Abstract
This chapter discusses equivalence classes of functions and solvability of optimal control problems. The set of functionals connected with an optimal control problem can be divided into classes of equivalence concerning optimal solutions being generated. The classification of functionals obtained in this way gives the basis for investigation of optimal control problems with several criteria and under limitations on features of solutions and kinds of input information. The chapter presents the construction of single–single-valued reflection of equivalence classes of functionals into the set of spectral vectors of the closed optimal system. The chapter also presents the applications to solvability of optimal stabilization problems for systems with essential incompleteness of information and under limitations on the spectrum of the closed system.
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