Memory Augmented Neural Network Adaptive Controllers: Performance and Stability
Deepan Muthirayan, Pramod P. Khargonekar
Abstract
In this article, we propose a novel control architecture, inspired from neuroscience, for adaptive control of continuous-time systems. The proposed architecture, in the setting of standard neural network (NN)-based adaptive control, augments an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">external working memory</i> to the NN. The controller, through a write operation, writes the hidden layer feature vector of the NN to the external working memory and can also update this information with the observed error in the output. Through a read operation, the controller retrieves information from the working memory to modify the final control signal. First, we consider a simpler estimation problem to theoretically study the effect of an external memory and prove that the estimation accuracy can be improved by incorporating memory. We, then, consider a model reference NN adaptive controller for linear systems with matched uncertainty to implement and illustrate our ideas. We prove that the resulting controller leads to a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">uniformly bounded</i> stable closed-loop system. Through extensive simulations and specific metrics, such as peak deviation and settling time, we show that memory augmentation improves learning significantly. Importantly, we also provide evidence for and insights on the mechanism by which this specific memory augmentation improves learning.