Parametric optimization and optimal control using algebraic geometry methods

DOI10.1080/00207170600726592zbMath1133.93337OpenAlexW1993600232MaRDI QIDQ5423850

Manfred Morari, Pablo A. Parrilo, Ioannis A. Fotiou, Philipp Rostalski

Publication date: 31 October 2007

Published in: International Journal of Control (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207170600726592

zbMATH Keywords

algebraic methodsdiscrete-time polynomial systemsnonlinear model predictive forms

Mathematics Subject Classification ID

Feedback control (93B52) Nonlinear systems in control theory (93C10) Algebraic methods (93B25) Optimality conditions for problems in abstract spaces (49K27)

Related Items

Semidefinite relaxations of dynamical programs under discrete constraints, A novel approach for solving multi-parametric problems with nonlinear constraints, Exact relaxations of non-convex variational problems, Special issue on the use of computer algebra systems for computer aided control system design, The exact solution of multiparametric quadratically constrained quadratic programming problems, A Numerical Method for Computing Border Curves of Bi-parametric Real Polynomial Systems and Applications, Applying Gröbner basis method to multiparametric polynomial nonlinear programming, Optimal control of hybrid switched systems: a brief survey

Uses Software

• Fermat
• QEPCAD

Cites Work

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• Semidefinite representations for finite varieties
• Global minimization of a multivariate polynomial using matrix methods
• Computation of the constrained infinite time linear quadratic regulator
• LQ control for constrained continuous-time systems
• Multivariate polynomial equations with multiple zeros solved by matrix eigenproblems
• Minimizing polynomials via sum of squares over the gradient ideal
• QEPCAD B
• The explicit linear quadratic regulator for constrained systems