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Article
Boundary Control of Two Dimensional Burgers PDE Using Approximate Dynamic Programming
Proceedings of the IEEE American Control Conference (2016, Boston, MA)
  • B. Talaei
  • Jagannathan Sarangapani, Missouri University of Science and Technology
  • John R. Singler, Missouri University of Science and Technology
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
IEEE American Control Conference (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
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
7-1-2016
Citation Information
B. Talaei, Jagannathan Sarangapani and John R. Singler. "Boundary Control of Two Dimensional Burgers PDE Using Approximate Dynamic Programming" Proceedings of the IEEE American Control Conference (2016, Boston, MA) (2016)
Available at: http://works.bepress.com/john-singler/17/