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

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

Keywords:

Adaptive control , Integral sliding mode control , Input saturation , Ant colony optimization