Learning variable structure control approaches for repeatable tracking control tasks

In this paper, we consider repeatable tracking control tasks using a new co ntrol approach-learning variable structure control (LVSC). LVSC synthesizes two main control strategies: variable structure control (VSC) as the robus t part and learning control as the intelligent part. The incorporation of t he powerful learning function, by virtue of the internal model principle, c ompletely nullifies the tracking error. The switching control mechanism on the other hand, retains the well appreciated properties of VSC, especially the insensitivity to unstructured system uncertainties. Through a rigorous proof based on energy function and Functional analysis, we show that the LV SC system achieves the Following novel properties: (1) the tracking error s equence converges uniformly to zero;(2) the bounded learning control sequen ce converges to the equivalent control, i.e. the desired control profile al most everywhere: (3) the system state sequence and VSC control sequence are uniformly continuous. To address important practical considerations, the l earning mechanism is implemented by means of Fourier series expansions, hen ce achieves better tracking performance. (C) 2001 Elsevier Science Ltd. All rights reserved.