Motion control of an inverted pendulum via final-state control

In this paper the author proposes a control method that can bring a system to an arbitrary final state even if the input is already saturated, by adopting a hyperbolic tangential function that describes the input limitation. Furthermore, by using the derivative of the function, the obtained input becomes continuous at terminal points of an initial time and a final time. This formulation of the input limitation can be described by a linear parameter-dependent system and the final-state control with error learning can be applied to the system. The effectiveness of this method is verified by carrying out both simulations and experiments of the swing-up motion control of a cart and inverted pendulum system, whose cart displacement is limited. This method does not require precise determination of the final time and can generate a continuous, smooth, feedforward control input when the output of the actuator is limited.