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This paper studies the distributed formation control problem of second-order multi-agent systems (MASs) with limited communication ranges and collision avoidance constraints. A novel connectivity preservation and collision-free distributed control algorithm is proposed by combining prescribed performance control (PPC) and exponential zeroing control barrier Lyapunov functions (EZCBFs). In particular, we impose the time-varying performance constraints on the relative position and velocity errors between the neighboring agents, and then a PPC-based formation control algorithm is developed such that the connectivity of the communication graph can be preserved at all times, and the prescribed transient and steady performance on the relative position and velocity error can be achieved. Subsequently, by introducing the EZCBFs method, an inequality constraint condition on the control input is derived to guarantee the collision-free formation motion. By regarding the PPC-based formation controller as a nominal input, an actual formation control input is given by solving the quadratic programming (QP) problem such that each agent achieves collision-free formation motion while guaranteeing the connectivity and prescribed performance as much as possible. Finally, numerical simulation is carried out to validate the effectiveness of the proposed algorithm., QC 20231201

This chapter considers synchronization of networked linear systems over networks with nonuniform time-varying delays. Since delays are inevitable in real systems and may change the stability of the original system, it is necessary and beneficial to study synchronization in the presence of delays. We focus on the case where the internal dynamics are time-varying but non-expansive (stable dynamics with a quadratic Lyapunov function). The case of directed graph is considered and we show that global asymptotic P-norm synchronization can be achieved over a directed graph with joint connectivity and arbitrarily bounded delays. Simulation results are provided to validate the theoretical results., QC 20220519

In most of the networked dynamical system literature, the consensus and synchronization problems have been extensively studied. To illustrate the rich behaviors of networked dynamical systems, this chapter considers the existence of periodic behaviors for discrete-time second-order networked dynamical systems with input saturation constraints. We consider both cases where the agent dynamics are neutrally stable and double integrator, respectively. In both cases, we establish conditions on the feedback gains of the linear control law for achieving periodic behaviors. Simulation results are used to validate the theoretical results., QC 20220525

Coordination of networked dynamical systems has drawn significant attention due to its broad applications in biology, social science, computer science, and engineering in recent years. Although different problems are modeled from different disciplines, the basic assignment of these networked dynamical systems is to accomplish a common desirable objective in a cooperative manner. One approach is through a completely centralized strategy, where a single decision maker gathers the entire system’s information, performs the computation, and sends back the solution to an individual agent. This centralized framework is subject to performance limitations, such as a single point of failure, high communication requirement and cost, substantial computational burden, limited flexibility and scalability, and lack of privacy. To overcome these limitations, an alternative distributed approach has received substantial attention in the area of systems and control. The idea is that by carefully designing distributed controllers, a group of autonomous agents can achieve a collective task by cooperatively and locally exchanging information. Interactions are local in the sense that an agent can only interact with a subset of agents. Under such a distributed framework, this book aims to provide some recent results on modeling, analysis, control, and applications of networked dynamical systems., Part of book: ISBN: 978-3-030-84682-4QC 20220530

In this chapter, we first introduce several commonly used networked dynamical models. We then introduce examples of the considered networked dynamical models., Part of book: ISBN: 978-3-030-84682-4QC 20220530

Part of book: ISBN: 978-3-030-84682-4QC 20220530

This paper proposes distributed algorithms for solving linear equations to seek a least square solution via multi-agent networks. We consider that each agent has only access to a small and imcomplete block of linear equations rather than the complete row or column in the existing literatures. Firstly, we focus on the case of a homogeneous partition of linear equations. A distributed algorithm is proposed via a single-layered grid network, in which each agent only needs to control three scalar states. Secondly, we consider the case of heterogeneous partitions of linear equations. Two distributed algorithms with doubled-layered network are developed, which allows each agent's states to have different dimensions and can be applied to heterogeneous agents with different storage and computation capability. Rigorous proofs show that the proposed distributed algorithms collaboratively obtain a least square solution with exponential convergence, and also own a solvability verification property, i.e., a criterion to verify whether the obtained solution is an exact solution. Finally, some simulation examples are provided to demonstrate the effectiveness of the proposed algorithms.

QC 20200103

In distributed optimization of multi-agent systems, agents cooperate to minimize a global function which is a sum of local objective functions. Motivated by applications including power systems, sensor networks, smart buildings, and smart manufacturing, various distributed optimization algorithms have been developed. In these algorithms, each agent performs local computation based on its own information and information received from its neighboring agents through the underlying communication network, so that the optimization problem can be solved in a distributed manner. This survey paper aims to offer a detailed overview of existing distributed optimization algorithms and their applications in power systems. More specifically, we first review discrete-time and continuous-time distributed optimization algorithms for undirected graphs. We then discuss how to extend these algorithms in various directions to handle more realistic scenarios. Finally, we focus on the application of distributed optimization in the optimal coordination of distributed energy resources., QC 20191022

This paper studies, the role of persistent flows in the convergence of infinite backward products of stochastic matrices of deterministic chains over networks with nonreciprocal interactions between agents. An arc describing the interaction strength between two agents is said to be persistent if its weight function has an infinite l(1) norm; convergence of the infinite backward products to a rank-one matrix of a deterministic chain of stochastic matrices is equivalent to achieving consensus at the node states. We discuss two balance conditions on the interactions between agents, which generalize the arc-balance and cut-balance conditions in the literature, respectively. The proposed conditions require that such a balance should be satisfied over each time window of a fixed length instead of at each time instant. We prove that in both cases global consensus is reached if and only if the persistent graph, which consists of all the persistent arcs, contains a directed spanning tree. The convergence rates of the system to consensus are also provided in terms of the interactions between agents having taken place. The results are obtained under a weak condition without assuming the existence of a positive lower bound of all the nonzero weights of arcs and are compared with the existing results. Illustrative examples are provided to validate the results and show the critical importance of the nontrivial lower boundedness of the self-confidence of the agents., QC 20190820

A typical formation shape control problem involves point agents sensing relative positions, that is, orientations and distances, of their neighbors and then moving so that these relative positions achieve some prespecified values. Such a procedure, requiring as it does sensing of orientations, implicitly presupposes that all agents have a shared understanding of the common orientations. On the other hand, there may be biases in sensors, variations in the earth's magnetic field interfering with compass-based sensing, or drift in inertial sensors, with the result that orientations are inconsistently measured or measured with error. In this paper, we investigate the formation control problem with mismatched coordinates in the 3-D space, considering the consequences of this error. First, the situation of a two-agent formation is considered. We show that the agents converge to a fixed but distorted formation exponentially fast. In contrast to the matched case, the formation is not asymptotically stationary, but rather instead translates with a certain constant velocity depending on the mismatches. The formation distortion between the actual one and the desired one is obtained, as well as the steady-state velocity of the formation for small mismatch orientations. The case of agents with double integrator dynamics is then considered and similar phenomena are observed. Based on the results, an estimation algorithm is given to obtain the mismatch rotation matrix, which allows a compensation algorithm to be proposed such that the desired formation is achieved with zero steady-state velocity for the formation as a whole. The case of n-agent formations is finally considered, first with a star graph and then with a general graph. Simulations are provided to validate the theoretical results.

In power system operation, the economic dispatch problem (EDP) aims to minimize the total generation cost while meeting the demand and satisfying generator capacity limits. This paper proposes an algorithm based on the gradient push-sum method to solve the EDP in a distributed manner over communication networks potentially with time-varying topologies and communication delays. This paper shows that the proposed algorithm is guaranteed to solve the EDP if the time-varying directed communication network is uniformly jointly strongly connected. Moreover, the proposed algorithm is also able to handle arbitrarily large but bounded time-varying delays on communication links. Numerical simulations are used to illustrate and validate the proposed algorithm.

We study the consensus problem of discrete-time systems under persistent flow and non-reciprocal interactions between agents. An arc describing the interaction strength between two agents is said to be persistent if its weight function has an infinite l(1) norm. We discuss two balance conditions on the interactions between agents which generalize the arc-balance and cut-balance conditions in the literature respectively. The proposed conditions require that such a balance should be satisfied over each time window of a fixed length instead of at each time instant. We prove that in both cases global consensus is reached if and only if the persistent graph, which consists of all the persistent arcs, contains a directed spanning tree. The convergence rates are also provided in terms of the number of node interactions that have taken place., QC 20180305

Attitude coordinated control of multiple underactuated spacecraft is studied in this paper. We adopt the parametrization proposed by Tsiotras et al. (1995) to describe attitude kinematics, which has been shown to be very convenient for control of underactuated axisymmetric spacecraft with two control torques. We first propose a partial attitude coordinated controller with angular velocity commands. The controller is based on the exchange of each spacecraft's information with local neighbors and a self-damping term. Under a necessary and general connectivity assumption and by use of a novel Lyapunov function, we show that the symmetry axes of all spacecraft are eventually aligned. Full attitude control of multiple underactuated spacecraft is also considered and a discontinuous distributed control algorithm is proposed. It is shown that the proposed algorithm succeeds in achieving stabilization given that control parameters are chosen properly. Discussions on the cases without self damping are also provided for both partial and full attitude controls. Simulations are given to validate the theoretical results and different steadystate behaviors are observed., QC 20180111

In this paper, we study the targeted agreement problem for a group of Lagrangian systems. Each system observes a convex set as its local target and the objective of the group is to reach a generalized coordinate agreement towards these target sets. Typically, the generalized coordinate represents position or angle. We first consider the case when the communication graphs are fixed. A control law is proposed based on each system's own target sensing and information exchange with neighbors. With necessary connectivity, the generalized coordinates of multiple Lagrangian systems are shown to achieve agreement in the intersection of all the local target sets while generalized coordinate derivatives are driven to zero. We also discuss the case when the intersection of the local target sets is empty. Exact targeted agreement cannot be achieved in this case. Instead, we show that approximate targeted agreement can be guaranteed if the control gains are properly chosen. In addition, when communication graphs are allowed to be switching, we propose a model-dependent control algorithm and show that global targeted agreement is achieved when joint connectivity is guaranteed and the intersection of local target sets is nonempty. Simulations are given to validate the theoretical results., QC 20171018

The self-learning Monte Carlo method is a powerful general-purpose numerical method recently introduced to simulate many-body systems. In this work, we extend it to an interacting fermion quantum system in the framework of the widely used determinant quantum Monte Carlo. This method can generally reduce the computational complexity and moreover can greatly suppress the autocorrelation time near a critical point. This enables us to simulate an interacting fermion system on a 100×100 lattice even at the critical point and obtain critical exponents with high precision. © 2017 American Physical Society.

We develop the self-learning Monte Carlo (SLMC) method, a general-purpose numerical method recently introduced to simulate many-body systems, for studying interacting fermion systems. Our method uses a highly efficient update algorithm, which we design and dub "cumulative update", to generate new candidate configurations in the Markov chain based on a self-learned bosonic effective model. From a general analysis and a numerical study of the double exchange model as an example, we find that the SLMC with cumulative update drastically reduces the computational cost of the simulation, while remaining statistically exact. Remarkably, its computational complexity is far less than the conventional algorithm with local updates. © 2017 American Physical Society.

Monte Carlo simulation is an unbiased numerical tool for studying classical and quantum many-body systems. One of its bottlenecks is the lack of a general and efficient update algorithm for large size systems close to the phase transition, for which local updates perform badly. In this Rapid Communication, we propose a general-purpose Monte Carlo method, dubbed self-learning Monte Carlo (SLMC), in which an efficient update algorithm is first learned from the training data generated in trial simulations and then used to speed up the actual simulation. We demonstrate the efficiency of SLMC in a spin model at the phase transition point, achieving a 10-20 times speedup. © 2017 American Physical Society.

The self-learning Monte Carlo method is a powerful general-purpose numerical method recently introduced to simulate many-body systems. In this work, we extend it to an interacting fermion quantum system in the framework of the widely used determinant quantum Monte Carlo. This method can generally reduce the computational complexity and moreover can greatly suppress the autocorrelation time near a critical point. This enables us to simulate an interacting fermion system on a 100×100 lattice even at the critical point and obtain critical exponents with high precision. © 2017 American Physical Society.

Monte Carlo simulation is an unbiased numerical tool for studying classical and quantum many-body systems. One of its bottlenecks is the lack of a general and efficient update algorithm for large size systems close to the phase transition, for which local updates perform badly. In this Rapid Communication, we propose a general-purpose Monte Carlo method, dubbed self-learning Monte Carlo (SLMC), in which an efficient update algorithm is first learned from the training data generated in trial simulations and then used to speed up the actual simulation. We demonstrate the efficiency of SLMC in a spin model at the phase transition point, achieving a 10-20 times speedup. © 2017 American Physical Society.

A typical formation shape control problem involves point agents sensing relative positions, i.e. orientations and distances, of their neighbors and then moving so that these relative positions achieve some prespecified values. Such a procedure, requiring as it does sensing of orientations, implicitly presupposes that all agents have a shared understanding of the common orientations. On the other hand, there may be biases in sensors, variations in the earth's magnetic field interfering with compass-based sensing, or drift in inertial sensors, with the result that orientations are inconsistently measured or measured with error. In this paper, we investigate the formation control problem with mismatched coordinates in the three-dimensional space, considering the consequences of this error. First, the situation of a two agent formation is first considered. We show that the agents converge to a fixed, but distorted formation exponentially fast. In contrast to the matched case, the formation is not asymptotically stationary, but rather instead translates with a certain constant velocity depending on the mismatches. The formation distortion between the actual one and the desired one is obtained, as well as the steady state velocity of the formation for small mismatch orientations. The case of agents with double integrator dynamics is then considered and similar phenomena are observed. Based on the results, an estimation algorithm is given to obtain the mismatch rotation matrix, which allows a compensation algorithm to be proposed such that the desired formation is achieved with zero steady-state velocity for the formation as a whole. The case of n-agent formations is finally considered, first with a star graph and then with a general graph. Simulations are provided to validate the theoretical results.

The self-learning Monte Carlo method is a powerful general-purpose numerical method recently introduced to simulate many-body systems. In this work, we extend it to an interacting fermion quantum system in the framework of the widely used determinant quantum Monte Carlo. This method can generally reduce the computational complexity and moreover can greatly suppress the autocorrelation time near a critical point. This enables us to simulate an interacting fermion system on a 100×100 lattice even at the critical point and obtain critical exponents with high precision. © 2017 American Physical Society.

Monte Carlo simulation is an unbiased numerical tool for studying classical and quantum many-body systems. One of its bottlenecks is the lack of a general and efficient update algorithm for large size systems close to the phase transition, for which local updates perform badly. In this Rapid Communication, we propose a general-purpose Monte Carlo method, dubbed self-learning Monte Carlo (SLMC), in which an efficient update algorithm is first learned from the training data generated in trial simulations and then used to speed up the actual simulation. We demonstrate the efficiency of SLMC in a spin model at the phase transition point, achieving a 10-20 times speedup. © 2017 American Physical Society.

We develop the self-learning Monte Carlo (SLMC) method, a general-purpose numerical method recently introduced to simulate many-body systems, for studying interacting fermion systems. Our method uses a highly efficient update algorithm, which we design and dub "cumulative update", to generate new candidate configurations in the Markov chain based on a self-learned bosonic effective model. From a general analysis and a numerical study of the double exchange model as an example, we find that the SLMC with cumulative update drastically reduces the computational cost of the simulation, while remaining statistically exact. Remarkably, its computational complexity is far less than the conventional algorithm with local updates. © 2017 American Physical Society.

This paper studies deterministic consensus networks with discrete-time dynamics under persistent flows and non-reciprocal agent interactions. An arc describing the interaction strength between two agents is said to be persistent if its weight function has an infinite $l_1$ norm. We discuss two balance conditions on the interactions between agents which generalize the arc-balance and cut-balance conditions in the literature respectively. The proposed conditions require that such a balance should be satisfied over each time window of a fixed length instead of at each time instant. We prove that in both cases global consensus is reached if and only if the persistent graph, which consists of all the persistent arcs, contains a directed spanning tree. The convergence rates of the system to consensus are also provided in terms of the interactions between agents having taken place. The results are obtained under a weak condition without assuming the existence of a positive lower bound of all the nonzero weights of arcs and are compared with the existing results. Illustrative examples are provided to show the critical importance of the nontrivial lower boundedness of the self-confidence of the agents.

This paper is concerned with the dynamics evolution of opinions in the presence of both cooperations and antagonisms. The class of Laplacian flows is addressed through signed digraphs subject to switching topologies. Further, a state transition matrix-based approach is developed for the analysis of opinion dynamics, regardless of any assumptions on connectivity, structural balance or digon sign-symmetry of signed digraphs. It is shown that based on the separation of cooperations and antagonisms, a relationship can be bridged between opinion dynamics under signed digraphs and under conventional digraphs. This helps to solve convergence problems for opinion dynamics. In particular, bipartite consensus (or stability) emerges if and only if the associated switching signed digraph is simultaneously structurally balanced (or unbalanced), which generalizes the use of structural balance theory in opinion dynamics to the case study of changing network topologies., Comment: 19 pages

This paper investigates the coordinated trajectory tracking problem of multiple vertical takeooff and landing (VTOL) unmanned aerial vehicles (UAVs). The case of unidirectional information flow is considered and the objective is to drive all the follower VTOL UAVs to accurately track the trajectory of the leader. Firstly, a novel distributed estimator is developed for each VTOL UAV to obtain the leader's desired information asymptotically. With the outputs of the estimators, the solution to the coordinated trajectory tracking problem of multiple VTOL UAVs is transformed to individually solving the tracking problem of each VTOL UAV. Due to the under-actuated nature of the VTOL UAV, a hierarchical framework is introduced for each VTOL UAV such that a command force and an applied torque are exploited in sequence, then the position tracking to the estimated desired position and the attitude tracking to the command attitude are achieved. Moreover, an auxiliary system with proper parameters is implemented to guarantee the singularity-free command attitude extraction and to obviate the use of the unavailable desired information. The stability analysis and simulations effectively validate the achievement of the coordinated trajectory tracking of multiple VTOL UAVs with the proposed control approach., Comment: 11 pages, 4 figures

This brief considers the synchronization problem of coupled nonlinear dynamical systems over time-varying interaction graphs. We first show that infinite joint connectivity is necessary for achieving globally asymptotic synchronization. We then show that the commonly used Lipschitz condition on the nonlinear self-dynamics is not sufficient to ensure synchronization even for an arbitrarily large coupling strength. A sufficient synchronization condition is established in terms of the times of connectivity, the integral of the Lipschitz gain, and the network parameters., QC 20160428

This paper considers the consensus problem for a network of nodes with random interactions and sampled-data control actions. We first show that consensus in expectation, in mean square, and almost surely are equivalent for a general random network model when the inter-sampling interval and maximum node degree satisfy a simple relation. The three types of consensus are shown to be simultaneously achieved over an independent or a Markovian random network defined on an underlying graph with a directed spanning tree. For both independent and Markovian random network models, necessary and sufficient conditions for mean-square consensus are derived in terms of the spectral radius of the corresponding state transition matrix. These conditions are then interpreted as the existence of critical value on the intersampling interval, below which a global mean-square consensus is achieved and above which the system diverges in a mean-square sense for some initial states. Finally, we establish an upper bound on the intersampling interval below which almost sure consensus is reached, and a lower bound on the intersampling interval above which almost sure divergence is reached. Some numerical simulations are given to validate the theoretical results and some discussions on the critical value of the inter-sampling intervals for the mean-square consensus are provided., QC 20161012

This brief considers the existence of periodic behaviors for discrete-time second-order multiagent systems with input saturation constraints. We first consider the case where the agent dynamics is a double integrator and then establish conditions on the feedback gains of the linear consensus control law for achieving periodic behaviors. This, in turn, shows that the previously established sufficient condition for reaching global consensus has a necessary aspect since these two conditions are exclusive. We further consider all other second-order agent dynamics and show that these multiagent systems under the linear consensus law exhibit periodic solutions provided the feedback gains satisfy certain conditions. Simulation results are used to validate the theoretical findings., QC 20160818

In this paper, we study the discrete-time consensus problem over networks with antagonistic and cooperative interactions. A cooperative interaction between two nodes takes place when one node receives the true state of the other while an antagonistic interaction happens when the former receives the opposite of the true state of the latter. We adopt a quite general model where the node communications can be either unidirectional or bidirectional, the network topology graph may vary over time, and the cooperative or antagonistic relations can be time-varying. It is proven that, the limits of all the node states exist, and the absolute values of the node states reach consensus if the switching interaction graph is uniformly jointly strongly connected for unidirectional topologies, or infinitely jointly connected for bidirectional topologies. These results are independent of the switching of the interaction relations. We construct a counterexample to indicate a rather surprising fact that quasi-strong connectivity of the interaction graph, i.e., the graph contains a directed spanning tree, is not sufficient to guarantee the consensus in absolute values even under fixed topologies. Based on these results, we also propose sufficient conditions for bipartite consensus to be achieved over the network with joint connectivity. Finally, simulation results using a discrete-time Kuramoto model are given to illustrate the convergence results showing that the proposed framework is applicable to a class of networks with general nonlinear dynamics., QC 20161114

This paper considers scheduled anti-windup design of linear systems in the presence of input saturation. We introduce the scheduled controller design method into the anticipatory anti-windup scheme. The proposed controllers are triggered depending on the response of the system, rather than only considering the worst noise case off-line, and then activating the anti-windup scheme before the physical actuator arrives saturation. The system stability and certain levels of performance are guaranteed under the proposed anti-windup scheme. The control feedback law is analyzed under the scheme of static feedback compensator, while the results are presented using the linear matrix inequality technique. The advantage of the proposed scheduled anticipatory scheme over immediate activation is illustrated through a numerical example., QC 20151123

In this paper, we consider the synchronization problem for a network of state diffusive coupled agents with identical but time-varying dynamics under switching communication topologies. Both leader-follower and leaderless networks are studied. For leader-follower networks, sufficient conditions are established regarding the connectivity of communication graphs for the network to achieve global exponential or asymptotic synchronization, respectively, for directed and undirected communications. For leaderless networks, sufficient conditions for asymptotic norm synchronization are established, respectively, for directed and undirected communications, in the sense that the norm of agents' states converges to a common value. We also show that if the communication graph is fixed, norm synchronization leads to state synchronization. The results reveal some important similarities and differences between leaderless and leader-follower networks for synchronization under directed switching communication graphs., QC 20151123

In this paper, we construct a framework to describe and study the coordinated output regulation problem for multiple heterogeneous linear systems. Each agent is modeled as a general linear multiple-input multiple-output system with an autonomous exosystem which represents the individual offset from the group reference for the agent. The multi-agent system as a whole has a group exogenous state which represents the tracking reference for the whole group. Under the constraints that the group exogenous output is only locally available to each agent and that the agents have only access to their neighbors' information, we propose observer-based feedback controllers to solve the coordinated output regulation problem using output feedback information. A high-gain approach is used and the information interactions are allowed to be switching over a finite set of networks containing both graphs that have a directed spanning tree and graphs that do not. Simulations are shown to validate the theoretical results., QC 20150505

This paper investigates agreement protocols over cooperative and cooperativeantagonistic multiagent networks with coupled continuous-time nonlinear dynamics. To guarantee convergence for such systems, it is common in the literature to assume that the vector field of each agent is pointing inside the convex hull formed by the states of the agent and its neighbors, given that the relative states between each agent and its neighbors are available. This convexity condition is relaxed in this paper, as we show that it is enough that the vector field belongs to a strict tangent cone based on a local supporting hyperrectangle. The new condition has the natural physical interpretation of requiring shared reference directions in addition to the available local relative states. Such shared reference directions can be further interpreted as if each agent holds a magnetic compass indicating the orientations of a global frame. It is proved that the cooperative multiagent system achieves exponential state agreement if and only if the time-varying interaction graph is uniformly jointly quasi-strongly connected. Cooperative-antagonistic multiagent systems are also considered. For these systems, the relation has a negative sign for arcs corresponding to antagonistic interactions. State agreement may not be achieved, but instead it is shown that all the agents’ states asymptotically converge, and their limits agree componentwise in absolute values if and in general only if the time-varying interaction graph is uniformly jointly strongly connected.

This paper considers the consensus problem for a network of nodes with random interactions and sampled-data control actions. We first show that consensus in expectation, in mean square, and almost surely are equivalent for a general random network model when the inter-sampling interval and network size satisfy a simple relation. The three types of consensus are shown to be simultaneously achieved over an independent or a Markovian random network defined on an underlying graph with a directed spanning tree. For both independent and Markovian random network models, necessary and sufficient conditions for mean-square consensus are derived in terms of the spectral radius of the corresponding state transition matrix. These conditions are then interpreted as the existence of critical value on the inter-sampling interval, below which global mean-square consensus is achieved and above which the system diverges in mean-square sense for some initial states. Finally, we establish an upper bound on the inter-sampling interval below which almost sure consensus is reached, and a lower bound on the inter-sampling interval above which almost sure divergence is reached. Some numerical simulations are given to validate the theoretical results and some discussions on the critical value of the inter-sampling intervals for the mean-square consensus are provided.

In this paper, we study the set target aggregation problem of multiple mechanical systems. Each system is modeled by a Lagrangian dynamical equation and observes a convex set as its local target. The objective of the group is to reach an aggregation towards these target sets.We propose a set target aggregation algorithm that is constructed based on each mechanical system's own target sensing and the exchange of its information with local neighbors. With necessary connectivity for both fixed and switching communication topologies, multiple mechanical systems are shown to converge to the intersection of all the local target sets while the vectors of generalized coordinate derivatives are driven to zero. Simulations are given to validate the theoretical results., QC 20151130

In this paper, we first study agreement protocols for coupled continuous-time nonlinear dynamics over cooperative multi-agent networks. To guarantee convergence for such systems, it is common in the literature to assume that the vector field of each agent is pointing inside the convex hull formed by the states of the agent and its neighbors given the relative states between each agent and its neighbors are available. This convexity condition is relaxed in this paper, as we show that it is enough that the vector field belongs to a strict tangent cone based on a local supporting hyperrectangle. The new condition has the natural physical interpretation of adding a compass for each agent in addition to the available local relative states, as each agent needs only to know in which orthant each of its neighbor is. It is proven that the multi-agent system achieves exponential state agreement if and only if the time-varying interaction graph is uniformly jointly quasi-strongly connected. Cooperative-antagonistic multi-agent networks are also considered. For these systems, the (cooperative-antagonistic) relation has a negative sign for arcs corresponding to antagonistic interactions. State agreement may not be achieved for cooperative-antagonistic multi-agent systems. Instead it is shown that asymptotic modulus agreement is achieved if the time-varying interaction graph is uniformly jointly strongly connected., QC 20150525

In this paper, we consider the global consensus problem for discrete-time multi-agent systems with input saturation constraints under fixed undirected topologies. We first give necessary conditions for achieving global consensus via a distributed protocol based on relative state measurements of the agent itself and its neighboring agents. We then focus on two special cases, where the agent model is either neutrally stable or a double integrator. For the neutrally stable case, any linear protocol of a particular form, which solves the consensus problem for the case without input saturation constraints, also solves the global consensus problem for the case with input saturation constraints. For the double integrator case, we show that a subset of linear protocols, which solve the consensus problem for the case without saturation constraints, also solve the global consensus problem for the case with input saturation constraints. The results are illustrated by numerical simulations., QC 20140314

This paper studies finite-time coordinated tracking problem for multiple double integrator systems with a time-varying leader's velocity and bounded external disturbances. We consider the dynamic feedback designs for two different cases. In the first case, the velocities of the followers and the leader are assumed to be unavailable, and the communication topology is assumed to be undirected and fixed. In the second case, the velocities of the followers and the leader are assumed to be available, and the communication topology is assumed to be directed and switching. Distributed finite-time observers are designed, respectively, to obtain the velocity information in the first case and the relative state information in the second case. The states of these observers are then used to design control inputs that achieve finite time robust coordinated tracking of multiple double integrator systems in the presence of bounded disturbances for these two cases. Simulation results are provided to validate the effectiveness of these theoretical results., QC 20141205

In this paper, we study the coordinated tracking problem of multiple heterogeneous Lagrange systems with a dynamic leader. Only nominal parameters of Lagrange dynamics are assumed to be available. Under the local interaction constraints, i.e., the followers only have access to their neighbors' information and the leader being a neighbor of only a subset of the followers, continuous coordinated tracking algorithms with adaptive coupling gains are proposed. Except for the benefit of the chattering-free control achieved, the proposed algorithm also has the attribute that it does not require the neighbors' generalized coordinate derivatives. Global asymptotic coordinated tracking is guaranteed, and the tracking errors between the followers and the leader are shown to converge to zero. Examples are given to validate the effectiveness of the proposed algorithms., QC 20140707

We study leaderless attitude synchronization problem of multiple underactuated spacecraft in this paper. We adopt the special parameterizations of attitude proposed by Tsiotras et al. (1995) to describe attitude kinematics, which has been shown to be very convenient for control of underactuated axisymmetric spacecraft with two control torques. It is assumed that angular velocity commands are possible and this paper is confined to the kinematic level. We first propose a partial attitude synchronization controller that is based on the exchange of each spacecraft's information with local neighbors. Under a necessary and general connectivity assumption and by use of an appropriate Lyapunov function, we show that the attitudes of spacecraft converge to a fixed or time-varying synchronization trajectory. Then, full attitude synchronization of multiple underactuated spacecraft is considered, where the discontinuous distributed algorithm is proposed. Simulations are given to validate the theoretical results and indicate several interesting observations., QC 20150123

This paper studies the containment and group dispersion control for a multi-robot system in the presence of dynamic leaders. Each robot is represented by a doubleintegrator dynamic model and a distributed control algorithm is developed to drive the multi-robot system to follow a group of dynamic leaders with containment and group dispersion behaviors. The effectiveness of the algorithm is then verified on a multi-robot control platform., QC 20161107

This paper constructs a framework to describe and study the coordinated output regulation problem for multiple heterogeneous linear systems. Each agent is modeled as a general linear multiple-input multiple-output system with an autonomous exosystem which represents the individual offset from the group reference for the agent. The multi-agent system as a whole has a group exogenous state which represents the tracking reference for the whole group. Under the constraints that the group exogenous output is only locally available to each agent and that the agents have only access to their neighbors' information, we propose observer-based feedback controllers to solve the coordinated output regulation problem using output feedback information. A high-gain approach is used and the information interactions are allowed to be switched over a finite set of fixed networks containing both graphs that have a directed spanning tree and graphs that do not. The fundamental relationship between the information interactions, the dwell time, the non-identical dynamics of different agents, and the high-gain parameters is given. Simulations are shown to validate the theoretical results.

In this paper, we provide two discrete-time multi-agent models which generate periodic behaviors. The first one is a multi-agent system of identical double integrators with input saturation constraints, while the other one is a multi-agent system of identical neutrally stable system with input saturation constraints. In each case, we show that if the feedback gain parameters of the local controller satisfy a certain condition, the multi-agent system exhibits a periodic solution., Comment: 15 pages, 7 figures

In this paper, we study the cooperative set tracking problem for a group of Lagrangian systems. Each system observes a convex set as its local target. The intersection of these local sets is the group aggregation target. We first propose a control law based on each system's own target sensing and information exchange with neighbors. With necessary connectivity for both cases of fixed and switching communication graphs, multiple Lagrangian systems are shown to achieve rendezvous on the intersection of all the local target sets while the vectors of generalized coordinate derivatives are driven to zero. Then, we introduce the collision avoidance control term into set aggregation control to ensure group dispersion. By defining an ultimate bound on the final generalized coordinate between each system and the intersection of all the local target sets, we show that multiple Lagrangian systems approach a bounded region near the intersection of all the local target sets while the collision avoidance is guaranteed during the movement. In addition, the vectors of generalized coordinate derivatives of all the mechanical systems are shown to be driven to zero. Simulation results are given to validate the theoretical results.

This paper considers the synchronization problem for networks of coupled nonlinear dynamical systems under switching communication topologies. Two types of nonlinear agent dynamics are considered. The first one is non-expansive dynamics (stable dynamics with a convex Lyapunov function $\varphi(\cdot)$) and the second one is dynamics that satisfies a global Lipschitz condition. For the non-expansive case, we show that various forms of joint connectivity for communication graphs are sufficient for networks to achieve global asymptotic $\varphi$-synchronization. We also show that $\varphi$-synchronization leads to state synchronization provided that certain additional conditions are satisfied. For the globally Lipschitz case, unlike the non-expansive case, joint connectivity alone is not sufficient for achieving synchronization. A sufficient condition for reaching global exponential synchronization is established in terms of the relationship between the global Lipschitz constant and the network parameters. We also extend the results to leader-follower networks., Comment: 27 pages, 0 figures