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- Tigran T. Tchrakian, Sergiy Zhuk
- 16th International IEEE Conference on Intelligent…
- 2013

In this paper, we propose a new framework for macroscopic traffic state estimation based on the Fourier-Galerkin projection method and minimax state estimation approach. We assign a Fourier-Galerkin reduced model to a partial differential equation describing a macroscopic model of traffic flow. Taking into account a priori estimates for the projection… (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 timevarying 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)

- Jason Frank, Sergiy Zhuk
- CDC
- 2014

The paper presents symplectic Möbius integrators for Riccati equations. All proposed methods preserve symmetry, positivity and quadratic invariants 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 system… (More)

This paper describes an innovative approach to estimate motion from image observations of divergence-free flows. Unlike most stateof-the-art methods, which only minimize the divergence of the motion field, our approach utilizes the vorticity-velocity formalism in order to construct a motion field in the subspace of divergence free functions. A 4DVAR-like… (More)

- 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
- 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)

- Sergiy Zhuk, Jason Frank, Isabelle Herlin, Robert Shorten
- SIAM J. Scientific Computing
- 2015

In this paper we propose a state estimation method for linear parabolic partial differential equations (PDE) that accounts for errors in the model, truncation, and observations. 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… (More)

- Sergiy Zhuk, Mihály Petreczky
- CDC
- 2013

In this paper we construct an infinite horizon minimax state observer for a linear stationary differentialalgebraic 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)

- Sergiy Zhuk, Sergiy Zhuk
- 2011

This paper describes a minimax state estimation approach for linear differential-algebraic equations (DAEs) with uncertain parameters. The approach addresses continuous-time DAEs with non-stationary rectangular matrices and uncertain bounded deterministic input. An observation’s noise is supposed to be random with zero mean and unknown bounded correlation… (More)

- Randall Cogill, Olivier Gallay, +9 authors Sergiy Zhuk
- ICCVE
- 2014

We introduce a new view of parked cars as a massive, flexible resource that is currently wasted. Given the power supply in batteries as well as computing, communication, and sensing facilities in cars in conjunction with the precise localization they can provide, parked cars have the potential to serve as a service delivery platform with a wide range of… (More)