Learning variable structure control approaches for repeatable tracking control tasks

Abstract

In this paper, we consider repeatable tracking control tasks using a new control approach - learning variable structure control (LVSC). LVSC synthesizes two main control strategies: variable structure control (VSC) as the robust part and learning control as the intelligent part. The incorporation of the powerful learning function, by virtue of the internal model principle, completely nullifies the tracking error. The switching control mechanism on the other hand, retains the well appreciated properties of VSC, especially theinsensitivity to unstructured system uncertainties. Through a rigorous proof based on energy function and functional analysis, we show that the LVSC system achieves the following novel properties: (1) the tracking error sequence converges uniformly to zero; (2) the bounded learning control sequence converges to the equivalent control, i.e. the desired control profile almost everywhere; (3) the system state sequence and VSC control sequence are uniformly continuous. To address important practical considerations, the learning mechanism is implemented by means of Fourier series expansions, hence achieves better tracking performance. © 2001 Elsevier Science Ltd.