Computing control invariant sets in high dimension is easy
Computing control invariant sets in high dimension is easy
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计算高维控制不变集很容易
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
M. Alamir
中科院分区：
文献类型：
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作者：
M. Fiacchini;M. Alamir
本文研究了输入和状态均受约束的高维线性受控系统的控制不变集的计算问题。控制不变性的集合包含条件，涉及的N-步骤集，并提出了线性规划问题的形式。这样的条件允许克服集合加法和顶点枚举所固有的复杂性限制，并且也可以应用于高维系统。通过对状态维和输入维分别为30和15的系统计算基于10步运算符的最大控制不变集的近似值，说明了该方法的效率和可扩展性。
In this paper we consider the problem of computing control invariant sets for linear controlled high-dimensional systems with constraints on the input and on the states. Set inclusions conditions for control invariance are presented that involve the N-step sets and are posed in form of linear programming problems. Such conditions allow to overcome the complexity limitation inherent to the set addition and vertices enumeration and can be applied also to high dimensional systems. The efficiency and scalability of the method are illustrated by computing approximations of the maximal control invariant set, based on the 10-step operator, for a system whose state and input dimensions are 30 and 15, respectively.