Neural networks simulation of distributed control problems with state and control constraints

Abstract

This paper is concerned with distributed optimal control problem. An adaptive critic neural networks solution is proposed to solve optimal distributed control problem for systems governed by parabolic differential equations, with control and state constraints and discrete time delay. The optimal control problem is discretized by using a finite element method in space and the implicit Crank-Nicolson midpoint scheme in time, then transcribed into nonlinear programming problem. To find optimal control and optimal trajectory feed forward adaptive critic neural networks are used to approximate co-state equations. The efficiency of our approach is demonstrated for a model problem related to a mixed nutrient uptake by phytoplankton with space diffusion and discrete time delay of nutrient uptake.