This study aims at establishing a robust and effective intelligent control method for nonlinear and complicated systems. In the method, a neural network for integrated control acquires suitable switching and integration of several controllers for a different local purpose by calculating the fitness function based on the system objective using the genetic algorithm. The proposed method is applied to an equilibrium point transfer and stabilization control of a double pendulum that possesses four equilibrium points. In order to verify the effectiveness of the proposed method, computational simulations and experiments using a real apparatus were carried out. As a result, it was demonstrated that the integrated intelligent controllers can transfer and stabilize the double pendulum from an arbitrary equilibrium point to a desired unstable equilibrium point without touching the cart position limit.