Extending H-infinity Control to Nonlinear Systems: Control of Nonlinear Systems to Achieve Performance Objectives (Advances in Design and Control, Series Number 1)

H-infinity control originated from an effort to codify classical control methods, where one shapes frequency response functions for linear systems 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.

J. William Helton is Professor of Mathematics at the University of California, San Diego. He is a member of SIAM and co-author of Classical Control Using H-infinity Methods: Theory, Optimization, and Design (SIAM, 1998) and Classical Control Using H-infinity Methods: An Introduction to Design (SIAM, 1998). He is also an Associate Editor of the SIAM Journal on Control and Optimization. Matthew R. James is in the Department of Engineering at the Australian National University. Both authors are Associate Editors for the SIAM Journal on Control and Optimization.