عنوان

Mathematical Control Theory

(Number (ISBN

9781461214168

(Number (ISBN

9781461271369

Number

b402756

Title Proper

Mathematical Control Theory

General Material Designation

[Book]

First Statement of Responsibility

edited by J. Baillieul, J. C. Willems.

Place of Publication, Distribution, etc.

New York, NY :

Name of Publisher, Distributor, etc.

Imprint: Springer,

Date of Publication, Distribution, etc.

1999.

Text of Note

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.

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Text of Note

Itisunclearwhenexactlythefieldofmathematicalelectricalengineeringwasborn, butthereisnodoubtthatKolmogoroff,Krein,Shannon,andWienergavethefielda definitiveforminthelatefortiesandearlyfiftiesthroughtheirworkonfilteringand prediction theory, information theory, and operatortheory. Kalman's introduction in the early sixties of the dynamical viewpoint in filtering and control-with its associatedmethodsofdifferentialequationsandMarkovprocesses-gavethefield new strength and vigor. The best work in systems and control theory makes it clear that the creative modeling ofphenomenaand theconceptualizationofsystems using mathematics and the subsequentmathematical analysis ofthese models to get a deeper under standing ofthe phenomenaare whatis central to the field. To paraphrase Galileo, the bookofthe engineered world is often written in the language ofhighermath ematics. Roger Brockett has been a remarkable contributor to this tradition of mathematical engineering. This book bears testimony to his creativity, virtuosity, and intellectual integrity. It gives me great pleasure to see the exploration of his ideasinthepapersthathavebeenwrittenforthisvolume.Assomebodywhoknows Roger Brockett's work well, Ican see his invisible touch throughout the book. One oftheprivileges ofbeing associatedwith auniversity is the satisfactionof seeinggraduate students develop their potential and becomecreative scientists in theirownright.Ihaveknownalltheauthorsformanyyears, somewhiletheywere stillgraduatestudents,andthereforeitisdoublyapleasuretoseetheircontributions in this volume. This is an auspicious momentin Roger's life. Notoften will hehave the oppor tunity to look both forwards and backwards, to take stockofthe past and predict the future. Itremains for me to wish that he will continue his creative life for the nextsixty years.

International Standard Book Number

9781461271369

Title

Springer eBooks

Mathematical optimization.

Mathematics.

Baillieul, J.

Willems, J. C.

SpringerLink (Online service)

Date of Transaction

20190307155300.0

Electronic name

[Book]

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