Adaptive Sliding Mode Control of Multi-Input Nonlinear Systems With Perturbations to Achieve Asymptotical Stability

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> A design of adaptive sliding surfaces for a class of multi-input (MI) nonlinear systems with matched and mismatched perturbations is proposed in this note to solve regulation problems based on the Lyapunov stability theorem and backstepping technique. By using some adaptive gains designed in the sliding surface function, the virtual input and the controllers, not only the mismatched perturbations are automatically overcome during the sliding mode, but also the property of asymptotical stability of controlled systems is achieved at the same time. Furthermore, the knowledge of the upper bound of partial perturbations is not required. Controlling a two-link robot manipulator is given to demonstrate the feasibility of the proposed control scheme. </para>