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.
Bristow, Douglas A.
Erickson, Kelvin T.
Electrical and Computer Engineering
Ph. D. in Electrical Engineering
Missouri University of Science and Technology
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
© 2016 Behzad Talaei, All rights reserved.
Dissertation - Open Access
Distributed parameter systems
Differential equations, Parabolic -- Numerical solutions -- Data processing
Electronic OCLC #
Talaei, Behzad, "Boundary control of parabolic PDE using adaptive dynamic programming" (2016). Doctoral Dissertations. 2491.