Generating Robust Control Equations with Genetic Programming for Control of a Rolling Inverted Pendulum

In control applications, to apply the results obtained by evolutions and simulations to real systems, it is indispensable for them to have high robustness in computer simulations. The goal of this study is to generate robust control equations for controlling the real system of a rolling inverted pendulum with Genetic Programming. The control equations for this system must swing a pole up from a hanging state and then keep the pole inversely standing. Therefore, we introduce the “compound fitness evaluation,” which consists of two simulations corresponding to two control requirements. As a result of the evolutionary experiments, five robust and stable control equations that swing a pole up and keep it standing are obtained. By theoretical analysis, it is proven that polecart systems using these control equations are asymptotically stable. The robustness of these equations are verified by dynamical simulations that vary each parameter of the pole-cart system.