Near optimal boundary control of distributed parameter systems modeled as parabolic pdes by using finite difference neural network approximation

This paper develops a novel neural network (NN) based near optimal boundary control scheme for distributed parameter systems (DPS) governed by semilinear parabolic partial differential equations (PDE) in the presence of control constraints and unknown system dynamics. First, finite difference method (FDM) is utilized to develop a reduced order system which represents the discretized dynamics of PDE system. Subsequently, a near optimal control scheme is proposed for the discretized system by using NN based approximate dynamic programming(ADP). To relax the requirement of system dynamics, a NN identifier is utilized. Moreover, a second NN is proposed to estimate a non-quadratic value function online. Subsequently, by using the identifier and the value function estimator, the optimal control input that inherently falls within actuator limits is obtained. A local uniformly ultimately boundedness(UUB) of the closed-loop system is verified by using standard Lyapunov theory. The performance of the proposed control scheme is successfully verified by simulation on a diffusion reaction process.