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 L 2 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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The authors are supported by DFG grant GE 1163/5-1.
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Gerdts, M., Hüpping, B. Virtual control regularization of state constrained linear quadratic optimal control problems. Comput Optim Appl 51, 867–882 (2012). https://doi.org/10.1007/s10589-010-9353-3
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DOI: https://doi.org/10.1007/s10589-010-9353-3