Observer based learning control for a class of nonlinear systems with time-varying parametric uncertainties

In this note, a new learning control approach, combined with state estimation, is developed to perform output tracking problems where the state information is not available. By virtue of the learning capability, the control mechanism is able to handle a class of rapid time-varying parametric uncertainties which are periodic and the only prior knowledge is the periodicity. Two classes of system nonlinearities are taken into account. The first class is the global Lipschitz continuous functions of the unknown state variables, and the second class is the local Lipschitz continuous functions of the accessible output variables. To facilitate the learning control design and property analysis, the Lyapunov-like energy function is employed, which allows the incorporation of any available system knowledge. Henceforth the new learning control approach widens the application scope comparing with the repetitive type learning control.