Stability Analysis of Evolved Continuous Time Recurrent Neural Networks that Balance a Double Inverted Pendulum on a Cart

Continuous Time Recurrent Neural Networks (CTRNN) display relevant properties of robustness to noise due to the stability of network dynamics. In this work we test the CTRNN model in a framework of NeuroEvolution (NE) for a real time control task, i.e. the balancing of an unstable nonlinear mechanical system. The task is used to review some theoretical results related to the analysis of stability of the network dynamics, as well as the primary results on the poles balancing task with CTRNNs, referring to similar task context in related works. The local stability of the neural controller dynamics does not undergo disruptive effects when evaluated in conditions different from the evolution ones. Thus, the controller is able to keep the equilibrium of the unstable system also in presence of noise significantly larger than the ratio experienced during the training phase.