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- Sergiy Zhuk
- 2012

This paper presents a generalization of the minimax state estimation approach for singular linear Differential-Algebraic Equations (DAE) with uncertain but bounded input and observation's noise. We apply generalized Kalman Duality principle to DAE in order to represent the minimax estimate as a solution of a dual control problem for adjoint DAE. The latter… (More)

- Sergiy Zhuk
- 2012

In this paper we present Kalman duality principle for a class of linear Differential-Algebraic Equations (DAE) with arbitrary index and time-varying coefficients. We apply it to an ill-posed minimax control problem with DAE constraint and derive a corresponding dual control problem. It turns out that the dual problem is ill-posed as well and so classical… (More)

- Sergiy Zhuk
- CDC
- 2013

— In this paper we present a minimax projection method for linear evolution equations in Hilbert space. The method extends classical Galerkin approach: it builds a differential-algebraic equation with uncertain parameters that models dynamics of exact projection coefficients representing the projection of the evolution equation's solution onto a… (More)

— In this paper we construct an infinite horizon minimax state observer for a linear stationary differential-algebraic equation (DAE) with uncertain but bounded input and noisy output. We do not assume regularity or existence of a (unique) solution for any initial state of the DAE. Our approach is based on a generalization of Kalman's duality principle. In… (More)

HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt età la diffusion… (More)

— The paper presents symplectic Möbius in-tegrators for Riccati equations. All proposed methods preserve symmetry, positivity and quadratic invari-ants for the Riccati equations, and non-stationary Lyapunov functions. In addition, an efficient and numerically stable discretization procedure based on reinitialization for the associated linear Hamiltonian… (More)

- Vivien Mallet, Sergiy Zhuk
- 2010

A reduced minimax state estimation approach is proposed for high-dimensional models. It is based on the reduction of the ordinary differential equation with high state space dimension to the low-dimensional Differential-Algebraic Equation (DAE) and on the subsequent application of the minimax state estimation to the resulting DAE. The DAE is composed of a… (More)

In this paper we propose a state estimation approach for linear parabolic Partial Differential Equations (PDE) with uncertain parameters. It is based on an extension of the Galerkin projection method. The extended method models projection coefficients, representing the state of the PDE in some basis, by means of a Differential-Algebraic Equation (DAE). The… (More)

- Sergiy Zhuk
- ArXiv
- 2011

Minimax state estimation for linear descriptor systems 01.05.04 – system analysis and optimal decision theory Author's Summary of the dissertation for the degree of the Candidate of Science (physics and mathematics)