Imperial College London


Faculty of Natural SciencesDepartment of Mathematics

Senior Teaching Fellow in Statistics







531Huxley BuildingSouth Kensington Campus





Publication Type

3 results found

Giesl P, Hamzi B, Rasmussen M, Webster KNet al., 2020, Approximation of Lyapunov functions from noisy data, Journal of Computational Dynamics, Vol: 7, Pages: 57-81, ISSN: 2158-2491

Methods have previously been developed for the approximation of Lyapunovfunctions using radial basis functions. However these methods assume that theevolution equations are known. We consider the problem of approximating a givenLyapunov function using radial basis functions where the evolution equationsare not known, but we instead have sampled data which is contaminated withnoise. We propose an algorithm in which we first approximate the underlyingvector field, and use this approximation to then approximate the Lyapunovfunction. Our approach combines elements of machine learning/statisticallearning theory with the existing theory of Lyapunov function approximation.Error estimates are provided for our algorithm.

Journal article

Rasmussen M, Rieger J, Webster KN, 2016, Approximation of reachable sets using optimal control and support vector machines, Journal of Computational and Applied Mathematics, Vol: 311, Pages: 68-83, ISSN: 0377-0427

We propose and discuss a new computational method for the numerical approximation of reachable sets for nonlinear control systems. It is based on the support vector machine algorithm and represents the set approximation as a sublevel set of a function chosen in a reproducing kernel Hilbert space. In some sense, the method can be considered as an extension to the optimal control algorithm approach recently developed by Baier, Gerdts and Xausa. The convergence of the method is illustrated numerically for selected examples.

Journal article

Knobloch J, Lamb JSW, Webster KN, 2014, Using Lin's method to solve Bykov's problems, JOURNAL OF DIFFERENTIAL EQUATIONS, Vol: 257, Pages: 2984-3047, ISSN: 0022-0396

Journal article

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