Learning in Dynamic Systems and Its Application to Adaptive PID Control

Deep learning using neural networks has revolutionized machine learning and put artificial intelligence into everyday life. In order to introduce self-learning to dynamic systems other than neural networks, we extend the Brandt-Lin learning algorithm of neural networks to a large class of dynamic systems. This extension is possible because the Brandt-Lin algorithm does not require a dedicated step to back-propagate the errors in neural networks. To this end, we first generalize signal-flow graphs so that they can be used to model nonlinear systems as well as linear systems. We then derive the extended Brandt-Lin algorithm that can be used to adapt the weights of branches in generalized signal-flow graphs. We show the applications of the new algorithm by applying it to adaptive PID control. In particular, we derive a new adaptation law for PID controllers. We verify the effectiveness of the method using simulations for linear and nonlinear plants, stable as well as unstable plants.