A framework for Lyapunov certificates for multi-vehicle rendezvous problems
A framework for Lyapunov certificates for multi-vehicle rendezvous problems
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DOI：
10.23919/acc.2004.1384743
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
A. Tiwari;J. Fung;J. M. Carson;R. Bhattacharya;R. Murray
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文献类型：
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作者：
A. Tiwari;J. Fung;J. M. Carson;R. Bhattacharya;R. Murray
在本文中，我们提出了一个动力系统表示的多智能体会合的相平面上。我们限制我们的注意力，两个代理，每个标量动力学。交会的问题被铸造作为一个稳定的问题，与一组的约束的轨迹上的代理，定义在相平面上。我们还描述了一种方法来生成控制李雅普诺夫函数，当使用与稳定控制律，如桑塔格的公式，确保两个代理系统达到会合。本文的主要结果是一个类似于李雅普诺夫的证书定理，它描述了一组约束条件，当满足这些约束条件时，足以保证交会。
In this paper, we present a dynamical systems representation for multi-agent rendezvous on the phase plane. We restrict our attention to two agents, each with scalar dynamics. The problem of rendezvous is cast as a stabilization problem, with a set of constraints on the trajectories of the agents, defined on the phase plane. We also describe a method to generate control Lyapunov functions that when used in conjunction with a stabilizing control law, such as Sontag's formula, makes sure that the two-agent system attains rendezvous. The main result of this paper is a Lyapunov-like certificate theorem that describes a set of constraints, which when satisfied are sufficient to guarantee rendezvous.