Application of adaptive critic design on angle bracket inverted pendulum control

The angle bracket Inverted pendulum is a complex nonlinear system, which is composed of a cart, a pole and a ramp supported by a bracket. Compared with normal inverted pendulum system, the angle bracket inverted pendulum has an inertia weight that caused by gravity downward along the ramp. The character of this system increases the difficulty of balancing the pole. In this paper, adaptive dynamic programming method is used for the system control. Two neural networks are designed separately to achieve the estimation of cost-to-go function and the output of control action through continuously learning. In the utility function design, the consideration of inertia influence is included which makes the estimation of system cost more exactly. In the output layer of the action network we use the S function as the transfer function that makes the outputs of control action be continuous variables. Furthermore, we increase a compensation part to decrease the influence caused by inertia factor. Simulation results show that the method has good results, also prove that it is feasible for the adaptive dynamic programming method to solve inertia problem.