Details:
Title  Parametric optimization and optimal control using algebraic geometry methods.  Author(s)  I.A. Fotiou, Möller H. M., P.A. Parrilo, Philipp Rostalski  Type  Article in Journal  Abstract  We present two algebraic methods to solve the parametric optimization problem that arises in nonlinear model predictive control. We consider constrained discretetime polynomial systems and the corresponding constrained finitetime 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 offline, by precomputing certain algebraic objects. Then, an online algorithm uses this precomputed 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.  ISSN  00207179; 13665820/e 
URL 
http://www.tandfonline.com/doi/abs/10.1080/00207170600726592 
Language  English  Journal  Int. J. Control  Volume  79  Number  11  Pages  13401358  Publisher  Taylor & Francis, London  Year  2006  Edition  0  Translation 
No  Refereed 
No 
