Robustness of nonlinear systems can be analyzed by computing robust forward invariant sets (RFISs). Knowledge of the smallest RFIS of a system, can help analyze system performance under perturbations. A novel algorithm is developed to compute an approximation of the smallest RFIS for two-dimensional nonlinear systems subjected to a bounded additive disturbance. The problem of computing an RFIS is formulated as a path planning problem, and the algorithm developed plans a path which iteratively converges to the boundary of an RFIS. Rigorous mathematical analysis shows that the proposed algorithm terminates in a finite number of iterations, and that the output of the proposed algorithm is an RFIS. Simulations are presented to illustrate the proposed algorithm, and to support the mathematical results. This work may aid future development, for use with higher dimensional systems.

中文翻译：

---

一种计算二维非线性系统鲁棒前向不变集的算法

非线性系统的鲁棒性可以通过计算鲁棒前向不变集 (RFIS) 来分析。了解系统的最小 RFIS 有助于分析扰动下的系统性能。开发了一种新算法来计算受有界附加扰动影响的二维非线性系统的最小 RFIS 的近似值。计算 RFIS 的问题被表述为路径规划问题，开发的算法规划一条路径，该路径迭代收敛到 RFIS 的边界。严格的数学分析表明，所提出的算法在有限次数的迭代中终止，并且所提出的算法的输出是RFIS。提出了模拟来说明所提出的算法，并支持数学结果。这项工作可能有助于未来的发展，