Control and nonlinearity / Jean-Michel Coron.

Format:

Book

Author/Creator:

Coron, Jean-Michel, 1956- author.

Series:

Mathematical surveys and monographs ; no. 136.

Mathematical surveys and monographs, 0076-5376 ; volume 136

Language:

English

Subjects (All):

Control theory.

Nonlinear control theory.

Physical Description:

1 online resource (442 p.)

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2007]

Summary:

This book presents methods to study the controllability and the stabilization of nonlinear control systems in finite and infinite dimensions. The emphasis is put on specific phenomena due to nonlinearities. In particular, many examples are given where nonlinearities turn out to be essential to get controllability or stabilization. Various methods are presented to study the controllability or to construct stabilizing feedback laws. The power of these methods is illustrated by numerous examples coming from such areas as celestial mechanics, fluid mechanics, and quantum mechanics. The book is addressed to graduate students in mathematics or control theory, and to mathematicians or engineers with an interest in nonlinear control systems governed by ordinary or partial differential equations.

Contents:

""2.7. Singular optimal control: A linear 1-D parabolic-hyperbolic example""""2.8. Bibliographical complements""; ""Part 2. Controllability of nonlinear control systems""; ""Chapter 3. Controllability of nonlinear systems in finite dimension""; ""3.1. The linear test""; ""3.2. Iterated Lie brackets and the Lie algebra rank condition""; ""3.3. Controllability of drift less control affine systems""; ""3.4. Bad and good iterated Lie brackets""; ""3.5. Global results""; ""3.6. Bibliographical complements""; ""Chapter 4. Linearized control systems and fixed-point methods""

""4.1. The Linear test: The regular case""""4.2. The linear test: The case of loss of derivatives""; ""4.3. Global controllability for perturbations of linear controllable systems""; ""Chapter 5. Iterated Lie brackets""; ""Chapter 6. Return method""; ""6.1. Description of the method""; ""6.2. Controllability of the Euler and Navier-Stokes equations""; ""6.3. Local controllability of a 1-D tank containing a fluid modeled by the Saint-Venant equations""; ""Chapter 7. Quasi-static deformations""; ""7.1. Description of the method""; ""7.2. Application to a semilinear heat equation""

""10.2. Direct applications to the stabilization of finite-dimensional control systems""""10.3. Gramian and stabilization""; ""Chapter 11. Stabilization of nonlinear control systems in finite dimension""; ""11.1. Obstructions to stationary feedback stabilization""; ""11.2. Time-varying feedback laws""; ""11.3. Output feedback stabilization""; ""11.4. Discontinuous feedback laws""; ""Chapter 12. Feedback design tools""; ""12.1. Control Lyapunov function""; ""12.2. Damping feedback laws""; ""12.3. Homogeneity""; ""12.4. Averaging""; ""12.5. Backstepping""; ""12.6. Forwarding""

""12.7. Transverse functions""

Notes:

Description based upon print version of record.

Includes bibliographical references (pages 397-420) and index.

Description based on print version record.

ISBN:

1-4704-1363-9