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This paper considers consensus strategy design for double-integrator multi-agent systems with matched disturbances under a directed graph. Specifically, we consider the case where both the control inputs and velocities of the agents are subject to different and asymmetric constraints. A novel distributed algorithm exploiting saturation functions is proposed to achieve asymptotic consensus without violating the predefined velocity and actuator saturation constraints. Subsequently, we extend the obtained results to event-triggered communication, where agent position broadcasting occurs only when specific triggering conditions are met. We rigorously prove that there exists a positive minimum inter-event time to rule out Zeno behavior. Finally, the simulation results confirm the theoretical findings and illustrate the achievable performance. [ABSTRACT FROM AUTHOR]

The stabilizing switching signal design of discrete-time linear compartmental switched systems (DT-LCSSs) has been heretofore unsolved. It has been proven that a DT-LCSS is stabilizable if and only if it is stabilizable by a periodic switching signal. However, it still needs to be determined whether the period of a stabilizing switching signal can be confined within a bound. Moreover, the existing design method for stabilizing periodic switching signals requires the diagonal entries of system matrices of all subsystems to be strictly positive. In this study, we propose a novel approach to solve this problem completely. We construct a discrete-time Markov chain for a given DT-LCSS, termed the associated Markov chain, and prove the equivalence of stability and stabilizability between the DT-LCSS and the associated Markov chain. Based on this, verifiable necessary and sufficient conditions for stability and stabilizability are derived. Especially, the period of a stabilizing switching signal for an n -dimensional DT-LCSS can always be chosen within the bound n 2 − n + 1. We propose a state-independent stabilizing switching signal design method for general stabilizable DT-LCSSs. We also prove the equivalence between stabilizability by state-independent switching laws and stabilizability by state-dependent switching laws. A state-dependent global stabilizing switching signal design method is also proposed. Additionally, the proposed results are applied to the consensus analysis of discrete-time leader–follower multi-agent systems with switching communication digraphs. The effectiveness of the theoretical results is demonstrated by examples. [ABSTRACT FROM AUTHOR]

Knowledge-based leader-following synchronization of heterogeneous nonlinear multi-agent systems is a challenging problem since the leader's dynamic information is unknown to any follower node. This paper proposes a learning-based fully distributed observer for a class of nonlinear leader systems, which can simultaneously learn the leader's dynamics and states. This class of leader dynamics is rather general and does not require a bounded Jacobian matrix. Based on this learning-based distributed observer, we further synthesize an adaptive distributed control law for solving the leader-following synchronization problem of multiple Euler–Lagrange systems subject to an uncertain nonlinear leader system. The results are illustrated by a simulation example. [ABSTRACT FROM AUTHOR]

Consensus of networked nonlinear nonparametric time-varying systems is studied, and the nonlinearity at input may possess arbitrary growth rate. In addition, the communication noise is also under consideration. The purely distributed control algorithm is designed on the basis of distributed stochastic approximation algorithm with expanding truncations (DSAAWET). The truncation mechanism neutralizes the divergent tendency caused by unknown nonlinearities and noises, which makes the algorithm well tackle more general nonlinearities with high growth rate and more complicated structure noises. We first prove the average consensus over fixed digraph, and then extend the results to averagely connected time-varying digraphs. Finally, the validity of the algorithm is justified by numerical simulations. [ABSTRACT FROM AUTHOR]

This paper focuses on the control of collective dynamics in large-scale multi-agent systems (MAS) operating in a 3-D space, with a specific emphasis on compensating for the influence of an unknown delay affecting the actuated leaders. The communication graph of the agents is defined on a mesh-grid 2-D cylindrical surface. We model the agents' collective dynamics by a complex- and a real-valued reaction–advection–diffusion 2-D partial differential equations (PDEs) whose states represent the 3-D position coordinates of the agents. The leader agents on the boundary suffer unknown actuator delay due to the cumulative computation and information transmission time. We design a delay-adaptive controller for the 2-D PDE by using PDE backstepping combined with a Lyapunov functional method, where the latter is employed to design an update law that generates real-time estimates of the unknown delay. Capitalizing on our recent result on the control of 1-D parabolic PDEs with unknown input delay, we use Fourier series expansion to bridge the control of 1-D PDEs to that of 2-D PDEs. To design the update law for the 2-D system, a new target system is defined to establish the closed-loop local boundedness of the system trajectories in H 2 norm and the regulation of the states to zero assuming a measurement of the spatially distributed plant's state. We illustrate the performance of the delay-adaptive controller by numerical simulations. [ABSTRACT FROM AUTHOR]

This paper considers the problem of the deployment of a set of agents distributed on a disk-shaped grid onto three-dimensional (3-D) profiles, by using a continuum approximation (valid in the limit for a large number of agents) and then a control methodology for partial differential equations (PDEs). The agents' collective behavior is modeled by a pair of radially-varying diffusion–reaction PDEs in polar coordinates, whose state determines the agents' position. Having a radially-varying reaction coefficient not only increases the challenge of kernel equations becoming singular in radius, but also brings more potential deployment manifolds. To stabilize and increase the convergence of the deployment, a boundary controller and a boundary observer are designed by combining an infinite-dimensional backstepping approach with a Fourier series decomposition technique, thus driving all agents to the desired profile. A key feature of the presented result is that the desired profile only needs to be known by the leaders, with the followers only needing to follow a simple control strategy which requires only the measurement of its current position and communication with its neighbors as defined by the multi-agent system topology. The method provides closed-loop exponential stability with any prescribed convergence rate in the L 2 norm. Simulation tests are shown to prove the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper proposes a distributed resilient consensus framework consisting of a distributed model predictive control (DMPC)-based consensus protocol and a new distributed attack detection mechanism, aiming to effectively handle the general linear constrained MAS under adversarial attacks. Based on the historical information from neighbors and a resilience set , we can evaluate the reliability of communication links via the attack detection mechanism. The proposed detection mechanism can significantly reduce the requirement on the network robustness compared with the well-known mean-subsequence-reduced (MSR) algorithms. The resilient consensus of general linear constrained MAS with F -locally adversarial attacks is achieved when the communication network is (F + 1)-robust. Furthermore, the DMPC-based resilient consensus framework exhibits the following key feature: the constrained consensus performance is optimized by minimizing a set of control variables. We demonstrate that the recursive feasibility of the associated DMPC optimization problem and the resilient consensus convergence of the constrained MAS can be guaranteed. Finally, the effectiveness of the proposed framework is illustrated through simulation experiments. [ABSTRACT FROM AUTHOR]

This paper is concerned with the output-feedback consensus problem of linear multi-agent systems on undirected graphs. Our focus is on reducing sensing and communication burdens between agents. Based on relative output measurements, a dynamic output-feedback (DOF) protocol is proposed, which, by leveraging the structure of the closed-loop dynamics, integrates a hybrid time/event-triggered sampling mechanism such that only intermittent interaction between agents is needed. Consensus conditions are established by the Lyapunov method and numerical simulations are provided for illustrating the effectiveness of the protocol. Compared with the existing results, the proposed DOF protocol has the following merits: (1) they rely on relative output measurements but do not need absolute measurements about agents; (2) they only require agents to intermittently interact with neighbors and thus can greatly reduce sensing and communication burdens between agents; and (3) the designed event-triggering conditions do not need to perform extra reconstruction operations that are computationally demanding. [ABSTRACT FROM AUTHOR]

In this paper, a randomized parallel algorithm is proposed to solve the distributed optimal consensus problem of multi-agent systems. Involving both the transient response and the final consensus state, the problem is described as a constrained non-separable optimization problem. Inspired by the randomized Jacobi proximal alternating direction method of multipliers, the proposed algorithm makes it possible for only a fraction of agents to solve their private subproblems in parallel at each iteration, which greatly saves computational resources and enhances running efficiency. The convergence analysis of the algorithm gives fully distributed convergence conditions. A trade-off between the convergence speed and resource savings is then obtained, where the convergence rate is estimated to be at least O 1 t . Furthermore, the algorithm can be accelerated to enjoy a convergence rate of O 1 t 2 by adaptively adjusting the auxiliary parameters properly. Numerical simulations demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the synchronization of heterogeneous agents interacting over a dynamical network is studied. The edge dynamics can model the inter-agent communications which are often heterogeneous by nature. They can also model the controllers of the agents which may be different for each agent or uniform for all the agents. Novel synchronization conditions are obtained for both cases from a phase perspective by exploiting a recently developed small phase theorem. The conditions scale well with the network and reveal the trade-off between the phases of node dynamics and edge dynamics. We also study the synchronizability problem which aims to characterize the allowable diversity of the agents for which controllers can be designed so as to achieve synchronization. The allowable diversity is captured in terms of phase conditions engaging the residue matrices of the agents at their persistent modes. Controller design algorithms are provided for the cases of agent-dependent and uniform controllers, respectively. [ABSTRACT FROM AUTHOR]

This paper deals with the control of collective dynamics of a large scale multi-agent system (MAS) moving in a 3-D space under the occurrence of arbitrarily large boundary input delay. The collective dynamics is described by a pair of reaction–advection–diffusion partial differential equations (PDEs) consisting of a complex-valued state whose real-part and imaginary-part denote the position coordinates x and y , respectively, and a real-valued state equation governing the evolution of the collective dynamics in the z coordinate. A 2-D cylindrical surface represents the indexes in a continuum and defines the topology where the agents communicate with each other based on a leader–follower strategy. The agents located at the boundary are chosen as the leaders and are subject to input delays that are practically induced by communication, measurement or even actuator constraints. A boundary control, which compensates the effect of the delay and drives all the agents to the desired formation is designed based on PDE-backstepping method. Here, the 2-D cylindrical coordinate leads to the existence of singular points in the gain kernels, which makes the stability analysis non-trivial in comparison to the 1-D problem. The proposed controller ensures the exponential stability of the MAS in H 2 norm under full-state measurement and transitions from one formation to another are achievable as illustrated by the simulation results. [ABSTRACT FROM AUTHOR]

This paper studies distributed time-varying formation control problems for a class of linear systems with heterogeneous uncertainties and directed graphs. Both the cases without and with an active leader having unknown control inputs are considered. Two new robust adaptive formation protocols are designed in a totally distributed fashion, both of which incorporate two parts: a fully distributed nominal controller relying on the neighbors' relative state information and an adaptive compensating signal to restrain the influences of uncertainties. An original adaptive compensating strategy is proposed herein to deal with uncertainties related to not only system states but also control inputs. On the basis of adaptive mechanism, the controller design requires neither global information about communication topologies nor the upper bounds of uncertainties and the leader's control inputs. Based on Lyapunov arguments, sufficient conditions to achieve the desired formation are derived in terms of Riccati equations. The proposed protocols guarantee that the formation errors can converge to zero. Finally, the theoretical results are demonstrated by numerical simulations. [ABSTRACT FROM AUTHOR]

This paper investigates the practical fixed-time consensus problem for a multi-agent system in networks with an undirected topology. Both node-based and edge-based fully distributed adaptive protocols are proposed to achieve the practical fixed-time consensus for the single integrator-type multi-agent systems, i.e., fixed-time attractiveness of a residual set as well as asymptotic consensus. Most notably, the settling time estimate can be computed without using any global information, which is distinctive from the existing fixed-time protocols. Furthermore, a scaling technique is applied for the proposed protocol such that the fixed-time attraction region can be contracted by only tuning a scaling parameter and the original settling time estimate remains unchanged. Finally, a numerical simulation example is given to validate the proposed protocols. [ABSTRACT FROM AUTHOR]

The agent dynamics of most of the multi-agent systems in practice are second-order. However, there is no existing min-consensus protocol for such systems. In this paper, we deal with this problem by proposing the first second-order min-consensus protocol with provable convergence. It is not trivial to extend the min-consensus result for the first-order case to the second-order one. Under certain conditions, the proposed protocol can guarantee global asymptotic min-consensus, even for the case with jointly connected communication graphs. An illustrative example is presented to verify the theoretical results and the efficiency of the proposed protocol. [ABSTRACT FROM AUTHOR]

This technical paper presents a distributed continuous-time algorithm to solve multi-agent optimization problem with the team objective being the sum of all local convex objective functions while subject to an equality constraint. The optimal solutions are achieved within fixed time which is independent of the initial conditions of agents. This advantage makes it possible to off-line preassign the settling time according to task requirements. The fixed-time convergence for the proposed algorithm is rigorously proved with the aid of convex optimization and fixed-time Lyapunov theory. Finally, the algorithm is valuated via an example. [ABSTRACT FROM AUTHOR]

This paper studies state synchronization of homogeneous multi-agent systems (MAS) with partial-state coupling. We identify four classes of agents, for which static linear protocol can be designed. They are agents which are squared-down passive, squared-down passifiable via output feedback, squared-down passifiable via input feedforward and squared-down minimum-phase with relative degree 1. We find that, for agents which are squared-down passive, the static protocol does not need any network information, as long as the network graph contains a directed spanning tree. For the other three classes of agents, the static protocol needs rough information on the network graph, that is either a lower bound for the real part or an upper bound for the modulus of the non-zero eigenvalues of the Laplacian matrix associated with the network graph. However, when adaptive nonlinear dynamic protocols are utilized, even this rough information about the network can be dispensed with. [ABSTRACT FROM AUTHOR]

In this paper, the localization and circumnavigation problem of an unknown stationary target is investigated. Unlike most existing results in which single agent is considered in two-dimensional (2D) space, in this paper multiple agents circumnavigating the target in three-dimensional (3D) space is addressed. Thus, new algorithms are needed to drive multiple non-coplanar agents to the same plane, and the coordination among the agents is also involved here. In addition, the agents measure only the bearing information to the target and each agent does not necessarily know the global normal vector of the objective orbit. An estimator is first established to localize the unknown position of the target and the control protocols are then designed to achieve the 3D circumnavigation of the target. Furthermore, the coordinators for the case with and without global orientation are designed, subsequently, the uniform circumnavigation and even circumnavigation are, respectively, achieved. Simulations are conducted to validate the benefits and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Cyclic pursuit frameworks, which are built upon pursuit interactions between neighboring agents in a cycle graph, provide an efficient way to create useful global behaviors in a collective of autonomous robots. Previous work had considered cyclic pursuit with a constant bearing (CB) pursuit law, and demonstrated the existence of circling equilibria for the corresponding dynamics. In this work, we propose a beacon-referenced version of the CB pursuit law, wherein a stationary beacon provides an additional reference for the individual agents in a collective. When implemented in a cyclic framework, we show that the resulting dynamics admit relative equilibria corresponding to a circling orbit around the beacon, with the circling radius and the distribution of agents along the orbit determined by parameters of the proposed pursuit law. We also derive necessary conditions for stability of the circling equilibria, which provides a guide for parameter selection. Finally, by introducing a change of variables, we demonstrate the existence of a family of invariant manifolds related to spiraling motions around the beacon which preserve the “pure shape” of the collective, and study the reduced dynamics on a representative manifold. [ABSTRACT FROM AUTHOR]

This paper focuses on robust nonlinear coordination of heterogeneous uncertain second-order multi-agent systems subject to directed communication topologies. We develop a nonlinear internal model principle based approach for the problem in a framework of cooperative global robust output regulation, independent of the a priori of the leader dynamics information except its order. As a major consequence, this study assures, by means of establishing a strict-Lyapunov function for the closed-loop system, not only a specified exponential convergence rate but also tolerable bounds of unmodeled disturbances. Hence, the former guarantees an appealing performance and the latter an important robustness property. [ABSTRACT FROM AUTHOR]

This paper investigates the appointed-time consensus problem under directed and periodical switching topologies. Here, the appointed finite time means that the consensus arriving time can be off-line pre-assigned according to task requirements without conservative estimation and is independent of the initial conditions of agents’ states. From a motion-planning perspective, a novel distributed appointed-time algorithm is developed for a multi-agent system with double-integrator dynamics. Under the assumption that the union of the directed periodical switching topologies contains a directed spanning tree, the proposed distributed algorithms can guarantee the multi-agent system to achieve consensus at an appointed time. Furthermore, the robustness and the practicability of the proposed algorithms are extended. It is the first time here to solve the finite- and appointed-time consensus problem for double-integrator systems under directed switching topologies. [ABSTRACT FROM AUTHOR]

In this paper, we consider robust finite-time connectivity preserving coordination problems for second-order multi-agent systems with limited sensing range. Based on integral sliding mode control and artificial potential field, a distributed controller is developed to achieve robust finite-time consensus and meanwhile maintain the connectivity of the communication network. The method is further extended to address a finite-time formation tracking control problem. Numerical examples are given to show the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper solves the coordinated optimal consensus problem for second-order multi-agent systems without velocity information from the distributed perspective. Particularly, all the agents are driven towards a consensus at an optimal solution inside the intersection of multiple feasible sets that minimizes a global target function aggregated by a group of convex local ones. Each local target function is exclusively assigned to a respective agent. Also, each feasible set constructed by inequality and set constraints privately belongs to a respective agent. Resorting to a novel auxiliary dynamics, a velocity-free distributed coordinated optimal control strategy is proposed without relying on global topology information. Using convex theory under the Lyapunov framework, it is demonstrated that the concerned coordinated optimal control objective is fulfilled by implementing the proposed distributed control strategy despite no velocity information. Examples are finally given to confirm the control effectiveness. [ABSTRACT FROM AUTHOR]

This paper derives conditions on the agents for the existence of a protocol which achieves synchronization of homogeneous multi-agent systems (MAS) with partial-state coupling, where the communication network is directed and weighted. These solvability conditions are necessary and sufficient for single-input agents and sufficient for multi-input agents. The solvability conditions reveal that the synchronization problem is primarily solvable for two classes of agents. This first class consists of at most weakly unstable agents (i.e. agents have all eigenvalues in the closed left half plane) and the second class consists of at most weakly non-minimum-phase agents (i.e. agents have all zeros in the closed left half plane). Under our solvability condition, we provide in this paper a design, utilizing H ∞ optimal control. [ABSTRACT FROM AUTHOR]

Cone-copositive piecewise quadratic Lyapunov functions (PWQ-LFs) for the stability analysis of continuous-time piecewise affine (PWA) systems are proposed. The state space is assumed to be partitioned into a finite number of convex, possibly unbounded, polyhedra. Preliminary conditions on PWQ functions for their sign in the polyhedra and continuity over the common boundaries are provided. The sign of each quadratic function is studied by means of cone-constrained matrix inequalities which are translated into linear matrix inequalities (LMIs) via cone-copositivity. The continuity is guaranteed by adding equality constraints over the polyhedra intersections. An asymptotic stability result for PWA systems is then obtained by finding a continuous PWQ-LF through the solution of a set of constrained LMIs. The effectiveness of the proposed approach is shown by analyzing an opinion dynamics model and two saturating control systems. [ABSTRACT FROM AUTHOR]

This paper investigates the consensus problem of homogeneous linear multi-agent systems using output feedback. An observer-type protocol is formulated, which only requires the relative output information of neighbours and does not require information exchange between controllers. It is shown that the protocol bridges some existing ones of the same nature. A robust control approach is presented for consensus protocol design, which requires one to solve a Riccati equation and a linear matrix inequality. Dual results are also discussed. By virtue of low- and high-gain techniques, it is shown that certain solvability conditions are to be satisfied to achieve consensus for agents that are not exponentially unstable or are minimum-phase, leading to a unified point of view for some existing results. A numerical example is provided to illustrate the advantages of the proposed design method. [ABSTRACT FROM AUTHOR]

Different from most existing distributed localization approaches in static networks where the agents in a network are static, this paper addresses the distributed localization problem in dynamic networks where the positions of the agents are time-varying. Firstly, complex constraints for the positions of the agents are constructed based on local relative position (distance and local bearing) measurements. Secondly, both algebraic condition and graph condition of network localizability in dynamic networks are given. Thirdly, a distributed localization protocol is proposed such that all the agents can cooperatively find their positions by solving the complex constraints in dynamic networks. Fourthly, the proposed method is extended to address the problem of integrated distributed localization and formation control. It is worth mentioning that the proposed algorithm can also be applied in the case that only distance and sign of direction measurements are available, where the sign of direction measurement is a kind of one bit local relative measurement and has less information than local bearing. [ABSTRACT FROM AUTHOR]

In this paper, the distributed resource allocation optimization problem is investigated. The allocation decisions are made to minimize the sum of all the agents’ local objective functions while satisfying both the global network resource constraint and the local allocation feasibility constraints. Here the data corresponding to each agent in this separable optimization problem, such as the network resources, the local allocation feasibility constraint, and the local objective function, is only accessible to individual agent and cannot be shared with others, which renders new challenges in this distributed optimization problem. Based on either projection or differentiated projection, two classes of continuous-time algorithms are proposed to solve this distributed optimization problem in an initialization-free and scalable manner. Thus, no re-initialization is required even if the operation environment or network configuration is changed, making it possible to achieve a “plug-and-play” optimal operation of networked heterogeneous agents. The algorithm convergence is guaranteed for strictly convex objective functions, and the exponential convergence is proved for strongly convex functions without local constraints. Then the proposed algorithm is applied to the distributed economic dispatch problem in power grids, to demonstrate how it can achieve the global optimum in a scalable way, even when the generation cost, or system load, or network configuration, is changing. [ABSTRACT FROM AUTHOR]

This paper proposes a novel control approach to solve the cooperative H ∞ output regulation problem for linear continuous-time multi-agent systems (MASs). Different from existing solutions to cooperative output regulation problems, a distributed feedforward-feedback controller is developed to achieve asymptotic tracking and reject both modeled and unmodeled disturbances. The feedforward control policy is computed via solving regulator equations, and the optimal feedback control policy is obtained through handling a zero-sum game. Instead of relying on the knowledge of system matrices in the state equations of the followers' dynamics and initial stabilizing feedback control gains, a value iteration (VI) algorithm is proposed to learn the optimal feedback control gain and feedforward control gain using online data. To the best of our knowledge, this paper is the first to show that the proposed VI algorithm can approximate the solution to continuous-time game algebraic Riccati equations with guaranteed convergence. Finally, the numerical analysis is provided to show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Many works on multi-agent consensus protocol designs rely on the full states of nodes or the node- observer-based procedures, under both of which the nodal information plays a key role in the consensus design. In this paper, we propose an edge-based augmented system approach for second-order nodal consensus, based on the edge loop transfer matrix of the closed-loop multi-agent system, which is defined by cutting the loop at the inputs of the edges. Each agent is allowed to be of single-output and additional poles and zeros are introduced into edges to construct the channel filter with previous data stored in the memories. We firstly focus on the consensus design by reserving two terms of the non-recursive filter and then propose a simplified design approach exploiting a single parameter, which is of low complexity and can be readily implemented. We also discuss the consensus design by using the non-recursive channel filter with higher-order realizations. Finally, as an extension, we discuss the consensus design based on the first-order recursive channel filter. The effectiveness of the proposed method is verified by the illustrative simulations. [ABSTRACT FROM AUTHOR]

This paper solves the simultaneous localization and formation (SLAF) problem for a multi-agent system moving in 2D plane. The multi-agent system consists of leaders who have the knowledge of their absolute positions in the global coordinate frame, and followers who do not know their absolute positions but have angle-only measurements and communication with respect to their neighboring agents. The aim of SLAF is to simultaneously localize and control the followers such that a desired formation among the leaders and followers can be achieved by using locally available sensing and communication information. To handle the challenging situation where the formation becomes unlocalizable at some nongeneric configurations, a perturbation-based SLAF algorithm is proposed such that the SLAF task can be achieved with an asymptotic convergence. To meet different tasks' requirements, three types of distributed SLAF algorithms are designed for the followers when the leaders are static, move with constant, or time-varying velocities, respectively. The effect of measurement noises, extension to other types of sensor measurements, requirement on agents' coordinate frames, collision and collinearity avoidance are also discussed. To validate the theoretical results, simulation examples corresponding to the discussed scenarios are carried out. [ABSTRACT FROM AUTHOR]

This paper presents a frequency domain resilient consensus problem of time-delayed multi-agent systems (MASs) under attacks. An internal model principle-based attack, a kind of network attack, is firstly analyzed and modeled in frequency domain. Then, a Quasi- H ∞ robust controller is designed for resilient consensus of the MAS with the help of an internal model controller. This scheme is different from the existing works in the sense that the attacker may inject an attacking signal on the node of an agent instead of a communication link. It is also novel because it can eliminate the impacts of attack without excluding compromised nodes and restricting the number of compromised nodes. The proposed control scheme is applied to a linear delayed MAS with single-input single-output agents and then transformed into multi-input and multi-output agents. An innovative approach is employed for the tuning of the proposed controller to track the performance of the MAS and its robustness. Some necessary and sufficient conditions are extracted using Pade ́ approximation and graph theory to minimize the impacts of time delay and attacks simultaneously. The results are extended for resilient consensus of the MAS under non-internal model principle-based attack. The simulation results are presented to demonstrate the validity of the proposed control strategy. [ABSTRACT FROM AUTHOR]

Time-varying formation analysis and design problems for multi-agent systems with general linear dynamics and switching directed interaction topologies are investigated. Different from the previous results, the formation in this paper can be defined by specified piecewise continuously differentiable vectors and the switching topologies are directed. Firstly, necessary and sufficient conditions for general linear multi-agent systems with switching directed topologies to achieve time-varying formations are proposed, where a description of the feasible time-varying formation set and approaches to expand the feasible formation set are given. Then an explicit expression of the time-varying formation reference function is derived to describe the macroscopic movement of the whole formation. An approach to assign the motion modes of the formation reference is provided. Moreover, an algorithm consisting of four steps to design the formation protocol is presented. In the case where the given time-varying formation belongs to the feasible formation set, it is proven that by designing the formation protocol using the proposed algorithm, time-varying formation can be achieved by multi-agent systems with general linear dynamics and switching directed topologies if the dwell time is larger than a positive threshold. Finally, numerical simulations are presented to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In a recent NATURE paper, Nagy et al. find a well-defined hierarchy among the individuals of the pigeon flock, which may lead to a rapid decision making in the directional choice dynamics of the flock. Motivated by this interesting discovery, we present a novel analysis on the efficiency of the hierarchical topology among the leader-following systems in this paper. To this end, we first propose a measurement of the convergence rate of leader-following consensus, and then connect the convergence rates with the communication topologies of leader-following systems. It is proved that the hierarchical network organization can achieve the best performance in terms of convergence rates. It is also established that the connections between the leader and the followers have effective impacts on increasing the convergence rates. Extensive numerical results are provided to show the effectiveness of our conclusions. [ABSTRACT FROM AUTHOR]

The finite-time leader-following consensus problem is addressed for a class of high-order multi-agent systems with uncertain nonlinear dynamics. Each follower node is modeled by lower-triangular system. By using recursive method, we develop the finite-time consensus control design scheme. Based on finite-time Lyapunov stability theorem and matrix theory, we prove that the finite-time consensus of high-order uncertain nonlinear multi-agent systems is guaranteed by non-lipschitz continuous control laws. Simulation results are given to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper addresses distributed optimal tracking control of multi-agent linear systems subject to external disturbances. The concept of differential game theory is utilized to formulate this distributed control problem into a multi-player zero-sum differential graphical game, which provides a new perspective on distributed tracking of multiple agents influenced by disturbances. In the presented differential graphical game, the dynamics and performance indices for each node depend on local neighbor information and disturbances. It is shown that the solution to the multi-agent differential graphical games in the presence of disturbances requires the solution to coupled Hamilton–Jacobi–Isaacs (HJI) equations. Multi-agent learning policy iteration (PI) algorithm is provided to find the solution to these coupled HJI equations and its convergence is proven. It is also shown that L 2 -bounded synchronization errors can be guaranteed using this technique. An online PI algorithm is given to solve the zero-sum game in real time. A simulation example is provided to show the effectiveness of the online approach. [ABSTRACT FROM AUTHOR]

In this paper, we study the leader-following attitude consensus problem for multiple rigid body systems by a distributed unit quaternion-based attitude feedback control law. The control law is based on the certainty equivalence principle and contains a distributed observer for estimating the state of the leader and an auxiliary system compensating for the unavailability of the angular velocity. It is shown that the problem is solvable under the standard assumption that each follower can access the information from the leader through a directed path. [ABSTRACT FROM AUTHOR]

This paper studies a distributed linear consensus protocol for second-order multi-agent systems under limited agent interaction ranges. In particular, two agents can interact with each other only if their distance is within a certain range. Under a linear consensus protocol with the relative state feedback, we derive a sufficient condition on the initial states and the interaction range to achieve the second-order consensus by using a Lyapunov functional approach. Finally, simulation examples are included to validate the theoretical result. [ABSTRACT FROM AUTHOR]

In this paper, four observer-based distributed controllers are proposed for general linear multi-agent systems to achieve finite-time coordinated tracking under different situations. Specifically, for the cases of undirected communication graphs and directed communication graphs among the followers, both the situations of relative state measurement and relative output measurement among neighboring agents are considered. Under both kinds of communication topologies, when relative state information of the neighbors is available, distributed observer-based controllers are designed which achieve exact coordinated tracking in finite-time. When only relative output information is available, another finite-time observer is introduced for each follower to estimate the relative state information. Together with the distributed controllers designed for the state feedback case, finite-time exact coordinated tracking can still be achieved in this situation. Numerical simulations are provided to illustrate the effectiveness of the proposed controllers. [ABSTRACT FROM AUTHOR]

A novel distributed consensus protocol, where only causal sampled position data are used, is firstly designed for second-order linear multi-agent systems with a directed communication topology. In this context, a necessary and sufficient condition depending upon the coupling gains, sampling period, and spectrum of the Laplacian matrix, is established for achieving consensus. It is revealed that second-order consensus in such a multi-agent system cannot be reached without using past sampled position data. It is also found that a relatively small sampling period does not necessarily improve the consensus performance. Then, a delay-induced consensus protocol is proposed based on sampled position data and with the help of time delay. It is found that consensus under this designed protocol cannot be reached in the absence of time delay. More interestingly, the time delay should have both lower and upper bounds in order to achieve consensus. Finally, the effectiveness of the theoretical results is demonstrated through numerical simulations. [ABSTRACT FROM AUTHOR]