Online Learning ARMA Controllers With Guaranteed Closed-Loop Stability

Abstract

This paper presents a novel online block adaptive learning algorithm for autoregressive moving average (ARMA) controller design based on the real data measured from the plant. The method employs ARMA input-output models both for the plant and the resulting closed-loop system. In a sliding window the plant model parameters are identified first offline using a supervised learning algorithm minimizing an epsilon-insensitive and regularized identification error which is the window average of the distances between the measured plant output and the model output for the input provided by the controller. The optimal controller parameters are then determined again offline for another sliding window as the solution to a constrained optimization problem where the cost is the epsilon-insensitive and regularized output tracking error and the constraints that are linear inequalities of the controller parameters are imposed for ensuring the closed-loop system to be Schur stable. Not only the identification phase but also the controller design phase uses the input-output samples measured from the plant during online learning. In the developed online controller design method the controller parameters can always be kept in a parameter region providing Schur stability for the closed-loop system. The e-insensitiveness provides robustness against disturbances so does the regularization better generalization performance in the identification and the control. The method is tested on benchmark plants including the inverted pendulum and dc motor models. The method is also tested on an emulated and also a real dc motor by online block adaptive learning ARMA controllers in particular Proportional-Integral-Derivative controllers.