A composite energy function-based learning control approach for nonlinear systems with time-varying parametric uncertainties

A new learning control approach is developed in this note to address a class of nonlinear systems with time-varying parametric uncertainties. The concept of composite energy function (CEF), which provides the system information along both time and learning repetition horizons, is introduced in the analysis of learning control. CEF consists of two parts. The first part is a standard Lyapunov function,. which is used to access system behavior along time horizon during each learning cycle. The second part is an L² norm of parametric learning errors which reflects the variation of the system status when the control system is updated on the basis of learning cycles. The proposed learning control algorithm achieves asymptotical convergence along a learning repetition horizon. At the same time, the boundedness and pointwise convergence of the tracking error along time horizon is guaranteed. The proposed learning control strategy is applicable to quite general classes of nonlinear systems without requiring the global Lipschitz continuity condition and zero relative degree condition.