Implicit self-tuning control for a class of nonlinear systems

Abstract

The stability of implicit self-tuning control has been proved, for the discrete-time linear case, by the use of a Lyapunov func-tion. Latter on the algorithm was extended for a class of bilinear systems. However real world systems are mostly nonlinear systems and it is of interest to extend the proposed algorithm to a more complex class of nonlinear models. In this research a nonlinear class of systems is defined, and then a generalized minimum variance control for the defined nonlinear class is developed. In addition, parameters of real world systems may change in time, and a good performance controller should be able to keep the overall system stability in such a case; to deal with this issue an implicit self-tuning control for the defined class of nonlinear systems is presented, the estimated parameters do not need to converge to their real values. The mathe-matical results show that with this new algorithm the self-tuning controller is able to keep the closed-loop system global stability for the defined class of nonlinear systems, and also the algorithm is a general case of the algorithms proposed in the literature for the bilinear and linear systems cases.