Abstract
In a recent paper, we proposed different relaxation procedures for optimal control problems involving time delays in the control functions. We introduced a notion of proper relaxation, applicable to problems without side constraints, where we required the minimum cost of the relaxed problem to coincide with the infimum cost of the original one. In this paper, a new and appropriate notion of relaxation for problems with side constraints is introduced. As examples of proper extensions, in the new sense, we describe in detail the standard procedure for delay-free problems and the procedure for one-delay systems which we recently proposed.
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