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We revise and slightly generalize some variational problems related to the "informational approach" in the classical optimization problem for automatic control systems which was popular from 1970-1990. We find extremals for various degenerated (derivative independent) functionals and propose some interpretations of obtained minimax relations. The main example of such functionals is given by the Gelfand-Pinsker-Yaglom formula for the information quantity contained in one random process in another one. We find some balance relations in a linear stationary one-dimensional system with Gaussian signal and interpret them in terms of Legendre duality.

On Energy–Information Balance in Automatic Control Systems Revisited