Learning Control For Nonlinear Systems With Non-Parametric Uncertainties

Learning control includes iterative learning control, repetitive control and repetitivelearning control, it is suitable for systems with strong nonlinearity, time varying uncertainties,delay, coupling and other characteristics and doesn't require to obtain accurate mathematicalmodel. Through constant "learning", learning control can continue to improve controlperformance. In adaptive learning control algorithms, the system uncertainties are often requiredto be parameterized, however, research results of nonlinear systems with non parametricuncertainties are very limited.Based on Lyapunov like method, this paper deeply discusses nonlinear systems withnon parametric uncertainties. The main contribution lies in:1. A robust iterative learning controller is designed of for a class of nonlinear systemswith non parametric uncertainties. The robust part uses the bounding information of the systemuncertainty and the iterative learning part can effectively eliminate the tracking error and and thetracking error is guaranteed to converge to zero over entire time interval.2. In practice, actuator saturation often exists, by the introduction of saturation function,the control input is confined to a pre specified range. A robust iterative learning control schemeis proposed for a class of nonlinear systems with non parametric and partially parametricuncertainties and an adaptive iterative learning control scheme is proposed for a class ofnonlinear systems with parametric uncertainties.3. A robust repetitive learning control scheme is proposed for a class of nonlinear systemswith non parametric uncertainties. Repetitive learning control only requires that the learnedvariables satisfy the repetitive condition like repetive learning control, and does not requirerepositioning like iterative control, which avoids the initial repositioning in iterative learningcontrol and extends the applicability of repetitive control.4. Repetitive control scheme is proposed for a class of time delay systems withnon parametric uncertainties. The global stability of the learning system and asymptoticconvergence of the tracking error are established for cases of both known and unknown boundedfunctions, respectively. 5. By using the Nussbaum function, repetitive control scheme is presented for a class ofnonlinear systems with non parametric uncertainties with unknown control direction, whichcontains two cases of both time delay and non delay. The proposed control laws can guaranteethat all the signals in the closed loop are bounded and the tracking error converges to zero astime approaches in?nite.