Marina Osipchuk
postdoc party Industrial Postdoctoral Member
Institute for Mathematics and its Applications
514 Vincent Hall
206 Church Street SE
University of Minnesota
Minneapolis, MN 55455-0436
Fax: (612) 626-7370

You have reached my virtual home. I'm not in at the moment, but if you would leave your name and message after the beep, I'll get back to you as soon as I can...

Any sufficiently advanced technology is indistinguishable from magic. -- Arthur C. Clarke

My main research interest is in nonlinear control theory. Control implies modification of system dynamics towards a desirable one. The main challenges on the way to "perfection" are uncertainty in a system description as well as nonlinearity of a real multivariable system. More detailed summary on classical control theory and modern control trends as well as description of my current and previous projects are available. While working on optimal control of spacecraft/aircraft systems I find inspiration in the interaction of the control theory with other disciplines (fluids, combustion, physiology)

Main Projects

Finite-Dimensional Nonlinear Control of Reaction-Diffusion System (RD)

Joint research with Prof. Yannis Kevrekidis, Princeton University

While the evolution of a RD system is governed by partial differential equations with infinite dimensional state the implementation issues require a controller to be finite-dimensional. At the same time the dissipative nature of the RD system lets one aproximate its long-term behaviour by a low-dimensional dynamical system. A nonlinear model reduction method was employed to approximate the long-term behavior of the PDE dynamics by a dynamical system of finite, small dimension. Closing the obtained system with a linear controller effectively stabilizes the PDE truncation locally; this does not, however, exploit the fully nonlinear reduced model. On the other hand, nonlinear, feedback linearizing control results in large control spillover to the residual modes. The high nonlinearity as well as input interaction of the resulting system are the main challenges for the design of a nonlinear controller stabilizing unstable steady-states. Robustness of the designed inverse optimal nonlinear controller with respect to fast unmodeled dynamics is analysed.

Attitude Determination in Satellite Constellation

Joint work with Prof. Fadil Santosa, University of Minnesota

The fiber-like quality along with globally provided, space-based communication are the distictive features of the broadband low Earth orbit (LEO) satellite system Teledesic. The high speed, high quality of data transmition is achieved via intersatellite communication (each satellite has laser links to eight adjacent satellites). To handle the system networking the satellites have to be positioned and oriented much more precisely than satellites which communicate only with the ground. In addition, to facilitate satellite crosslinks the satellites will have on-board computers thus increasing the cost of the system and power consumption in the orbit. Our desire is to develop navigation and control concepts which employ the existing communication system and hence do not require much additional cost.

The developed attitude determination strategy employs maximum probability search to establish contacts between non-oriented satellites in the groups and updates the estimate of the satellite attitude. Once the satellites are linked within the group the accuracy in attitude detemination is limited only by hardware resolution. Efficiency in contact establishment is guaranteed while using the suggested nonlinear programming search. Finally, the described attitude determination method exploits existing communication hardware thus eliminating additional cost for commonly used sensors.

Teledesic-related links:


My CV contains a more detailed list of my previous projects.

Control and Dynamical Systems Web Sites
Software for Dynamical Systems Theory
System and Control Archive at Dallas (SCAD)
Control Engineering Virtual Library
E-LETTER on Systems, Control, and Signal Processing

My unofficial homepage "is a click away..."

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