Composite Neural Networks for Controlling Semi-Linear Dynamical Systrms: Example from Inverted Pendulum Problem

In this paper, we propose a neural network for learning to control semi-linear dynamical systems. The network is a composite system of four three-layer backpropagation subnetworks, and is able to control inverted pendulums better than systems based on modern control theory at least in some ranges of parameters. Three of the four subnetworks in our network system process angles, velocities, and positions of a moving inverted pendulum, respectively. The outputs from those three subnetworks are input to the remaining subnetwork that makes control decisions. Each of the four subnetworks learns connection weights independently by backpropagation algorithms. Teaching signals are given by the human operator. Also, input signals are generated by the human operator, but they are converted by preprocessors to actual input data for the three subnetworks except for the network for control decisions. The whole system is implemented on both of 16 bit personal computers and 32 bit workstations. First, we briefly provide the research background and the inverted pendulum problem itself, followed by the description of our composite neural network model. Next, some results from the simulation are given, which are subsequently compared with the results from a control system based on modern control theory. Then, some discussions and conclusion follow.