Parameter estimation for Euler equations with uncertain inputs
Sergiy Zhuk, Tigran Tchrakian
CDC 2015
In this paper we propose a new sequential data assimilation method for nonlinear ordinary differential equations with compact state space. The method is designed so that the Lyapunov exponents of the corresponding estimation error dynamics are negative, i.e. the estimation error decays exponentially fast. The latter is shown to be the case for generic regular flow maps if and only if the observation matrix H satisfies detectability conditions. In particular this implies that the rank of H must be at least as great as the number of nonnegative Lyapunov exponents of the underlying attractor. Numerical experiments illustrate the exponential convergence of the method and the sharpness of the theory for the case of Lorenz '96 and Burgers equations with incomplete and noisy observations.
Sergiy Zhuk, Tigran Tchrakian
CDC 2015
Markus Tranninger, Richard Seeber, et al.
IEEE L-CSS
Mihály Petreczky, Sergiy Zhuk
Automatica
Sergiy Zhuk, Olexander Nakonechnyi
Minimax Theory and its Applications