Constructive Nonlinear Control

Abstract

In this book several streams of nonlinear control theory are merged and directed towards a constructive solution of the feedback stabilization problem. Analytic, geometric and asymptotic concepts are assembled as design tools for a wide variety of nonlinear phenomena and structures. Differential-geometric concepts reveal important structural properties of nonlinear systems, but allow no margin for modeling errors. To overcome this deficiency, we combine them with analytic concepts of passivity, optimality and Lyapunov stability. In this way geometry serves as a guide for construction of design procedures, while analysis provides robustness tools which geometry lacks.Our main tool is passivity. As a common thread, it connects all the chapters of the book. Passivity properties are induced by feedback passivation designs. Until recently, these designs were restricted to weakly minimum phase systems with relative degree one. Our recursive designs remove these restrictions. They are applicable to wider classes of nonlinear systems characterized by feedback, feedforward, and interlaced structures.After the introductory chapter, the presentation is organized in two major parts. The basic nonlinear system concepts -passivity, optimality, and stability margins -are presented in Chapters 2 and 3 in a novel way as design tools. Most of the new results appear in Chapters 4, 5, and 6. For cascade systems, and then, recursively, for larger classes of nonlinear systems, we construct design procedures which result in feedback systems with optimality properties and stability margins.The book differs from other books on nonlinear control. It is more designoriented than the differential-geometric texts by Isidori [43] and Nijmeijer and Van der Schaft [84]. It complements the books by Krstić, Kanellakopoulos and Kokotović [61] and Freeman and Kokotović [26], by broadening the class of systems and design tools. The book is written for an audience of graduate students, control engineers, and applied mathematicians interested in control theory. It is self-contained and accessible with a basic knowledge of control theory as in Anderson and Moore [1], and nonlinear systems as in Khalil [56]. vii viii For clarity, most of the concepts are introduced through and explained by examples. Design applications are illustrated on several physical models of practical interest.The book can be used for a first level graduate course on nonlinear control, or as a collateral reading for a broader control theory course. Chapters 2, 3, and 4 are suitable for a first course on nonlinear control, while Chapters 5 and 6 can be incorporated in a more advanced course on nonlinear feedback design.

Flight Control Design Using Backstepping

“…P Since the derived control law does not rely on exact cancellation of the system nonlinearity f , intuition tells us that it should possess some robustness properties. This can be confirmed using the inverse optimality tools of (Sepulchre et al, 1997). It can be shown that for the system (13), the backstepping control law (18) minimizes the cost functional…”

Robustness of Aggregation in Networked Dynamical Systems

“…In general, to prove that an operator is (relaxed) co-coercive, it is possible to use a storage function approach assuming zero initial conditions (the interested reader is referred to the references [14] and [15]). Consider one of the systems in (17) and suppose that there exists a scalar function S (called incremental storage function) such that for every two input-output pairs σ 1 , y 1 and σ 2 , y 2 ,…”

Robust synchronization in networks of cyclic feedback systems

“…We now aim to write incremental dissipation inequalities satisfied by the incremental subsystems of the CFSs and refer the reader to [14], [15] for comprehensive treatments of passivity and the more general concept of dissipativity. We will show that in general these inequalities will be such that these subsystems are incrementally output semipassive: that is, they are incrementally output passive outside a ball centered on the origin |Πy i | = 0.…”