Abstract
NUMERICAL methods mostly have to be used to solve optimal control problems, where we have to minimize a functional specified on the trajectories of a set of differential equations. The initial “differential” problem is usually replaced by a difference problem, and we have to consider whether the solution of the difference optimization problem is convergent to the solution of the differential problem. We discuss this convergence in the present paper for a wide class of optimal control problems. Apart from proving “convergence with respect to the functional”, we also consider regularization of the difference approximations in order to obtain a minimizing sequence of controls, strongly convergent in L 2. We shall assume that the computations involve errors. The results obtained are independent of the method of solving the difference optimization problem.
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