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This is a public course note about the optimal control problem.

https://math.berkeley.edu/~evans/control.course.pdf

There is one condition that I do not get. Is there any intuition that we need "the mapping is constant"? And how does that be derived? It seems very strong. I usually do not see that in the textbook.

Problem

Theorem

KCd
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  • This is true in general for optimal control problems where the Hamiltonian is autonomous, i.e. doesn't depend explicitly on $t$. I don't have a digital reference on hand, but "autonomous" is the keyword to search for. – DMcMor Feb 12 '21 at 17:32

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