An Integrated Learning Variable Structure Control Method

Abstract

In this chapter, 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 the insensitivity to norm-bounded system uncertainties. Through a rigorous proof based on the 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 it achieves better tracking performance.