Stability analysis of recurrent neural-based controllers

Abstract

Scope and Method of Study:

In the last two decades, more attention has been given to Recurrent Neural Networks(RNNs) and their applications. The ability of RNNs to solve complex problems in control, system identification, signal processing, communication, pattern recognition, etc. is well understood. Although RNNs are more powerful than feedforward networks, this comes at the expense of more difficult training and the potential for instabilities. It has become more and more important to have efficient methods for determining the stability of RNNs. The purpose of this research is to develop improved methods for determining the stability of RNNs.

Findings and Conclusions:

The main contribution of this research is the development of an efficient algorithm to detect global asymptotic stability of RNNs and then use the stable RNNs for the purpose of control and system identification. Three Lyapunov-based algorithms, RODD-LB2,RODD-EB and RODD-Hybrid, are developed to detect global asymptotic stability of RNNs. We found that the RODD-Hybrid method generally produced the fastest and the most consistent results. The applications of the proposed algorithms have been applied to neural network control problems.