Fixed‐time linear quadratic adaptive sliding mode control for a class of cart‐pendulum robots

This article is concerned with the fixed‐time path‐following control problem of a perturbed cart‐pendulum robot with linear quadratic (LQ) performance optimization. In order to ensure the displacements of cart and pendulum of the robot following the desired paths within fixed‐time, adaptive anti‐perturbation sliding mode control schemes with a novel fixed‐time sliding mode surface are developed to withstand the adverse influence of perturbations. Furthermore, an adaptive radial basis function neural network (RBFNN)‐based sliding mode control algorithm is employed to approximate the continuous perturbations, so that the path‐following LQ control problem can be further dealt with. The fixed‐time stability and path‐following results of the cart‐pendulum robotic system are achieved by Lyapunov stability theory. A simulation example for a heavy material handling agricultural robot is proposed to verify the effectiveness of the developed method.