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Selected Works of John R. Singler
Article
Boundary Control of 2-D Burgers' PDE: An Adaptive Dynamic Programming Approach
IEEE Transactions on Neural Networks and Learning Systems
  • Behzad Talaei
  • Jagannathan Sarangapani, Missouri University of Science and Technology
  • John R. Singler, Missouri University of Science and Technology
Link
Abstract

In this paper, an adaptive dynamic programming-based near optimal boundary controller is developed for partial differential equations (PDEs) modeled by the uncertain Burgers' equation under Neumann boundary condition in 2-D. Initially, Hamilton-Jacobi-Bellman equation is derived in infinite-dimensional space. Subsequently, a novel neural network (NN) identifier is introduced to approximate the nonlinear dynamics in the 2-D PDE. The optimal control input is derived by online estimation of the value function through an additional NN-based forward-in-time estimation and approximated dynamic model. Novel update laws are developed for estimation of the identifier and value function online. The designed control policy can be applied using a finite number of actuators at the boundaries. Local ultimate boundedness of the closed-loop system is studied in detail using Lyapunov theory. Simulation results confirm the optimizing performance of the proposed controller on an unstable 2-D Burgers' equation.

Department(s)
Electrical and Computer Engineering
Second Department
Mathematics and Statistics
Research Center/Lab(s)
Center for High Performance Computing Research
Comments
This work was supported in part by NSF under Grant ECCS1128281 and in part by the Intelligent Systems Center.
Keywords and Phrases
  • Actuators,
  • Boundary conditions,
  • Closed loop systems,
  • Controllers,
  • Dynamical systems,
  • Estimation,
  • Mathematical models,
  • Neural networks,
  • Nonlinear dynamical systems,
  • Nonlinear equations,
  • Optimal control systems,
  • Partial differential equations,
  • Approximate dynamic programming,
  • Boundary controls,
  • Burgers' equations,
  • Optimal controls,
  • Partial Differential Equations (PDEs),
  • Reduced order systems,
  • Stability analysis,
  • Dynamic programming,
  • 2-D partial differential equations (PDEs),
  • Burgers' equation,
  • PDE boundary control
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2018 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.
Publication Date
8-1-2018
Publication Date
01 Aug 2018
Disciplines
Citation Information
Behzad Talaei, Jagannathan Sarangapani and John R. Singler. "Boundary Control of 2-D Burgers' PDE: An Adaptive Dynamic Programming Approach" IEEE Transactions on Neural Networks and Learning Systems Vol. 29 Iss. 8 (2018) p. 3669 - 3681 ISSN: 2162-237X; 2162-2388
Available at: http://works.bepress.com/john-singler/47/