Ziyang Meng

Leaderless and Leader-Following Consensus With Communication and Input Delays Under a Directed Network Topology

In this paper, time-domain (Lyapunov theorems) and frequency-domain (the Nyquist stability criterion) approaches are used to study leaderless and leader-following consensus algorithms with communication and input delays under a directed network topology. We consider both the first-order and second-order cases and present stability or boundedness conditions. Several interesting phenomena are analyzed and explained. Simulation results are presented to support the theoretical results.

On global leader-following consensus of identical linear dynamic systems subject to actuator saturation ☆

Abstract This paper studies the leader-following consensus problem for a group of agents with identical linear systems subject to control input saturation. We focus on two classes of linear systems, neutrally stable systems and double integrator systems. For neurally stable systems, we establish that global consensus can be achieved by linear local feedback laws over a fixed communication topology, and with proper choices of relative potential functions, global consensus can also be achieved over a switching communication topology. For double integrator systems, we establish that global consensus can be achieved by linear local feedback laws over a fixed communication topology, and with the help of a simple saturation function in the local feedback laws, global consensus can also be achieved over a switching communication topology. Simulation results illustrate the theoretical results.

Global consensus for discrete-time multi-agent systems with input saturation constraints

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.

Leader–follower swarm tracking for networked Lagrange systems☆

Abstract In this paper, swarm tracking problems with group dispersion and cohesion behaviors are discussed for a group of Lagrange systems. The agent group is separated into two subgroups. One is called the leader group, whose members are encapsulated with the desired generalized coordinates and generalized coordinate derivatives. The other one, referred to as the follower group, is guided by the leader group. The objective is to guarantee distributed tracking of generalized coordinate derivatives for the followers and to drive the generalized coordinates of the followers close to the convex hull formed by those of the leaders. Both the case of constant leaders’ generalized coordinate derivatives and the case of time-varying leaders’ generalized coordinate derivatives are considered. The proposed control algorithms are shown to achieve velocity matching, connectivity maintenance and collision avoidance. In addition, the sum of the steady-state distances between the followers and the convex hull formed by the leaders is shown to be bounded and the bound is explicitly given. Simulation results are presented to validate the effectiveness of theoretical conclusions.

Robust cooperative tracking for multiple non-identical second-order nonlinear systems

In this paper, a distributed cooperative tracking problem is studied for a group of non-identical second-order nonlinear systems with bounded external disturbances. The control goal is to drive the states of the followers to converge to those of a time-varying leader in the presence of only local information interactions from the leader to the followers and between the followers. We first propose a simple distributed control algorithm for the case when both the relative position and relative velocity measurements are available for feedback. It is shown that distributed cooperative tracking can be achieved if in the sensing topology the leader has directed paths to all followers. Then, the extension to the case when the velocity measurements are not available is studied. We consider two different scenarios, i.e., when the absolute position measurements and local communication between neighbors are available and only the relative position measurements are available. Distributed observers and distributed control inputs are designed to address these two scenarios. Numerical studies are carried out to illustrate the theoretical results.

Delay-Induced Synchronization of Identical Linear Multiagent Systems

This paper studies a class of fast consensus algorithms for a group of identical multiagent systems each described by the linear state-space model. By using both the current and delayed state information, the proposed delay-induced consensus algorithm is shown to achieve synchronization with a faster convergence speed than the standard one when the eigenvalues of the open-loop system, control parameters, the Laplacian matrix of the network, and the delay satisfy certain conditions. In addition, some sufficient or necessary and sufficient conditions are established to guarantee the closed-loop stability of the delay-induced consensus algorithm, where an extra control parameter on the coupling strength is introduced to adjust the convergence speed of the closed-loop system flexibly. We then show that the delay-induced algorithm is robust to the small intrinsic communication or input delays, i.e., the proposed delay-induced consensus algorithm may also produce a faster convergence speed than the standard one even if there exist small intrinsic communication or input delays. Furthermore, we extend the results from the case of an undirected communication topology to those of a directed communication topology and a switching communication topology. Several simulation examples are presented to illustrate the theoretical results.

Behaviors of networks with antagonistic interactions and switching topologies

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.

On global consensus of linear multi-agent systems subject to input saturation

This paper studies the leader-following consensus problem for a group of agents with identical linear systems subject to control input saturation. We focus on two classes of linear systems, neutrally stable systems and double integrator systems. For neurally stable systems, we establish that global consensus can be achieved by linear local feedback laws over an undirected fixed or a switching communication topology. For double integrator systems, we establish that global consensus can be achieved by linear local feedback laws over a fixed communication topology and, with the help of a simple saturation function in the local feedback laws, global consensus can also be achieved over a switching undirected topology. Simulation results illustrate the theoretical results.

Pulse width modulation for multi-agent systems

This paper studies the consensus problem for multi-agent systems. A distributed consensus algorithm is developed by constructing homogeneous pulse width modulators for agents in the network. In particular, a certain percentage of the sampling period named duty cycle is modulated according to some state difference with respect to the neighbors at each sampling instant. During each duty cycle, the amplitude of the pulse is fixed. The proposed pulse width modulation scheme enables all agents to sample asynchronously with arbitrarily large sampling periods. It provides an alternative digital implementation strategy for multi-agent systems. We show that consensus is achieved asymptotically under the proposed scheme. The results are compared with the self-triggered ternary controller.

Formation control with mismatched compasses

This article addresses the formation control problem with mismatched compasses. Depending on the sensing and communication technology, compass mismatches may arise due to biases in measurement, drift in inertial sensing despite initial alignment, and even spatial variations in the earths magnetic field. To illustrate the key concepts underlying what happens, we first consider the two agent case and show that the agents converge to a fixed, but distorted formation exponentially fast. In contrast to the matched compass case, the formation is not asymptotically stationary. The distance error and the angular error between the actual final formation and the desired formation are explicitly given, as is the steady state velocity of the formation. The case of time-varying mismatched compasses is also studied. Based on the results, we then propose estimators to obtain the mismatched angle, which allow a compensation algorithm to be proposed such that the desired formation shape is achieved. Finally, the extensions to the n agent case are also considered and similar phenomena are encountered. Simulations are provided to validate the theoretical results.