Dynamic cloud motion forecasting from satellite images
Sergiy Zhuk, Tigran Tchrakian, et al.
CDC 2017
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, et al.
CDC 2017
Giovanni Russo, Sergiy Zhuk
CDC 2018
Sergiy Zhuk, Orest V. Iftime, et al.
Systems and Control Letters
Albert Akhriev, Stephen Moore, et al.
EAGE Workshop 2016