Simulation Relations and Controllability Properties of Linear and Nonlinear Control Systems
Simulation Relations and Controllability Properties of Linear and Nonlinear Control Systems
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DOI：
10.1137/130949646
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发表时间：
2015-06
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影响因子：
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通讯作者：
K. Grasse;Nancy Ho
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文献类型：
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作者：
K. Grasse;Nancy Ho
我们研究通过模拟关系连接的非线性输入干扰系统在多大程度上共享某些可控特性。我们得出了符合以下范式的几个结果：如果系统 $B$ 与系统 $A$ 存在模拟关系，并且如果系统 $A$ 具有指定的可控性属性，则系统 $B$ 也具有相同的属性。正如预期的那样，只有通过对系统和/或模拟关系施加适当的假设，才能将范式转化为实际的定理。我们证明了三个这样的结果。我们获得的第一个结果涉及完全可控性的属性，其中我们对输入扰动系统施加最小的假设，但要求模拟关系是满足特定紧致性条件的系统状态空间之间的平滑满射图。第二个结果涉及以线性映射内核为模的可控性概念，其中假设系统 $B$ “几乎 l...
We examine to what extent nonlinear input-disturbance systems that are connected by a simulation relation share certain controllability properties. We derive several results that fit within the paradigm that if there is a simulation relation of a system $A$ by a system $B$, and if system $A$ has a specified controllability property, then system $B$ has that same property. As expected, one can only turn the paradigm into actual theorems by imposing appropriate assumptions on the systems and/or the simulation relation. We prove three such results. The first result we obtain deals with the property of complete controllability, where we impose minimal assumptions on the input-disturbance systems but require that the simulation relation be the graph of a smooth surjection between the systems' state spaces that satisfies a certain compactness condition. The second result deals with a somewhat weaker notion of controllability modulo the kernel of a linear mapping, where it is assumed that system $B$ is “almost l...