An algebraic geometry approach to nonlinear parametric optimization in control

We present a method for nonlinear parametric optimization based on algebraic geometry. The problem to be studied, which arises in optimal control, is to minimize a polynomial function with parameters subject to semialgebraic constraints. The method uses Grobner bases computation in conjunction with...

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Bibliographic Details
Main Authors: Fotiou, I.A., Rostalski, P., Sturmfels, B., Morari, M.
Format: Conference Proceeding
Language:English
Subjects:
Constraint optimization
Eigenvalues and eigenfunctions
Geometry
Nonlinear control systems
Nonlinear equations
Optimal control
Optimization methods
Polynomials
Predictive control
Predictive models
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Summary:We present a method for nonlinear parametric optimization based on algebraic geometry. The problem to be studied, which arises in optimal control, is to minimize a polynomial function with parameters subject to semialgebraic constraints. The method uses Grobner bases computation in conjunction with the eigenvalue method for solving systems of polynomial equations. In this way, certain companion matrices are constructed off-line. Then, given the parameter value, an on-line algorithm is used to efficiently obtain the optimizer of the original optimization problem in real time
ISSN:0743-1619
2378-5861
DOI:10.1109/ACC.2006.1657280