Geometric Control of Mechanical Systems: Modeling, Analysis, and Design for Simple Mechanical Control Systems (Texts in Applied Mathematics, 49)

✍ Scribed by Francesco Bullo, Andrew D. Lewis

• Publisher: Springer
• Year: 2004
• Tongue: English
• Leaves: 955
• Edition: 2004
• Category: Library

✦ Synopsis

The area of analysis and control of mechanical systems using differential geometry is flourishing.

This book collects many results over the last decade and provides a comprehensive introduction to the area.

✦ Table of Contents

Preface
Contents
Part I Modeling of mechanical systems
1 Introductory examples and problems
2 Linear and multilinear algebra
3 Differential geometry
4 Simple mechanical control systems
5 Lie groups, systems on groups, and symmetries
Part II Analysis of mechanical control systems
6 Stability
7 Controllability
8 Low-order controllability and kinematic reduction
9 Perturbation analysis
Part III A sampling of design methodologies
10 Linear and nonlinear potential shaping for stabilization
11 Stabilization and tracking for fully actuated systems
12 Stabilization and tracking using oscillatory controls
13 Motion planning for underactuated systems
A Time-dependent vector fields
B Some proofs
References
Symbol index
Subject index
Supplementary Material
S1 Tangent and cotangent bundle geometry
S2 Controllability
S3 Linearization and stabilization of relative equilibria
S4 Optimal control theory
S5 Mathematica packages
References
Symbol index
A guide to examples and exercises
Errata and addenda