Tracking problem of uncertain nth degree non-linear system by sliding mode control

Deals with the tracking problem of the continuous nth degree nonlinear system in the form x⁽ⁿ⁾(t)=f(x(t))+b(x(t))u(t), with an arbitrary initial state condition x(0). Here x(t)=[x(t) x˙(t)...x^(n-1)(t)]^T is the state vector while f(x(t)) and b(x(t)) are uncertain scalar nonlinear functions satisfying a certain assumption concerning their minimum and maximum bounds. The paper utilizes sliding mode control (SMC) characterized by fast reaching phase to speed up convergence to the designed sliding surface. The validity of the theoretical concepts discussed in the paper is supported by simulation results