On general relations between null-controllable and controlled invariant sets for linear constrained systems
On general relations between null-controllable and controlled invariant sets for linear constrained systems
复制标题
线性约束系统零可控与受控不变集之间的一般关系
DOI：
10.1109/cdc.2014.7040380
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
M. Mönnigmann
中科院分区：
文献类型：
--
作者：
M. S. Darup;M. Mönnigmann
证明了具有输入约束和状态约束的线性系统的零可控和受控不变量集之间的一般关系。证明了最大零可控集的闭包等价于最大控制不变量集。为了证明这一说法，我们证明了在线性情况下，每个控制不变集的内部都是零可控的。虽然这些性质中的一些似乎是显而易见的，但据作者所知，没有正式的证明。为了强调仔细证明的重要性，我们表明这些性质是特定于线性系统的，并且通常在非线性情况下不成立。
We prove some general relations between null-controllable and controlled invariant sets for linear systems with input and state constraints.We show that the closure of the largest null-controllable set is identical to the largest controlled invariant set. In order to prove this claim, we demonstrate that the interior of every controlled invariant set is null-controllable in the linear case. While some of these properties appear to be obvious, formal proofs are missing to the best of the authors' knowledge. To highlight the importance of careful proofs, we show that these properties are specific to linear systems and generally do not hold in the nonlinear case.