Asymptotic learning control for a class of cascaded nonlinear uncertain systems

In this note, the problem of learning unknown functions in a class of cascaded nonlinear systems will be studied. The functions to be learned are those functions that are imbedded in the system dynamics and are of known period of time. In addition to the unknown periodic time functions, nonlinear uncertainties bounded by known functions of the state are also admissible. The objective of the note is to find an iterative learning control under which the class of nonlinear systems are globally stabilized (in the sense of being uniform bounded), their outputs are asymptotically convergent, and a combination of the time functions contained in system dynamics are asymptotically learned. To this end, a new type of differential-difference learning law is utilized to generate the proposed learning control that yields both asymptotic stability of the system output and asymptotic convergence of the learning error. The design is carried out by applying the Lyapunov direct method and the backward recursive design method.