Enclosing the Reachable Set of Parametric ODEs using Taylor Models and Ellipsoidal Calculus
Mario Villanueva, Radoslav Paulen, Boris Houska and Benoît Chachuat, Centre for Process Systems Engineering, Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK.
Abstract
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 ...
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