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.
Acknowledgments Preface 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 Introduction Formulation of Control System and Interpolation Spaces Examples with Unbounded Sensing and Control Examples Linear Regulation Introduction 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 Introduction 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 Nonlinear Examples Introduction 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 Bibliography Index 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.