A global optimal sliding-mode control for the minimum time trajectory tracking with bounded inputs

A new design of the sliding mode control is proposed for the uncertain linear time-varying second order system. The proposed control drives system states to the target point in the minimum time with specified ranges of parametric uncertainties and disturbances, One of the advantages of the proposed control scheme is that the control inputs do not go beyond saturation limits of the actuators. The other advantage is that the minimum arrival time and the acceleration of the second order actuators system can be estimated with given parametric bounds and can be expressed in the closed form; conversely, the designer can select actuators based on the condition of the minimum arrival time to the target point. The superior performance of the proposed control scheme to other sliding mode controllers is validated by computer simulations.