论文标题
非自治系统的变异集成剂，并应用多代理形成的应用
Variational integrators for non-autonomous systems with applications to stabilization of multi-agent formations
论文作者
论文摘要
保留系统几何不变的数值方法，例如能量，动量或符号形式，称为几何积分器。变分积分是一类重要的几何积分器。这些变分集成商的一般思想是以保留原始系统的某些不变性的方式离散汉密尔顿的原理，而不是运动方程。在本文中，我们以固定的时间步长构建变异集成符，以实现时间依赖的拉格朗日系统，以建模一类重要的自主耗散系统。这些集成器是通过一个离散拉格朗日函数的家族来得出的，每个功能都可以固定时步。这允许在离散序列集合的每个步骤中恢复自主拉格朗日系统的变分集成剂的保存属性，例如这些系统的符号性或向后误差分析。我们还为此类系统提供了一个离散定理。结果显示了用于多代理系统形成稳定的问题。
Numerical methods that preserve geometric invariants of the system, such as energy, momentum or the symplectic form, are called geometric integrators. Variational integrators are an important class of geometric integrators. The general idea for those variational integrators is to discretize Hamilton's principle rather than the equations of motion in a way that preserves some of the invariants of the original system. In this paper we construct variational integrators with fixed time step for time-dependent Lagrangian systems modelling an important class of autonomous dissipative systems. These integrators are derived via a family of discrete Lagrangian functions each one for a fixed time-step. This allows to recover at each step on the set of discrete sequences the preservation properties of variational integrators for autonomous Lagrangian systems, such as symplecticity or backward error analysis for these systems. We also present a discrete Noether theorem for this class of systems. Applications of the results are shown for the problem of formation stabilization of multi-agent systems.
