Jonathan P. Epperlein, Sergiy Zhuk, et al.
Automatica
The paper presents analytic expressions of minimax (worst-case) estimates for solutions of linear abstract Neumann problems in Hilbert space with uncertain (not necessarily bounded!) inputs and boundary conditions given incomplete observations with stochastic noise. The latter is assumed to have uncertain but bounded correlation operator. It is demonstrated that the minimax estimate is asymptotically exact under mild assumptions on the observation operator and the bounding sets. A relationship between the proposed estimates and a robust pseudo-inversion of compact operators is revealed. This relationship is demonstrated on an academic numerical example: homogeneous Neumann problem for Poisson equation in two spatial dimensions.
Jonathan P. Epperlein, Sergiy Zhuk, et al.
Automatica
Sergiy Zhuk, Tigran Tchrakian, et al.
CDC 2017
Jason Frank, Sergiy Zhuk
Nonlinearity
Stephen Moore, Kerry Halupka, et al.
CinC 2018