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首页> 外文期刊>SIAM Journal on Control and Optimization >On the global controllability of nonlinear systems: Fountains, recurrence, and applications to Hamiltonian systems
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On the global controllability of nonlinear systems: Fountains, recurrence, and applications to Hamiltonian systems

机译：关于非线性系统的全局可控性：喷泉，递归及其在哈密顿系统中的应用

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In this paper, a form of open local accessibility for nonlinear control systems is introduced called the continuous fountain condition. Subject to the conditions that (i) the states of a system are continuous fountains and (ii) one of various recurrence conditions holds, it is established that the system state space is (globally) controllable. It is shown that these controllability results imply the controllability of certain subsets of the state space of Hamiltonian control systems called energy slices. The relations between the notion of a fountain and (i) local accessibility and (ii) the full Lie algebra rank condition for control affine systems are investigated. Finally, the results in this paper are shown to have application to hierarchical hybrid control theory in that they give conditions for a finite analytic partition to satisfy the so-called in-block controllability property; this is illustrated with a linear mass-spring system example. [References: 26]
机译：在本文中，介绍了一种非线性控制系统的开放局部可访问性形式，称为连续喷泉状态。在满足以下条件的情况下：（i）系统状态是连续的喷泉，并且（ii）各种重复条件之一成立，从而确定系统状态空间是（全局）可控制的。结果表明，这些可控性结果暗示了哈密顿控制系统状态空间某些子集的可控性，即能量切片。研究了喷泉的概念与（i）局部可及性（ii）控制仿射系统的完整李代数秩条件之间的关系。最后，本文的结果显示出可应用于分层混合控制理论，因为它们为有限的解析分区提供了满足所谓的块内可控制性的条件。线性质量弹簧系统示例对此进行了说明。 [参考：26]

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