Adaptive Dynamic Programming Boundary Control of Uncertain Coupled Semi-Linear Parabolic PDE
Abstract
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.
Recommended Citation
B. Talaei et al., "Adaptive Dynamic Programming Boundary Control of Uncertain Coupled Semi-Linear Parabolic PDE," Proceedings of the IEEE International Symposium on Intelligent Control (2015, Sydney, Australia), Institute of Electrical and Electronics Engineers (IEEE), Sep 2015.
The definitive version is available at https://doi.org/10.1109/ISIC.2015.7307299
Meeting Name
IEEE International Symposium on Intelligent Control (2015: Sep. 21-23, Sydney, Australia)
Department(s)
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
Citation
File Type
text
Language(s)
English
Rights
© 2015 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.
Publication Date
01 Sep 2015
