On the computation of invariant sets for constrained nonlinear systems: An interval arithmetic approach
On the computation of invariant sets for constrained nonlinear systems: An interval arithmetic approach
复制标题
DOI：
10.1016/j.automatica.2005.04.015
复制
发表时间：
2003-09
期刊：
影响因子：
--
通讯作者：
J. M. Bravo;D. Limón;T. Alamo;E. Camacho
中科院分区：
文献类型：
--
作者：
J. M. Bravo;D. Limón;T. Alamo;E. Camacho
研究了约束非线性系统控制不变量集的计算问题。所提出的方法是基于单步集的内逼近的计算，即可以通过允许的控制动作引导到给定目标集的状态集。基于此程序，控制不变量集可以通过递归计算。给出了一种用区间算法计算一步集的方法。所提出的分支定界算法提供了误差给定界的内逼近；这使得在计算集的准确性和计算负担之间实现折衷成为可能。此外，还提出了一种用内有界多面体逼近单步集的算法；这允许我们放松所获得集合的复杂性，并使集合的递归和存储更容易。
This paper deals with the computation of control invariant sets for constrained nonlinear systems. The proposed approach is based on the computation of an inner approximation of the one step set, that is, the set of states that can be steered to a given target set by an admissible control action. Based on this procedure, control invariant sets can be computed by recursion. We present a method for the computation of the one-step set using interval arithmetic. The proposed specialized branch and bound algorithm provides an inner approximation with a given bound of the error; this makes it possible to achieve a trade off between accuracy of the computed set and computational burden. Furthermore an algorithm to approximate the one step set by an inner bounded polyhedron is also presented; this allows us to relax the complexity of the obtained set, and to make easier the recursion and storage of the sets.