Search

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

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

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.

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

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

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

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

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

Anti-windup design is an intuitive and efficient way to deal with input saturation nonlinearities. In the classic anti-windup design, the compensator is set to be activated immediately as the control signal saturates the actuator. An important innovation in the anti-windup activation mechanism is to delay the activation of the anti-windup mechanism until the saturation reaches to a certain severity which led to a performance improvement of the resulting closed-loop system. More recently, it was shown that by activating a static anti-windup mechanism in anticipation of actuator saturation, significant further performance improvements can be achieved in comparison with the delayed activation design. In addition, we have combined both the delayed and anticipatory activation mechanisms, to develop the multiple activation strategy, in terms of L2 gain performance. This paper furthermore considers the problem of enlarging domain of attraction and demonstrates that the multiple activation of a static multiple feedback anti-windup mechanism would also lead to significant performance improvements over both the immediate and delayed activation schemes., QC 20140121

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 double-integrator 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 20140121

A multiple anti-windup loops under multiple dynamic activations strategy is proposed to enlarge the domain of attraction. This work is parallel to the multiple activation case with static compensators. The traditional anti-windup compensator is activated immediately as the saturation occurs. It was shown recently that, by delaying the activation of the anti-windup mechanism to a certain level, the performance can be improved for the closed-loop system. It was further shown that better performance can be obtained by activating an anti-windup mechanism in anticipation of actuator saturation, in comparison with the delayed activation design. This paper considers the anti-windup design problem of enlarging domain of attraction under a dynamic multiple activation scheme. In this multiple activation scheme, the anticipatory, delayed and immediate activation mechanism is incorporated in the same framework simultaneously. A furthermore significant performance improvements over both the immediate and delayed activation schemes can be observed. The proposed dynamic multiple activation scheme established a unified anti-windup framework and can be readily extended to the traditional immediate, delayed and anticipatory activation anti-windup mechanisms., QC 20140121

In this paper, we give necessary conditions for achieving global consensus in homogeneous networks of discrete-time linear time-invariant agents with input saturation constraints under fixed undirected topologies. For two special cases, where the agent model is either neutrally stable or a double integrator, these necessary conditions together with a gain condition are also sufficient. We show this by designing a linear protocol based on the combination of state differences between the agent and its neighbors. In particular, for the neutrally stable case, we show that 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 in the presence of input saturation. The results are illustrated by numerical simulations., QC 20140325

The coordinated output regulation problem for multiple heterogeneous linear systems is studied in this paper. Each agent is modeled as a linear multiple-input multiple-output (MIMO) system with an exogenous input which represents the individual tracking objective for the agent. The multi-agent system as a whole has a group exogenous input which represents the tracking objective for the whole group. Under the constraints that the group exogenous input is only locally available to each agent and that the agents have only access to their neighbors' information, we propose an observer-based feedback controller to solve the coordinated output regulation problem. A high-gain approach is introduced and the information interactions are allowed to be switching over a finite set of fixed networks containing both graphs having a spanning tree and graphs that do not. A lower bound of the high gain parameters is explicitly given. It describes a fundamental relationship between the information interactions, the dwell time, the non-identical dynamics of different agents, and the high gain parameters., QC 20140911

In this paper, we study the coordinated tracking problem of multiple Lagrange systems with a time-varying leader's generalized coordinate derivative. Under a purely local interaction constraint, i.e., the followers only have access to their local neighbors' information and the leader is a neighbor of only a subset of the followers, a continuous coordinated tracking algorithm with adaptive coupling gains is proposed. Tracking errors between the followers and the leader are shown to converge to zero. Then, we extend this result to the case when the leader's generalized coordinate derivative is constant. Examples are given to validate the effectiveness of the proposed continuous coordinated tracking algorithms., QC 20140911

In this paper, we give conditions for the existence of periodic behaviors in a multi-agent system of identical discrete-time double integrators with input saturation constraints. If the feedback gain parameters of the controllers, which are based on relative state measurements of the agent itself and its neighboring agents, are bounded by a value depending on the largest eigenvalue of the Laplacian matrix, then the multi-agent system exhibits a periodic solution for certain initial conditions., QC 20140912