Diagonal recurrent neural networks for control of dynamic systems
Chao-Chee Ku · 1993
A new neural network architecture called Diagonal Recurrent Neural Network (DRNN) is presented. The architecture of DRNN is a modified model of fully connected recurrent neural network with one hidden layer. The hidden layer is comprised of self-recurrent neurons, each feeding its output only into itself and not to other neurons in the hidden layer. Two DRNNs 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. 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. Convergence and the closed-loop stability are established for the DRNN based control system when the plant is BIBO stable. The proposed DRNN model is tested on a number of examples. Two different approaches for selecting learning rates, namely the fixed learning rate and the adaptive learning rate approaches, are investigated. The generalization ability, a BIBO nonlinear control, a non-BIBO nonlinear control, the on-line adapting ability of the DRNN based control, and an unstable plant control are investigated. The results show that the DRNN based control system requires much fewer neurons and weights, and that the number of training cycles required is reduced considerably. Moreover, the convergence, which is guaranteed for a BIBO plant, is also fast and the result is a closed-loop system which tracks reference input very well. An unstable plant was also controlled successfully by incorporating temperature and scaling schemes. The DRNN is also applied in a practical problem: nuclear reactor temperature control, and the simulation results demonstrated that the DRNN based control is very promising for future real-time applications.