Boundary Control of Two Dimensional Burgers PDE Using Approximate Dynamic Programming

Abstract

An approximate dynamic programming (ADP) based near optimal boundary control of distributed parameter systems (DPS) governed by uncertain two dimensional (2D) Burgers equation under Neumann boundary condition is introduced. First, Hamilton-Jacobi-Bellman (HJB) equation is formulated without any model reduction. Next, optimal boundary control policy is derived in terms of value functional which is obtained as the solution to the HJB equation. Subsequently, a novel identifier is developed to estimate the unknown nonlinearity in the partial differential equation (PDE) dynamics. The suboptimal control policy is obtained by forward-in-time approximation of the value functional using a neural network (NN) based online approximator and the identified dynamics. Adaptive weight tuning laws are proposed for online learning of the value functional and identifier. Local ultimate boundedness (UB) of the closed-loop system is verified by using Lyapunov theory.

Meeting Name

2016 American Control Conference, ACC (2016: Jul. 6-8, Boston, MA)

Department(s)

Electrical and Computer Engineering

Second Department

Mathematics and Statistics

Research Center/Lab(s)

Center for High Performance Computing Research

Second Research Center/Lab

Intelligent Systems Center

Comments

Research supported in part by NSF grant ECCS#1128281 and Intelligent Systems Center.

International Standard Book Number (ISBN)

978-1-4673-8682-1

International Standard Serial Number (ISSN)

0743-1619; 2378-5861

Document Type

Article - Conference proceedings

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2016 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Jul 2016

Link to Full Text

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