Enclosing the Reachable Set of Parametric ODEs using Taylor Models and Ellipsoidal Calculus

A major bottleneck in state-of-the-art algorithms for global dynamic optimization using complete methods is computing enclosures for the solutions of nonlinear parametric differential equations. This paper presents a new algorithm for computing such enclosures, which features a combination of Taylor model propagation and ellipsoidal calculus. The former enables high-order convergence to the exact reachable set as the parameter set shrinks, while the latter mitigates bound explosion compared to interval analysis. The convergence properties of the proposed bounding technique are analyzed and conditions under which higher order convergence can be achieved are given. Implementation details are also discussed and the approach is demonstrated on a numerical case study.