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We present two algebraic methods to solve the parametric optimization problem that arises in nonlinear model predictive control. We consider constrained discrete-time polynomial systems and the corresponding constrained finite-time optimal control problem. The first method is based on cylindrical algebraic decomposition. The second uses Gröbner bases and… (More)

- Jean B. Lasserre, Monique Laurent, Philipp Rostalski
- Foundations of Computational Mathematics
- 2008

For an ideal I ⊆ R[x] given by a set of generators, a new semidefinite characterization of its real radical I(VR(I)) is presented, provided it is zero-dimensional (even if I is not). Moreover we propose an algorithm using numerical linear algebra and semidefinite optimization techniques, to compute all (finitely many) points of the real variety VR(I) as… (More)

- Jean B. Lasserre, Monique Laurent, Philipp Rostalski
- Theor. Comput. Sci.
- 2009

We provide a real algebraic symbolic-numeric algorithm for computing the real variety VR(I) of an ideal I ⊆ R[x], assuming VR(I) is finite (while VC(I) could be infinite). Our approach uses sets of linear functionals on R[x], vanishing on a given set of polynomials generating I and their prolongations up to a given degree, as well as on polynomials of the… (More)

In this paper we propose a unified methodology for computing the set VK(I) of complex (K = C) or real (K = R) roots of an ideal I ⊆ R[x], assuming VK(I) is finite. We show how moment matrices, defined in terms of a given set of generators of the ideal I, can be used to (numerically) find not only the real variety VR(I), as shown in the authors’ previous… (More)

Solving systems of polynomial equations is a classical problem of mathematics with an emerging number of modern applications, such as coding theory, robotics, computational statistics, etc. Its importance is reflected by the broad literature that deals with algorithms, ranging from numerical continuation methods to exact methods based e.g. on Gröbner… (More)

- Philipp Rostalski, Thomas Besselmann, Miroslav Baric, Femke van Belzen, Manfred Morari
- Int. J. Control
- 2007

- Philipp Rostalski, Ioannis A. Fotiou, Daniel J. Bates, A. Giovanni Beccuti, Manfred Morari
- SIAM Journal on Optimization
- 2011

A new technique for solving polynomial nonlinear constrained optimal control problems is presented. The problem is reformulated into a parametric optimization problem, which in turn is solved in a two step procedure. First, in a pre-computation step, the equation part of the corresponding first order optimality conditions is solved for a generic value of… (More)

- Avinash Bhardwaj, Philipp Rostalski, Raman Sanyal
- SIAM Journal on Optimization
- 2015

Spectrahedra are linear sections of the cone of positive semidefinite matrices which, as convex bodies, generalize the class of polyhedra. In this paper we investigate the problem of recognizing when a spectrahedron is polyhedral. We generalize and strengthen results of [M. V. Ramana, Polyhedra, spectrahedra, and semidefinite programming, in Topics in… (More)

In this article we present the moment based approach for computing all real solutions of a given system of polynomial equations. This approach builds upon a lifting method for constructing semidefinite relaxations of several nonconvex optimization problems, using sums of squares of polynomials and the dual theory of moments. A crucial ingredient is a… (More)

- Herbert Buchner, Eike Petersen, Marcus Eger, Philipp Rostalski
- EMBC
- 2016

The electromyogram (EMG) is an important tool for assessing the activity of a muscle and thus also a valuable measure for the diagnosis and control of respiratory support. In this article we propose convolutive blind source separation (BSS) as an effective tool to pre-process surface electromyogram (sEMG) data of the human respiratory muscles. Specifically,… (More)