Comparative Testing of the Neural Network and Semi-empirical Method on the Stabilization Problem of Inverted Pendulum

Abstract

In the article we have presented the results of comparative testing of non-standard methods of dynamic systems’ control. We’ve implemented the testing by the example of solving the problem of bringing the pendulum to the neighborhood of unstable equilibrium position in the shortest time under conditions of limited control. We’ve compared four approaches - a one-step approach based on the exact solution of the pendulum equation and three two-step approaches. The first two-step approach we’ve based on the method of restarts. The second two-step approach we’ve built on the neural network training. In the third two-step approach, we’ve used our modifications of the algorithm for constructing approximate solutions of ordinary differential equations. Based on computational experiments, we’ve concluded that the one-step approach is significantly less effective than the two-step one. All three two-step approaches have approximately the same rate of convergence. At the same time, the approach based on the method of restarts requires much more time, although it is more resistant to changes in the starting point. Approaches based on the use of a pre-trained neural network and our modification of the implicit Euler method require significantly less computing resources for their work. The disadvantage of these methods is the process’s elongation of bringing the pendulum into the neighborhood of an unstable equilibrium position for some initial conditions.