A suboptimal learning control scheme for non-linear systems with time-varying parametric uncertainties

In this paper, learning control is integrated with non-linear optimal control to enhance control performance of a class of non-linear systems with time-varying parametric uncertainties. A suboptimal control strategy based on a control Lyapunov function and Sontag's formula provides suboptimal performance as well as stability along the time horizon for the nominal part of the non-linear dynamic system. The proposed learning mechanism learns the unknown time-varying parametric uncertainties so as to eliminate uncertain effects. System information both in time horizon and learning repetition horizon are incorporated in a composite energy function. The proposed control scheme achieves asymptotic convergence along the learning repetition horizon and boundedness and pointwise convergence of the tracking error (perfect tracking performance) along the time horizon.