Integral sliding mode control with adaptive boundary of nonlinearities for robot manipulators

In this paper, we propose an integral sliding mode control with the bound estimation of the uncertain nonlinear parameters for the robot dynamics. For the bound estimation, we assume that the upper bound of the uncertain nonlinearities is represented as a Fredholm integral equation of the first kind. We also provide a sufficient condition for the existence of such a representation. The construction of an adaptation law is only dependent on the sliding surface function. Using the estimated bound, the integral sliding mode control is constructed in such a way that the prescribed sliding surface will attract every system´s trajectory and the trajectory will remain within a small boundary layer of the sliding surface for all subsequent time.