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.

本文涉及约束非线性系统的最大鲁棒控制不变集（RCIS）的计算。所提出的方法基于将对不变集的搜索转换为图理论问题。具体来说，考虑一类一般的离散时间时不变非线性系统。首先，用有向图来近似非线性系统的动力学。随后，推导了鲁棒控制不变性的条件，并提出了一种计算鲁棒控制不变性的算法。该算法将迭代细分技术与鲁棒控制不变性条件相结合，以在每次迭代时生成最大鲁棒控制不变性集的外部近似。按照此，当迭代进行到无穷大时，我们证明了算法已收敛到最大的RCIS。基于已开发的算法，还提出了一种计算RCIS内近似的算法。还考虑了输入仿射和干扰仿射系统的特殊情况。最后，给出了两个数值示例，以证明该方法的有效性。