On the computation of local invariant sets for nonlinear systems
On the computation of local invariant sets for nonlinear systems
复制标题
非线性系统局部不变集的计算
DOI：
10.1109/cdc.2007.4434950
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
E. Camacho
中科院分区：
文献类型：
--
作者：
M. Fiacchini;T. Alamo;E. Camacho
不变集在控制中的重要性是因为它们定义了空间中的一个区域，在这个区域中，稳定性和潜在的渐近收敛得到了保证。因此，许多控制设计策略都与不变集的计算有关。对于基于滚动范围的策略，如模型预测控制，情况尤其如此。本文提出了一种计算非线性系统的凸不变集的方法。利用D.C.函数可以表示为两个凸函数之差的性质，以及任何连续的非线性函数都可以表示为D.C.函数，或者至少可以用D.C.函数很好地逼近的事实，我们提出了一个计算多面体不变集的算法，该算法不需要求解全局优化问题。如果非线性系统是局部稳定的，则所提出的策略保证提供一个非空的局部不变集。
The importance of invariant sets in control is due to the fact that they define a region of the space where stability, and potentially asymptotic convergence, are assured. For this reason many control design strategies are related to the computation of an invariant set. This is particularly the case for receding horizon based strategies as model predictive control. This paper presents a method for computing a convex invariant set for nonlinear systems. Using properties of D.C. functions, which are functions that can be expressed as difference of two convex functions, and the fact that any continuous nonlinear function can be expressed as D.C. functions, or, at least, well approximated by them, we propose an algorithm for computing a polyhedral invariant set in which no global optimization problem has to be solved. The proposed strategy is guaranteed to provide a non-empty local invariant set provided the nonlinear system is locally stable.