Virtual control regularization of state constrained linear quadratic optimal control problems

Matthias Gerdts 1 Björn Hüppinng 2
1 Institut für Mathematik und Rechneranwendung [Munchen]
2 Institut für Mathematik
Abstract : A numerical method for linear quadratic optimal control problems with pure state constraints is analyzed. Using the virtual control concept introduced by Cherednichenko et al. (Inverse Probl. 24:1-21, 2008) and Krumbiegel and Rösch (Control Cybern. 37(2):369-392, 2008), the state constrained optimal control problem is embedded into a family of optimal control problems with mixed control-state constraints using a regularization parameter α > 0. It is shown that the solutions of the problems with mixed control-state constraints converge to the solution of the state constrained problem in the L2 norm as α tends to zero. The regularized problems can be solved by a semi-smooth Newton method for every α > 0 and thus the solution of the original state constrained problem can be approximated arbitrarily close as α approaches zero. Two numerical examples with benchmark problems are provided.
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Article dans une revue
Computational Optimization and Applications, Springer Verlag, 2012, 51 (2), pp.867-882. 〈10.1007/s10589-010-9353-3〉
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https://hal.inria.fr/hal-00724866
Contributeur : Estelle Bouzat <>
Soumis le : mercredi 22 août 2012 - 19:38:12
Dernière modification le : mercredi 10 octobre 2018 - 20:44:13

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Matthias Gerdts, Björn Hüppinng. Virtual control regularization of state constrained linear quadratic optimal control problems. Computational Optimization and Applications, Springer Verlag, 2012, 51 (2), pp.867-882. 〈10.1007/s10589-010-9353-3〉. 〈hal-00724866〉

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