Doctoral Dissertations


Behzad Talaei

Keywords and Phrases

Adaptive Dynamic Programming; Boundary Control; Optimal Control; Output Feedback; Parabolic PDE; Reaction Diffusion Equations


"In this dissertation, novel adaptive/approximate dynamic programming (ADP) based state and output feedback control methods are presented for distributed parameter systems (DPS) which are expressed as uncertain parabolic partial differential equations (PDEs) in one and two dimensional domains. In the first step, the output feedback control design using an early lumping method is introduced after model reduction. Subsequently controllers were developed in four stages; Unlike current approaches in the literature, state and output feedback approaches were designed without utilizing model reduction for uncertain linear, coupled nonlinear and two-dimensional parabolic PDEs, respectively. In all of these techniques, the infinite horizon cost function was considered and controller design was obtained in a forward-in-time and online manner without solving the algebraic Riccati equation (ARE) or using value and policy iterations techniques.

Providing the stability analysis in the original infinite dimensional domain was a major challenge. Using Lyapunov criterion, the ultimate boundedness (UB) result was demonstrated for the regulation of closed-loop system using all the techniques developed herein. Moreover, due to distributed and large scale nature of state space, pure state feedback control design for DPS has proven to be practically obsolete. Therefore, output feedback design using limited point sensors in the domain or at boundaries are introduced. In the final two papers, the developed state feedback ADP control method was extended to regulate multi-dimensional and more complicated nonlinear parabolic PDE dynamics"--Abstract, page iv.


Sarangapani, Jagannathan, 1965-
Singler, John R.

Committee Member(s)

Acar, Levent
Bristow, Douglas A.
Erickson, Kelvin T.


Electrical and Computer Engineering

Degree Name

Ph. D. in Electrical Engineering


Missouri University of Science and Technology

Publication Date

Spring 2016

Journal article titles appearing in thesis/dissertation

  • Near optimal constrained output feedback boundary control of one-dimensional semi-linear parabolic PDE
  • Boundary control of linear uncertain one-dimensional parabolic PDE using approximate dynamic programming
  • Output feedback boundary control of uncertain coupled semi-linear parabolic PDE using neuro dynamic programming
  • Boundary control of two dimensional burgers PDE using approximate dynamic programming
  • Output feedback boundary control of two dimensional nonlinear parabolic PDE: An adaptive dynamic programming approach


x, 188 pages

Note about bibliography

Includes bibliographic references.


© 2016 Behzad Talaei, All rights reserved.

Document Type

Dissertation - Open Access

File Type




Subject Headings

Dynamic programming
Distributed parameter systems
Reaction-diffusion equations
Differential equations, Parabolic -- Numerical solutions -- Data processing

Thesis Number

T 10927

Electronic OCLC #