Command filtered dual backstepping variable structure robust switching control of uncertain nonlinear system

This paper presents the design and stability analysis of a dual backstepping variable structure robust controller based on command filter for a class of nonlinear system with bounded uncertain structure. First, a normal backstepping recursive design procedure is divided into two distinguished sub-backstepping recursive sequences according to different control objectives or tasks. Then, a set of the switching logic is introduced from the variable structure switching scheme to connect different sub-backstepping controllers. The switching logic function divides the whole process into saturation switching phase and linear transient phase. Meanwhile, command filters are employed to suppress the redouble explosion of the derivation terms from sequences. This mechanism is proposed to make up the shortcoming of chatting in variable structure switching and give more flexibility in designing feedback control law to protect the beneficial nonlinear characteristics. Furthermore, compared with the existing traditional single backstepping method, the developed method not only guarantees the uniform ultimately bounded of all the closed-loop system with uncertainty, but also improves the tracking performance. The steady output tracking error can be made arbitrarily small by choosing control parameters appropriately. Finally, the effectiveness and advantages of this mechanism are illustrated by a practical example.