Partial State Feedback Sliding Mode Control of Double-pendulum Crane Systems using Neural Networks

In this paper, a neural network-based partial state feedback incremental sliding mode control scheme is proposed for double-pendulum overhead crane systems. First of all, it is proved that if the hook stays at the equilibrium point, then the payload also stays at the equilibrium point. Based on this, we provide access to address the control issue of the double-pendulum crane without the need for prior knowledge and feedback signals of the payload. Secondly, two neural networks contained in the equivalent control law are used to approximate unknown nonlinear dynamic terms caused by the lack of information such as the mass, swing angle, swing angular velocity, and swing angular acceleration of the payload, as well as the length of the cable connecting the hook and payload. Thirdly, we designed a switching control law to compensate for the unmodeled dynamics such as the parameter uncertainties and unknown bounded external disturbances. Then, we theoretically proved the asymptotic stability of all the sliding surfaces and all state variables. Finally, some simulations are performed to validate the effectiveness of the proposed method.