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I received yesterday a query from a scholar using my book Applied Optimal Control published 47 years ago. Having slept on it over night, I gave the following reply to his question in the WORD attachment (I cannot post the text directly due to software difficulty of displaying mathematical formula.)

This may be used as an oral qualifying exam question for ph.d degree. Try it on your students or colleagues.

Question from a scholar.docx

Note added: There is a small typo in this WORD attachment where on the fourth line u=  x/dt should be u=dx/dt. .