This paper is concerned with some aspects of the adaptive optimal control of processes whose dynamic characteristics are not completely specified but assumed to be varying slowly with time. It is shown that the identification procedure involves the evaluation of process output differentials, without requiring the explicit determination of the unknown process parameters. The process input and output functions are taken to be elements ofLp-spaces and the optimization procedure is briefly outlined. For any practical application of the identification algorithm the process output differentials are approximated by first-order differences of output time segments, and their corresponding adjoints by a truncated series of time sequences. Utilizing the techniques of functional analysis the Lp-space convergence of these approximating algorithms is shown.