A class of under-actuated and uncertain nonlinear dynamic systems by hybrid neural-network-based variable structure control

Due to the under-actuated feature, the reference signals using the combination of the system outputs, whose number is larger than that of reference signal, are designed so that the number of control inputs and sliding surfaces is the same, and that the uncontrolled mode is indirectly controlled. Under the uncertain environment, the variable structure under-actuated control (VSUC) with the satisfaction of suitable condition is designed to asymptotically track the reference signal. Otherwise, a bounded tracking result is obtained for the mild condition. In this situation, an on-line neural network modeling for the uncertainty is applied to construct a neural-network-based variable structure under-actuated control (NVSUC) to improve the system performance; e.g., the bounded tracking result of previous VSUC becomes an asymptotical tracking. The proposed hybrid neural-network-based variable structure under-actuated control (HNVSUC) combining VSUC and NVSUC with a transition can be employed to a class of under-actuated and uncertain nonlinear systems. Finally, the corresponding simulations of the balance control of a double inverted pendulum on a cart are undertaken to confirm the efficiency and effectiveness of the proposed method.