2020/01/29 by Sanja Živanović Gonzalez, Sanja Zivanovic Gonzalez, Gonzalez, Sanja Zivanovic +8
Computer Science · Decision Sciences · Engineering · Mathematics · Physics and Astronomy · #34A60 #65L70 #65Y20 #Control Systems and Identification #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design #cs.NA #math.NA #msc:34A60 #msc:65L70 #msc:65Y20
paper · pdf · doi:10.48550/arxiv.2001.11330
arXiv admin note: text overlap with arXiv:1206.6563
arxiv created 2020/01/29 · openalex publication_date 2020/01/29 · arxiv updated 2020/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Uncertainty is unavoidable in modeling dynamical systems and it may be represented mathematically by differential inclusions. In the past, we proposed an algorithm to compute validated solutions of differential inclusions; here we provide several theoretical improvements to the algorithm, including its extension to piecewise constant and sinusoidal approximations of uncertain inputs, updates on the affine approximation bounds and a generalized formula for the analytical error. The approach proposed is able to achieve higher order convergence with respect to the current state-of-the-art. We implemented the methodology in Ariadne, a library for the verification of continuous and hybrid systems. For evaluation purposes, we introduce ten systems from the literature, with varying degrees of nonlinearity, number of variables and uncertain inputs. The results are hereby compared with two state-of-the-art approaches to time-varying uncertainties in nonlinear systems.