论文标题
计算约束非线性系统的鲁棒控制不变集：图形算法方法
Computing robust control invariant sets of constrained nonlinear systems: A graph algorithm approach
论文作者
论文摘要
本文介绍了约束非线性系统最大的鲁棒控制不变集（RCISS）的计算。所提出的方法是基于对不变集作为图理论问题的搜索。具体而言，考虑了一般的离散时间不变的非线性系统。首先，使用有向图近似非线性系统的动力学。随后，得出了鲁棒控制不变性的条件，并提出了用于计算鲁棒控制不变集的算法。该算法将迭代细分技术与健壮的控制不变性条件结合在一起，以在每次迭代时产生最大的稳健控制不变设置的外部近似值。在此之后，随着迭代开始无限，我们证明了算法与最大的RCI的融合。基于开发的算法，还提供了一种计算RCI的内部近似值的算法。还考虑了输入仿射和干扰仿射系统的特殊情况。最后，提出了两个数值示例，以证明该方法的功效。
This paper deals with the computation of the largest robust control invariant sets (RCISs) of constrained nonlinear systems. The proposed approach is based on casting the search for the invariant set as a graph theoretical problem. Specifically, a general class of discrete-time time-invariant nonlinear systems is considered. First, the dynamics of a nonlinear system is approximated with a directed graph. Subsequently, the condition for robust control invariance is derived and an algorithm for computing the robust control invariant set is presented. The algorithm combines the iterative subdivision technique with the robust control invariance condition to produce outer approximations of the largest robust control invariant set at each iteration. Following this, we prove convergence of the algorithm to the largest RCIS as the iterations proceed to infinity. Based on the developed algorithms, an algorithm to compute inner approximations of the RCIS is also presented. A special case of input affine and disturbance affine systems is also considered. Finally, two numerical examples are presented to demonstrate the efficacy of the proposed method.
