Exact penalization of terminal constraints in the objective functions of optimal control problems

What is it about?

Here we show that it is possible to replace terminal constraints in optimal control problems with a suitably chosen penalty term in the objective function. As in finite dimensional optimization, this is only possible if the penalty term is not smooth. It can be designed using L1 or L-infinity norms. Also the L2-norm can be used, but not the squared L2-norm that appears frequently in tracking terms.

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Photo by Markus Spiske on Unsplash

Photo by Markus Spiske on Unsplash

Why is it important?

In optimal control problems, terminal constraints appear naturally. This can be seen in the optimal control probems with the wave equation studied by Jacques-Louis Lions. However, for numerical algorithms it is sometimes convenient to circumvent this type of constraints.

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