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Mathematical Control Theory

Bibliographic Details
Other Authors: Baillieul, John B. (Editor), Willems, J.C. (Editor)
Format: eBook
Language:English
Published: New York, NY Springer New York 1999, 1999
Edition:1st ed. 1999
Subjects:
Calculus Of Variations And Optimization
Mathematical Optimization
Calculus Of Variations
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 2.14 Estimation Algebra of the Identification Problem
  • 2.15 Solutions to the Riccati P.D.E
  • 2.16 Filters with Non-Gaussian Initial Conditions
  • 2.17 Back to the Beginning
  • 2.18 Acknowledgement
  • 3 Feedback Linearization
  • 3.1 Introduction
  • 3.2 Linearization of a Smooth Vector Field
  • 3.3 Linearization of a Smooth Control System by Change-of-State Coordinates
  • 3.4 Feedback Linearization
  • 3.5 Input-Output Linearization
  • 3.6 Approximate Feedback Linearization
  • 3.7 Normal Forms of Control Systems
  • 3.8 Observers with Linearizable Error Dynamics
  • 3.9 Nonlinear Regulation and Model Matching
  • 3.10 Backstepping
  • 3.11 Feedback Linearization and System Inversion
  • 3.12 Conclusion
  • 4 On the Global Analysis of Linear Systems
  • 4.1 Introduction
  • 4.2 The Geometry of Rational Functions
  • 4.3 Group Actions and the Geometry of Linear Systems
  • 4.4 The Geometry of Inverse Eigenvalue Problems
  • 4.5 Nonlinear Optimization on Spaces of Systems
  • 7.2 Variational Problems with Constraints and Optimal Control
  • 7.3 Invariant Optimal Problems on Lie Groups
  • 7.4 Sub-Riemannian Spheres—The Contact Case
  • 7.5 Sub-Riemannian Systems on Lie Groups
  • 7.6 Heavy Top and the Elastic Problem
  • 7.7 Conclusion
  • 8 Optimal Control, Optimization, and Analytical Mechanics
  • 8.1 Introduction
  • 8.2 Modeling Variational Problems in Mechanics and Control
  • 8.3 Optimization
  • 8.4 Optimal Control Problems and Integrable Systems
  • 9 The Geometry of Controlled Mechanical Systems
  • 9.1 Introduction
  • 9.2 Second-Order Generalized Control Systems
  • 9.3 Flat Systems and Systems with Flat Inputs
  • 9.4 Averaging Lagrangian and Hamiltonian Systems with Oscillatory Inputs
  • 9.5 Stability and Flatness in Mechanical Systems with Oscillatory Inputs
  • 9.6 Concluding Remarks
  • 1 Path Integrals and Stability
  • 1.1 Introduction
  • 1.2 Path Independence
  • 1.3 Positivity of Quadratic Differential Forms
  • 1.4 Lyapunov Theory for High-Order Differential Equations
  • 1.5 The Bezoutian
  • 1.6 Dissipative Systems
  • 1.7 Stability of Nonautonomous Systems
  • 1.8 Conclusions
  • 1.9 Appendixes
  • 2 The Estimation Algebra of Nonlinear Filtering Systems
  • 2.1 Introduction
  • 2.2 The Filtering Model and Background
  • 2.3 Starting from the Beginning
  • 2.4 Early Results on the Homomorphism Principle
  • 2.5 Automorphisms that Preserve Estimation Algebras
  • 2.6 BM Estimation Algebra
  • 2.7 Structure of Exact Estimation Algebra
  • 2.8 Structure of BM Estimation Algebras
  • 2.9 Connection with Metaplectic Groups
  • 2.10 Wei-Norman Representation of Filters
  • 2.11 Perturbation Algebra and Estimation Algebra
  • 2.12 Lie-Algebraic Classification of Maximal Rank Estimation Algebras
  • 2.13 Complete Characterization of Finite-Dimensional Estimation Algebras
  • 5 Geometry and Optimal Control
  • 5.1 Introduction
  • 5.2 From Queen Dido to the Maximum Principle
  • 5.3 Invariance, Covariance, and Lie Brackets
  • 5.4 The Maximum Principle
  • 5.5 The Maximum Principle as a Necessary Condition for Set Separation
  • 5.6 Weakly Approximating Cones and Transversality
  • 5.7 A Streamlined Version of the Classical Maximum Principle
  • 5.8 Clarke’s Nonsmooth Version and the ?ojasiewicz Improvement
  • 5.9 Multidifferentials, Flows, and a General Version of the Maximum Principle
  • 5.10 Three Ways to Make the Maximum Principle Intrinsic on Manifolds
  • 5.11 Conclusion
  • 6 Languages, Behaviors, Hybrid Architectures, and Motion Control
  • 6.1 Introduction
  • 6.2 MDLe: A Language for Motion Control
  • 6.3 Hybrid Architecture
  • 6.4 Application of MDLe to Path Planning with Nonholonomic Robots
  • 6.5 PNMR: Path Planner for Nonholonomic Mobile Robots
  • 6.6 Conclusions
  • 7 Optimal Control, Geometry, and Mechanics
  • 7.1 Introduction

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