Invariance Entropy of Control Sets
Invariance Entropy of Control Sets
复制标题
控制集的不变熵
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
C. Kawan
中科院分区：
文献类型：
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作者：
C. Kawan
连续时间控制系统的不变性熵测量开环控制必须更新的频率，以便使状态空间的受控不变子集不变。受控不变集的一种特殊类型是控制集，即，近似可控性的最大集合。本文研究了这类集合的不变熵的性质。我们的主要结果给出了这个量的上限的控制集的内部的周期解的正李雅普诺夫指数。此外，对于一维控制仿射系统与一个单一的控制向量场，我们提供了一个解析公式的控制集的不变性熵的漂移向量场，控制向量场，及其衍生物。作为应用，我们研究了受控双线性振荡器。
Invariance entropy for continuous-time control systems measures how often open-loop controls have to be updated in order to render a controlled invariant subset of the state space invariant. A special type of a controlled invariant set is a control set, i.e., a maximal set of approximate controllability. In this paper, we investigate the properties of the invariance entropy of such sets. Our main result gives an upper bound of this quantity in terms of the positive Lyapunov exponents of a periodic solution in the interior of the control set. Moreover, for one-dimensional control-affine systems with a single control vector field we provide an analytical formula for the invariance entropy of a control set in terms of the drift vector field, the control vector field, and their derivatives. As an application, we study a controlled bilinear oscillator.