Mathematical Control Theory / edited by J. Baillieul, J. C. Willems
| データ種別 | 電子ブック |
|---|---|
| 出版者 | New York, NY : Springer New York : Imprint: Springer |
| 出版年 | 1999 |
| 本文言語 | 英語 |
| 大きさ | XXXII, 360 p : online resource |
書誌詳細を非表示
| 内容注記 | 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 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 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 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 |
|---|---|
| 著者標目 | Baillieul, J. editor Willems, J. C. editor SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Calculus of variations FREE:Mathematics FREE:Calculus of Variations and Optimal Control; Optimization |
| 分 類 | DC23:515.64 |
| 巻冊次 | ISBN:9781461214168 
|
| ISBN | 9781461214168 |
| URL | http://dx.doi.org/10.1007/978-1-4612-1416-8 |
目次／あらすじ