Neural networks solution of optimal control problems with discrete time delays and time-dependent learning of infinitesimal dynamic system

Abstract

The paper presented describes two possible applications of artificial neural networks. The first application is related to solve optimal control problems with discrete time delays in state and control variables subject to control and state constraints. The optimal control problem is transcribed into nonlinear programming problem which is implemented with feed forward adaptive critic neural network to find optimal control and optimal trajectory. The proposed simulation methods are illustrated by the optimal control problem of nitrogen transformation cycle model with discrete time delay of nutrient uptake. The second application deals with back-propagation learning of infinite-dimensional dynamical systems. The proposed simulation methods are illustrated by the back-propagation learning of continuous multilayer Hopfield neural network with discrete time delay using optimal trajectory as teacher signal. Results show that adaptive critic based systematic approach are promising in obtaining the optimal control with discrete time delays in state and control variables subject to control and state constraints and that continuous Hopfield neural networks are able to approximate signals generated from optimal trajectory.