Abstract
Four distinct, though closely related, inverse optimal control problems are considered. Given a closed, convex setU in a real Hilbert spaceX and an elementu0 inU, it is desired to find all functionals of the form (u,Ru) such that (i)R is a self-adjoint positive operator and (u,Ru) is minimized over the setU at the pointu0, (ii)R is self-adjoint, positive definite and (u,Ru) is minimized overU atu0, (iv)R is self-adjoint, positive definite and (u,Ru) is uniquely minimized overU atu0. The interrelationships among the sets of solutions of these problems are pointed out. Necessary and sufficient conditions which explicitly characterize the solutions to each of these problems are derived. The question of existence of a solution (namely, Given a particular setU and a particular elementu0, under what conditions does there exist an operatorR having certain required properties?) is discussed. The results derived are illustrated by an example.
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