Robust control of nonlinear systems with input unmodeled dynamics

Krstić, Miroslav; Sun, Jing; Kokotović, P.V.

doi:10.1109/9.506250

Cited by 123 publications

(71 citation statements)

References 16 publications

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“…A gain margin introduced by Sontag [102] deals with nonlinear additive uncertainty. The small gain stability margins, which are implicit in the recent global stability results by Krstić, Sun, and Kokotović [62] and Praly and Wang [89], can be an alternative to our passivity based margins.…”

Section: Notes and Referencesmentioning

confidence: 99%

Constructive Nonlinear Control

Sepulchre

Janković

Kokotović

1997

Communications and Control Engineering

1,682

1,088

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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.

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Section: Notes and Referencesmentioning

confidence: 99%

Constructive Nonlinear Control

Sepulchre

Janković

Kokotović

1997

Communications and Control Engineering

1,682

1,088

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“…In these works the small gain theorem is combined with backstepping to deal with unstructured uncertainty. This new approach is based on the input to state stability (ISS) concept introduced by Sontag (1995) and was presented in Jiang et al (1994), Krstić et al (1996), Praly and Wang (1996) and Jiang and Mareels (1997). However, these designs require the unmodelled dynamics to have bounded ISS-gain.…”

Section: Feedback Linearizationmentioning

confidence: 99%

“…Finally, in Kokotović and Arcak (2001) the small gain and strict passivity conditions were relaxed by combining dynamic nonlinear normalizing design of Krstić et al (1996) with the L g V -backstepping scheme in Arcak et al (1999).…”

Section: Feedback Linearizationmentioning

confidence: 99%

Robustness analysis of nonlinear systems with feedback linearizing control

Al-Gburi

French

Freeman

2013

52nd IEEE Conference on Decision and Control

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The feedback linearization approach is a control method which employs feedback to stabilize systems containing nonlinearities. In order to accomplish this, it assumes perfect knowledge of the system model to linearize the input-output relationship. In the absence of perfect system knowledge, modelling errors inevitably affect the performance of the feedback controller. This thesis introduces a design and analysis approach for robust feedback linearizing controllers for nonlinear systems. This approach takes into account these model errors and provides robustness margins to guarantee the stability of feedback linearized systems.Based on robust stability theory, two important tools, namely the small gain theorem and the gap metric, are used to derive and validate robustness and performance margins for the feedback linearized systems. It is shown that the small gain theorem can provide unsatisfactory results, since the stability conditions found using this approach require the nonlinear plant to be stable. However, the gap metric approach is shown to yield general stability conditions which can be applied to both stable and unstable plants.These conditions show that the stability of the linearized systems depends on how exact the inversion of the plant nonlinearity is, within the nonlinear part of the controller. Furthermore, this thesis introduces an improved robust feedback linearizing controller which can classify the system nonlinearity into stable and unstable components and preserve the stabilizing action of the inherently stabilizing nonlinearities in the plant, cancelling only the unstable nonlinear part of the plant. Using this controller, it is shown that system stability depends on the bound on the input nonlinear component of the plant and how exact the inversion of the unstable nonlinear of the plant is, within the nonlinear part of the controller.

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“…This naturally points to the use of backstepping methods, first developed by Kokotović [21,22,25], in the context of constructing control barrier functions.…”

Section: Introductionmentioning

confidence: 99%

Control barrier function based quadratic programs with application to bipedal robotic walking

Hsu

Ames

2015

2015 American Control Conference (ACC)

172

122

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This thesis presents a methodology for the development of control barrier functions (CBFs) through a backstepping inspired approach. Given a set defined as the superlevel set of a function, h, the main result is a constructive means for generating control barrier functions that guarantee forward invariance of this set. In particular, if the function defining the set has relative degree n, an iterative methodology utilizing higher order derivatives of h provably results in a control barrier function that can be explicitly derived. To demonstrate these formal results, they are applied in the context of bipedal robotic walking. Physical constraints, e.g., joint limits, are represented by control barrier functions and unified with control objectives expressed through control Lyapunov functions (CLFs) via quadratic program (QP) based controllers. The end result is the generation of stable walking satisfying physical realizability constraints for a model of the bipedal robot AMBER2.

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Robust control of nonlinear systems with input unmodeled dynamics

Cited by 123 publications

References 16 publications

Constructive Nonlinear Control

Constructive Nonlinear Control

Robustness analysis of nonlinear systems with feedback linearizing control

Control barrier function based quadratic programs with application to bipedal robotic walking

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