Necessary and Sufficient Conditions for Consensus of Second-Order Multiagent Systems Under Directed Topologies Without Global Gain Dependency

Abstract

The consensus problem for second-order multiagent systems with absolute velocity damping under directed topologies is investigated. In contrast to the existing results, which rely on a sufficiently large common absolute velocity damping gain above a lower bound dependent on global information, this paper focuses on novel algorithms to overcome this limitation. A novel consensus algorithm, where different agents use different absolute velocity damping gains, is first proposed. In the absence of delays, based on a system transformation method, the consensus problem for second-order multiagent systems is converted into that for first-order multiagent systems with the agent number doubled. Necessary and sufficient conditions are then derived under directed topologies by relating the topologies associated with the doubled number of agents and the original team of agents. In the presence of multiple constant delays, based on a further system transformation method, the consensus problem for second-order multiagent systems is converted into the stability problem for corresponding systems. Necessary and sufficient conditions are presented to guarantee consensus under a directed fixed topology. For systems with a uniform constant delay, more concrete necessary and sufficient conditions on how large the delay can be to guarantee consensus is given. Numerical simulations are provided to illustrate the effectiveness of the obtained theoretical results.

Distributed Consensus for Multiple Lagrangian Systems With Parametric Uncertainties and External Disturbances Under Directed Graphs

“…Lemma 3.1: Suppose that the directed graph G contains a directed spanning tree. All the eigenvalues of Q∆L A Q T have positive real parts, where Q is defined in (10), L A is the Laplacian matrix associated with G, and ∆ = diag(α 1 , · · · , α n ) with α i being positive constants defined in (6). Furthermore, for any time-varying vector…”

“…includes single or double integrators [8]- [10], general linear systems [11], [12], and nonlinear systems [13]. As a special case of nonlinear systems, Lagrangian system can be used to represent a large class of mechanical systems including robotic manipulators, autonomous vehicles, and rigid bodies [14].…”

Distributed finite‐time containment control for multiple Euler‐Lagrange systems with communication delays

“…Based on Section 3, the error constraint conditions are introduced and a distributed finite-time error constrained containment control protocol is designed in this section. The position error is the same as (9), and the constraint equation of errors is given as…”

“…can only be obtained by a subset of followers and there exist communication delays among agents. Under Assumptions 1 to 3, if the distributed containment control law is designed as (44) and NN adaptive laws are designed as (47) and (48), then the states of the systems will move to the sliding surface s 1i = 0 in (42) in finite time so that the multiple EL systems can achieve distributed finite-time containment control and the error variable (9) satisfies the requirement for error constraint (37). Besides, the containment error is bounded.…”

“…The control problems for MASs with first‐order dynamics were discussed in the works of Xiao et al and Cao and Ren . Liu et al, Fu et al, and Zhao et al investigated the control methods for the MASs modeled by second‐order linear dynamic equations. The research works of Xiao et al, Cao and Ren, Liu et al, Fu et al, and Zhao et al did not consider the nonlinear dynamic characteristics, which exist in most actual physical systems.…”