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

Abstract

In this paper, a novel composite energy function (CEF) is introduced to provide a general framework for incorporating system information along both time and learning repetition horizon. Based on the CEF, learning control is integrated with nonlinear sub-optimal control to enhance control performance for a class of nonlinear system with time-varying parametric uncertainties. Sub-optimal control strategy based on control Lyapunov function (CLF) and Sontag's formula provides a sub-optimal performance as well as stability along time horizon for the nominal part of the nonlinear dynamic system. Learning mechanism tries to learn unknown time-varying parametric uncertainties so as to eliminate uncertain effects. The proposed control scheme achieves asymptotical convergence along learning repetition horizon. At the same time, the boundedness and pointwise convergence of the tracking error along time horizon are also ensured.