Computing Robust Forward Invariant Sets of Multidimensional Nonlinear Systems via Geometric Deformation of Polytopes

This article develops an algorithm to compute the sequences of polytopic robust forward invariant sets (RFIS) that vary in size for a nonlinear dynamical system. This is done through a novel approach that geometrically deforms a polytope into an invariant set using a sequence of homeomorphisms, based on an invariance condition that only needs to be satisfied at a finite set of test points. A fast computational test is also developed to check if a given polytopic set is an RFIS. Our approach is applicable to arbitrary Lipschitz continuous nonlinear systems in the presence of bounded additive disturbances, and its versatility is presented through simulation results on a variety of nonlinear dynamical systems in two and three dimensions.