Simultaneous Identification and Control of Time-Varying Systems

The paper addresses two complementary problems. The first one is to derive a rigorous formulation of adaptive control when the parameters of the plant are time-varying. To make the problem tractable, the time-variation is approximated by a piecewise-constant function assuming a finite number N of unknown values. The instants at which the parameters switch are also unknown. A proof of stability is presented assuming that an algorithm for simultaneous identification of N values exists. In the second part of the paper, an algorithm is designed which causes N adaptive models to converge to N different locations in parameter space in a self-organizing fashion. Work has been in progress but the proof of convergence has defied solution for over three years. The paper discusses the theoretical difficulties encountered, solutions obtained in special cases, new mathematical tools that are being investigated, and potential applications of the approach