The paper relates to an approach introduced by Kulikowski for adaptive optimal control of nonlinear systems. In this approach, the plant dynamics are represented symbolically by an operator which transforms or maps input time functions into corresponding output time functions. The contributions of the paper arise mainly from the physical considerations associated with such an operator representation, specifically the memory of the plant, and the influence of these considerations upon the formulation. It is shown that the optimal control problem may be formulated in various ways for a given plant and given performance criteria depending upon how the memory of the plant is taken into account.

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