of distributed control protocols are designed, which rely on robust and adaptive control strategies, respectively. The protocols consist of two components: The first is that the nonlinearities of MASs are eliminated by state feedback and the poles are configured in the light of performance requirements; the second is that robust or adaptive control strategy is employed to compensate for uncertainties, depending on the characteristics of the uncertain dynamics. Based on Lyapunov stability theory, the sufficient conditions to achieve TVGFT under two proposed control protocols are provided and proved, and the decay rates of TVGFT error associated with these protocols are further analyzed. Besides, each agent can possess an equivalent status and play the role of either a leader or a follower according to the actual need, and a general procedure is given to label the agents. Simulation results illustrate the effectiveness of theoretical results.