Nonlinear control design : By Riccardo Marino and Patrizio Tomei

Nonlinear control theory has received considerable attention m the last decades. As a result, there exists nowadays a sophisticated framework using (differential) geometric methods for dealmg with a large number of controller design problems. The book under review, Nonlinear Control Design, Geometric, Adaptiue and Robust presents according to the back cover of the book “A self-contained introduction to nonlinear feedback control design for contmuous time, finite-dimensional uncertain systems. It deals with nonlinear systems affected by uncertainties such as unknown constant parameters, time-varying dtsturbances and uncertain nonlinearities. Both state feedback and output feedback are considered .“. The book consists of seven chapters and two appendices. Chapter 1. the Introductton, presents in a lucid manner what the book is about, By means of simple instructive examples an illustration is given of possible controller designs, such as state feedback controllers, output feedback controllers or their adaptive modifications. The Introduction also describes models of a number of real-world physical systems, such as an induction motor, a rigid robot. a rigid body, a synchronous generator, a synchronous motor and others. These systems are used in the following chapters as to illustrate the various control schemes. Following the Introduction, the material of the book is organized in two parts. First, Chapters 24, all deal with state feedback controllers, whereas Chapters 5-7 form their counterparts in which observers and output feedback controllers are considered. Throughout the book the authors have concentrated on single input and, where relevant, single output affine nonlinear control systems. i.e. 1 =f(x) + g(x)u, y = h(x). with at the end of each chapter a short resume on how to deal with the multtvariable case. Chapter 2 deals with the feedback linearization and the partial feedback linearization problem. That is, differential geometric conditions are derived such that under application of a suitable coordinate transformation 3 = cp(.x) and suitable state feedback u = x(x) + p(x)o the system becomes linear f = ‘43 + br, or partially linear. which means the system in the new coordinates is a cascade of a lower-dimensional linear system and nonlinear system. In particular. m the latter case the stabtlization for partially linear triangular form nonlinear systems is described. The recursive procedure for deriving the stabilizing feedback sometimes called (integrator) backstepping. Krstic et a/. (1995) is a very useful tool in feedback stabilization. Chapter 3 IS entitled Adaptive Feedback Linearization, but also contains a study of feedback stabilization of linearizable systems m the presence of structured (‘matched’) uncertainties. This mcludes robust stabilization and a self-tuning regulator, all on the basis of either static or dynamic state feedback. Once the unknown parameters enter in such a way that the parametrized system admits a triangular form, which for ‘frozen’ parameter values is equivalent to feedback hnearizabihty of the ‘frozen’ system, then also the adaptive feedback linearizatton problem is solved. In Chapter 4 the problem of output feedback tracking 1s considered. Typcially. the main ingredient to address the track-