Lp-convergence of an optimal adaptive control algorithm

This paper is concerned with 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 certain essential process characteristics, i.e. measurable differentials, without requiring the determination of the unknown process parameters. The process input and output functions are taken to be elements of Lp - spaces and the optimization procedure is briefly described. 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 retaining only a finite number of terms in an infinite series expression. Utilizing the techniques of Functional Analysis the LP - space convergence of these approximating algorithms is shown.