Adaptive hierarchical sliding mode control based on fuzzy neural network for an underactuated system

We present an adaptive hierarchical sliding mode control based on fuzzy neural network (AFNNHSMC) for a class of underactuated nonlinear systems. The approach is applied to the problem of high-precision trajectory tracking. The underactuated nonlinear system is viewed as several subsystems. One subsystem is used to design the first layer sliding surface, which constructs the second layer sliding surface with another subsystem. When the top layer, the nth layer, includes all the subsystems, the design process is finished. Meanwhile, the equivalent control law and the switching control law are achieved at every layer. Because the hierarchical sliding mode control (HSMC) law relies excessively on the requirement of detailed information of the underactuated dynamic system, and because that method causes an inevitable chattering phenomenon, an online fuzzy neural network (FNN) system is applied to mimic the HSMC law. Moreover, the bounds of system uncertainties, time-varying external disturbances, and modeling error caused by the fuzzy neural network system are estimated online by a robust term. The stability of the closed-loop system is guaranteed based on the Lyapunov theory and the Barbalat’s Lemma. Finally, the example of a single-pendulum-type overhead crane system is simulated and used to verify the effectiveness and robustness of the proposed method compared with the conventional HSMC method.