An algorithm for computing robust forward invariant sets of two dimensional nonlinear systems

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.

Automated summary

This paper investigates the algorithm for computing the robust forward invariant sets of nonlinear systems, proposing a new approach for approximation calculation. The algorithm plans a path that iteratively converges to the boundary of RFIS and rigorous mathematical analysis confirms its effectiveness.