The adaptive fuzzy tracking control for double inverted pendulums in the presence of unknown control directions

In this paper, an adaptive fuzzy control scheme for two inverted pendulums mounted on two carts with unknown control directions is proposed. A kind of Nussbaum-type functions is designed, with which the effect of multiple unknown control directions can be handled. Fuzzy functions are used to approximate the unknown terms and by combining adaptive laws with backstepping procedure, constructed adaptive fuzzy controller can guarantee the two inverted pendulum systems asymptotically stable and all states in the closed-loop systems are bounded. Finally, numerical simulation results show that two inverted pendulums mounted on two carts can move toward stability.