Finite Time Adaptive Optimal Integral Sliding Mode Control for a Class of Uncertain Second Order Nonlinear Systems with Input Nonlinearity

In this paper, a new robust controller based on geometric homogeneity and adaptive integral sliding mode is proposed for a class of second order systems. The upper bound of the system disturbances is not required. Fully unknown parameters have been considered in the described model and its finite–time convergence to zero equilibrium point is proved. Moreover, the controller is developed in the presence of control singularity and unknown non-symmetric input saturation. The finite time stability of the proposed controller has been proved via classical Lyapunov criteria. In order to tune the control parameters, all the positive constant gains are optimized by ant colony optimization algorithm during the offline input-output training data. Two polar robots are introduced to show the performance of the designed controller. The robustness and error accuracy are proved in simulation results. Moreover, the effects of input nonlinearity such as input saturation have been considered in the simulation.