Diagonal recurrent neural networks for dynamic systems control

TLDR

The paper introduces the diagonal recurrent neural network (DRNN) as a new neural paradigm. DRNN comprises a self‑recurrent hidden layer and is used in a control system as a diagonal recurrent neuroidentifier (DRNI) that models the plant and a diagonal recurrent neurocontroller (DRNC) that exploits the identified dynamics, both trained with a generalized dynamic backpropagation algorithm and accelerated by adaptive learning rates derived from a Lyapunov function. The authors prove convergence theorems for the adaptive backpropagation algorithms of DRNI and DRNC and demonstrate the approach on numerical problems with favorable simulation results.

Abstract

A new neural paradigm called diagonal recurrent neural network (DRNN) is presented. The architecture of DRNN is a modified model of the fully connected recurrent neural network with one hidden layer, and the hidden layer comprises self-recurrent neurons. Two DRNN's are utilized in a control system, one as an identifier called diagonal recurrent neuroidentifier (DRNI) and the other as a controller called diagonal recurrent neurocontroller (DRNC). A controlled plant is identified by the DRNI, which then provides the sensitivity information of the plant to the DRNC. A generalized dynamic backpropagation algorithm (DBP) is developed and used to train both DRNC and DRNI. Due to the recurrence, the DRNN can capture the dynamic behavior of a system. To guarantee convergence and for faster learning, an approach that uses adaptive learning rates is developed by introducing a Lyapunov function. Convergence theorems for the adaptive backpropagation algorithms are developed for both DRNI and DRNC. The proposed DRNN paradigm is applied to numerical problems and the simulation results are included.