A Practical Guide to Geometric Regulation for Distributed Parameter Systems

This book provides an introduction to geometric control design methodologies for asymptotic tracking and disturbance rejection of infinite dimensional systems. It also introduces several new control algorithms inspired by geometric invariance and asymptotic attraction for a wide range of dynamical control systems. The book covers the regulation of both linear and nonlinear systems and offers an extensive collection of both types of problems. Examples range from one-dimensional heat and wave equations to control of non-isothermal Boussinesq flows.

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.