J. William Helton

H-Infinity control originated from an effort to codify classical control methods, where one shapes frequency response functions to meet certain objectives. H-Infinity control underwent tremendous development in the 1980s and made considerable strides toward systematizing classical control. This book addresses the next major issue of how this extends to nonlinear systems. At the core of nonlinear control theory lie two partial differential equations (PDEs). One is a first-order evolution equation called the information state equation, which constitutes the dynamics of the controller. One can view this equation as a nonlinear dynamical system. Much of this volume is concerned with basic properties of this system, such as the nature of trajectories, stability, and, most important, how it leads to a general solution of the nonlinear H-Infinity control problem. The second PDE actually builds on a classical type of partial differential inequality (PDI) called a Bellman-Isaacs inequality. While the information state PDE determines the dynamics of the controller, the PDI determines the output of the controller.The authors explore the system theoretic significance of the PDI and present its gross structure. These equations are only a few years old and their study is an expanding area of research. This book also emphasizes the theory effecting computer solvability of the information state equation, which at the outset looks numerically intractable, but which surprisingly is in many cases tractable. For example, the theory shows that careful initialization has a major influence on computer solvability. The authors keep the book self-contained by using the appendices to help explain certain prerequisite material. The reader should have a basic knowledge of control theory, real analysis and differential equations, nonlinear operator theory, and nonlinear PDEs.

This versatile book teaches control system design using H? techniques that are simple and compatible with classical control, yet powerful enough to quickly allow the solution of physically meaningful problems. The authors begin by teaching how to formulate control system design problems as mathematical optimization problems and then discuss the theory and numerics for these optimization problems. Their approach is simple and direct, and since the book is modular, the parts on theory can be read independently of the design parts and vice versa, allowing readers to enjoy the book on many levels. The development of H? engineering was one of the main accomplishments of control in the 1980s. However, until now, there has not been a publication suitable for teaching the topic at the undergraduate level. This book fills that gap by teaching control system design using H? techniques at a level within reach of the typical engineering and mathematics student. It also contains a readable account of recent developments and mathematical connections. The authors treat control design problems in a physically correct way.They present a small set of specific rules that the reader can apply to convert a particular design problem to the fundamental optimization problem of H? control. This precisely formulated mathematics problem can then be solved on a computer. The book introduces the control software package OPTDesign, which allows the reader to easily reproduce the calculations done in the solved examples and even try variations on them. The description of how to convert an engineering problem to a form suitable for CAD is simpler than in other books.

One of the main accomplishments of control in the 1980s was the development of H? techniques. This book teaches control system design using H? methods. Students will find this book easy to use because it is conceptually simple. They will find it useful because of the widespread appeal of classical frequency domain methods. Classical control has always been presented as trial and error applied to specific cases; Helton and Merino provide a much more precise approach. This has the tremendous advantage of converting an engineering problem to one that can be put directly into a mathematical optimization package. After completing this course, students will be familiar with how engineering specs are coded as precise mathematical constraints.