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Virtual control regularization of state constrained linear quadratic optimal control problems

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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https://hal.inria.fr/hal-00724866
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Submitted on : Wednesday, August 22, 2012 - 7:38:12 PM
Last modification on : Friday, September 17, 2021 - 2:50:09 PM

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

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