Fuzzy sliding mode control for a class of underactuated systems

A fuzzy sliding mode control strategy is designed in this paper for a class of second-order underactuated systems. This kind of system is divided into two subsystems, and two sub-sliding planes are designed respectively for them. A total sliding plane is then constructed using these two sub-sliding planes. A control law is derived from Lyapunov law to make the system reach the total sliding plane, and sequentially the two subsystems slide into their own sliding planes. Adaptive fuzzy logic systems, with parameter optimized using a genetic algorithm, are used to approximate the unknown nonlinear functions. The asymptotic stability of all sliding planes is proved theoretically. The validity of this control method is also proved by a simulation of an inverted pendulum system.