在线控制多粒子系统。I
Controlling Multiparticle System on a Line. I
摘要：
我们研究了一个经典的多粒子系统（如户田晶格），我们打算通过施加到系统的几个粒子的力来控制其动力学。各种问题的设置，典型的控制理论提出了这个模型，其中：研究可及性和可控性的属性，结构属性和反馈线性化的各个控制系统，时间最优的粒子重新定位。我们获得了所提出问题的完整或部分答案;采用了几何控制理论的标准和方法。第一部分考虑非周期多粒子系统。在即将到来的第二部分中，我们将讨论受周期边界条件约束的多粒子系统的能控性问题。这项研究需要对已知的几何控制方法进行扩展和改进。
英文摘要：
We study a classical multiparticle system (such as Toda lattice) whose dynamics we intend to control by forces applied to few particles of the system. Various problem settings, typical for control theory are posed for this model; among those: studying accessibility and controllability properties, structure properties and feedback linearization of respective control system, time-optimal relocation of particles. We obtain complete or partial answers to the posed questions; criteria and methods of geometric control theory are employed. In the present part I we consider nonperiodic multiparticle system. In the forthcoming Part II we address controllability issue for multiparticle system subject to periodic boundary conditions. That study would require an extension and refinement of known methods of geometric control.
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