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TitleParametric optimization and optimal control using algebraic geometry methods.
Author(s) I.A. Fotiou, Möller H. M., P.A. Parrilo, Philipp Rostalski
TypeArticle in Journal
AbstractWe present two algebraic methods to solve the parametric optimization problem that arises in non-linear 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 the eigenvalue method for solving systems of polynomial equations. Both methods aim at moving most of the computational burden associated with the optimization problem off-line, by pre-computing certain algebraic objects. Then, an on-line algorithm uses this pre-computed information to obtain the solution of the original optimization problem in real time fast and efficiently. Introductory material is provided as appropriate and the algorithms are accompanied by illustrative examples.
ISSN0020-7179; 1366-5820/e
URL http://www.tandfonline.com/doi/abs/10.1080/00207170600726592
JournalInt. J. Control
PublisherTaylor & Francis, London
Translation No
Refereed No