A Practical Guide to Geometric Regulation for Distributed Parameter Systems provides an introduction to geometric control design methodologies for asymptotic tracking and disturbance rejection of infinite-dimensional systems. The book also introduces several new control algorithms inspired by geometric invariance and asymptotic attraction for a wide range of dynamical control systems.
The first part of the book is devoted to regulation of linear systems, beginning with the mathematical setup, general theory, and solution strategy for regulation problems with bounded input and output operators. The book then considers the more interesting case of unbounded control and sensing. Mathematically, this case is more complicated and general theorems in this area have become available only recently. The authors also provide a collection of interesting linear regulation examples from physics and engineering.
The second part focuses on regulation for nonlinear systems. It begins with a discussion of theoretical results, characterizing solvability of nonlinear regulator problems with bounded input and output operators. The book progresses to problems for which the geometric theory based on center manifolds does not directly apply. The authors show how the idea of attractive invariance can be used to solve a series of increasingly complex regulation problems. The book concludes with the solutions of challenging nonlinear regulation examples from physics and engineering.
Table of Contents
Regulation for Linear Systems
Regulation: Bounded Input and Output Operators
Setup and Statement of Problem
Main Theoretical Result
The Transfer Function
SISO Examples with Bounded Control and Sensing
The MIMO Case
Linear Regulation with Unbounded Control and Sensing
Formulation of Control System and Interpolation Spaces
Examples with Unbounded Sensing and Control
Examples Linear Regulation
Harmonic Tracking for a Coupled Wave Equation
Control of a Damped Rayleigh Beam
Vibration Regulation of a 2D Plate
Control of a Linearized Stokes Flow in 2 Dimensions
Thermal Control of a 2D Fluid Flow
Thermal Regulation in a 3D Room
Using Fourier Series for Tracking Periodic Signals
Zero Dynamics Inverse Design
Regulation for Nonlinear Systems
Nonlinear Distributed Parameter Systems
Nonlinear State Feedback Regulation Problem
Set-Point Regulation for Nonlinear Systems
Tracking/Rejection of Piecewise Constant Signals
Nonlinear Regulation for Time-Dependent Signals
Fourier Series Methods for Nonlinear Regulation
Zero Dynamics Design for Nonlinear Systems
Navier-Stokes Flow in a 2D Forked Channel
Non-Isothermal Navier-Stokes Flow in a 2D Box
2D Chafee-Infante with Time-Dependent Regulation
Regulation of 2D Burgers' Using Fourier Series
Back-Step Navier-Stokes Flow
Nonlinear Regulation Using Zero Dynamics Design
List of Symbols
Eugenio Aulisa is an associate professor in the Department of Mathematics and Statistics at Texas Tech University, Lubbock, USA. His primary research interests are in computational fluid mechanics, modeling and simulation of multiphase flows, fluid-structure interaction problems, non-linear analysis of fluid flow filtration in porous media, and multigrid solvers with domain decomposition methods. He holds a Ph.D in energetic, nuclear, and environmental control engineering from the University of Bologna, Italy.
David Gilliam is a professor in the Department of Mathematics and Statistics at Texas Tech University, Lubbock, USA. He also has held visiting and/or affiliate positions at Arizona State University, Tempe, USA; Colorado School of Mines, Golden, USA; University of Texas at Dallas, Richardson, USA; and Washington University in St. Louis, Missouri, USA. His current research interests are in the control of distributed parameter systems governed by partial differential equations. He holds a Ph.D from the University of Utah, Salt Lake City, USA.