Adaptive Dynamic Programming Boundary Control of Uncertain Coupled Semi-Linear Parabolic PDE


This paper develops an adaptive dynamic programming (ADP) based near optimal boundary control of distributed parameter systems (DPS) governed by uncertain coupled semi-linear parabolic partial differential equations (PDE) under Neumann boundary control condition. First, Hamilton-Jacobi-Bellman (HJB) equation is formulated without any model reduction and the optimal control policy is derived. Subsequently, a novel identifier is developed to estimate the unknown nonlinearity in PDE dynamics. Accordingly, the sub-optimal control policy is obtained by forward-in-time estimation of the value functional using a neural network (NN) online approximator and the identifier. Adaptive tuning laws are proposed for learning the value functional online. Local ultimate boundedness (UB) of the closed-loop system is verified by using Lyapunov theory. The performance of proposed controller is verified via simulation on an unstable coupled diffusion reaction process.

Meeting Name

IEEE International Symposium on Intelligent Control (2015: Sep. 21-23, Sydney, Australia)


Electrical and Computer Engineering

Second Department

Mathematics and Statistics

Research Center/Lab(s)

Center for High Performance Computing Research

Document Type

Article - Conference proceedings

Document Version


File Type





© 2015 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Sep 2015