Personal Webpage of Philipp Rostalski

Philipp Rostalski

Feodor Lynen Scholar (PostDoc)

Department of Mathematics
University of California, Berkeley

Office:
1067 Evans Hall

Address:
1067 Evans Hall
Dept. of Mathematics
University of California
Berkeley, CA 94720 - 3840

Email:

Phone:
+1 (510) 642-2149

General

After obtaining my PhD from ETH Zurich in 2009, I am now employed as a Feodor Lynen scholar with Bernd Sturmfels at the Department of Mathematics at the University of California, Berkeley. The scholarship is funded by the German Alexander von Humboldt foundation and UC Berkeley.

Curriculum Vitae

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Convex Algebraic Geometry

The Convex Algebraic Geometry Wiki is now online! It features plenty of tutorials for computations in Convex Algberaic Geometry, supporting software (Check out the Bertini Interface for Numerical Algebraic Decomposition!) and some beautiful pictures of spectrahedra.

Together with Bernd Sturmfels I organizinged the Convex Algebraic Geometry seminar in spring 2010.

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Research

My research interest lies in the intersection of Optimization, Systems and control theory
and polynomial algebra. The following figure gives an overview about some resent activities:

Many of these activities have been started while I was at the Automatic Control Lab., ETH Zurich, and
I am glad to continue this interdisciplinary research as a postdoctoral scholar in the newly founded
NSF Focused Research Group on "Semidefinite Optimization and Convex Algebraic Geometry".

* Projects marked with a star are discontinued. You can find further information on my old homepage.

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Projects:

Algebraic Methods in Optimization and Control

Applications Projects

- Energy efficient ventilation
- Control of mechanical systems with backlash (discontinued)
- Control of river powerplants (now continued by Akin Sahin)
- Vehicle stabilisation (now continued by Thomas Besslemann)

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List of Publications:

Book chapters
The Approach of Moments for Polynomial Equations.
M. Laurent, and P. Rostalski. in Handbook on Semidefinite, Cone and Polynomial Optimization: Theory, Algorithms, Software and Applications., (M.F. Anjos, J.B. Lasserre, eds.), to appear 2010–2011.

A unified approach for real and complex zeros of zero-dimensional ideals.
J.B. Lasserre, M. Laurent, and P. Rostalski. in Emerging Applications of
Algebraic Geometry., (M. Putinar and S. Sullivant, eds.), Vol. 149, Springer,
125–156, 2008.
Journal publications
Dualities in Convex Algebraic Geometry. P. Rostalski, B. Sturmfels.
Rendiconti di Matematica, Serie VII, Volume 30, Roma (2010), 249–291.

Numerical algebraic geometry for optimal control applications.
P. Rostalski, I.A. Fotiou, D.J. Bates, A.G. Beccuti, and M. Morari.
SIAM Journal on Control and Optimization, 2010. Accepted.

A prolongation-projection algorithm for computing the finite real variety of
an ideal. J.B. Lasserre, M. Laurent and P. Rostalski*, Theoretical Computer
Science, Vol. 410(27-29), 2685–2700, 2009.

Application of model predictive control to a cascade of river power plants.
C. Setz, A. Heinrich, P. Rostalski, G. Papafotiou and M. Morari. in Proceedings
of the 17th. IFAC World Congress, Seoul, Korea, 11876–11983, 2008.

Semidefinite characterization and computation of real radical ideals.
J.B. Lasserre, M. Laurent and P. Rostalski. Foundations of Computational
Mathematics, Vol. 8(5), 607–647, 2008.

A hybrid approach to modelling, control and state estimation of mechanical
systems with backlash. P. Rostalski, T. Besselmann, M. Barić, F. van Belzen
and M. Morari. International Journal of Control. Vol. 80, No. 11, 1729–
1740, 2007.

Parametric optimization and optimal control using algebraic geometry methods.
I. Fotiou, P. Rostalski, P. Parrilo and M. Morari. International Journal
of Control, Vol. 79, No. 11, 1340–1358, 2006.
Contributions to conferences
Removing redundant quadratic constraints. M. Baes, P. Rostalski, D. Adjiashvili
accepted at the ICMS, Kobe, 2010.

Computing the real variety of an ideal: a real algebraic and symbolic-numeric
algorithm. J.B. Lasserre, M. Laurent, P. Rostalski. SAC ’08: Proceedings
of the 2008 ACM Symposium on Applied Computing, Fortaleza, Brazil, 1845–1846, 2008.

A numerical algebraic geometry approach to nonlinear constrained optimal
control. D.J. Bates, I.A. Fotiou, and P. Rostalski. 46th IEEE Conference
on Decision and Control, New Orleans, USA, 6256–6261, 2007.

Hybrid parameter-varying model predictive control for lateral vehicle stabilization.
T. Besselmann, P. Rostalski and M. Morari. European Control
Conference, Kos, Greece, 1068–1075, 2007.

An algebraic geometry approach to nonlinear parametric optimization in
control. I. Fotiou, P. Rostalski, B. Sturmfels and M. Morari, American
Control Conference, Minneapolis, USA, 3818–3623, 2006.

Using Path Integral Short Time Propagators for Numerical Analysis of
Stochastic Hybrid Systems. G. Lichtenberg and P. Rostalski. IFAC Conference
on Analysis and Design of Hybrid Systems, ADHS, Alghero, Italy,
179–184, 2006.
PhD thesis
Algebraic Moments - Real Root Finding and Related Topics. ETH Dissertation No. 13871
Official Version

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Selected Talks:

Algebraic Moments - Real Root finding and Related Topics. PhD Defense Presentation, ETH Zurich, Switzerland in May 2009

Moment matrices and real root finding. Presented at the MSRI Workshop on Algebraic Statistics, Berkeley, USA in December 2008.

Real Radical Ideals and the Hankel Operator. Presented at the Discrete Mathematics Seminar, UC Berkeley, USA in November 2008 (and UC Davis Dec. 8, 2008).

Quasi-Hankel matrices and the real radical ideal. Presented at the CWI-DIAMANT Seminar "Combinatorics and Optimization", CWI Amsterdam, The Netherlands in September 2008.

Application of Model Predictive Control to a Cascade of River Power Plants. Presented at the 17th. IFAC World Congress, Seoul, Korea in June 2008.

Pre-computing in Polynomial MPC. Presented at ABB Corporate Research, Baden-Dättwil, Switzerland in December 2007.

Analysis and Distributed Control of HVAC Systems, Presented at NCCR MICS Workshop, Neuchtel, Switzerland in July 2007.

Characterizing and computing the Real Radical - An SDP Approach, Presented at the Control Group Seminar, University of Cambridge, Cambridge, UK in April 2007.

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