عنوان

Stochastic Systems The Mathematics of Filtering and Identification and Applications:

9400985460

9789400985469

b594005

Stochastic Systems The Mathematics of Filtering and Identification and Applications:

[Book]

Proceedings of the NATO Advanced Study Institute Held at Les Arcs, Savoie, France, J.

Hazewinkel, Michiel

Springer Verlag

2013

1. The Main Themes of the ASI "Stochastic Systems": The Mathematics of Filtering and Identification and Applications.- 1.1. Introduction: An Annotated Navigation Chart and Sketch of the Main Themes in This Volume and their Interrelations.- 2. Introductory Tutorial Material for Identification and Filtering Problems.- 2.1. The LQG-Problem: A Brief Tutorial Exposition.- 2.2. A Tutorial Article on the Ito Integral and the Stochastic Calculus.- 2.3. An Introduction to Nonlinear Filtering.- 2.4. A Tutorial Introduction to Differentiable Manifolds and Vector Fields.- 2.5. A Short Tutorial on Lie Algebras.- 3. Foundations of Stochastic Systems and Modeling Issues and Applications.- 3.1. Mathematical Models of Chemical Reactions.- 3.2. Qualitative Theory of Real Noise Excited Systems.- 3.3. Stochastic Models of Computer Networks.- 3.4. State Space Models for Gaussian Stochastic Processes.- 3.5. Ergodic Theory of Linear Parameter-excited systems.- 4. Identification.- 4.1. System Identification.- 4.2. Recursive Identification.- 4.3. The Properties of the Parameterization of ARMAX Systems in Structural Specification and their Relevance for Estimation.- 4.4. Tests of Adequacy for ARMA Models and Tests of Separated Hypotheses.- 4.5. Some Nonlinear Filtering Problems Arising in Recursive Identification.- 5. Linear Filtering.- 5.1. Some Topics in Linear Estimation.- 5.2. Inverse Scattering and Linear Prediction, the Time Continuous Case.- 5.3. Harmonic Analysis and the Mathematics behind Filtering and Prediction (d'apres P. Cartier d'apres N. Wiener, A. N. Kolmogorov) Abstract only.- 6. Adaptive Control.- 6.1. Deterministic and Stochastic Model Reference Adaptive Control.- 6.2. Adaptive Control of Systems Subject to a Class of Random Parameter Variations and Disturbances.- 6.3. On Stochastic Self-Tuning Methods.- 7. Nonlinear Filtering.- 7.1. Nonlinear systems and Nonlinear Estimation Theory.- 7.2. Non-linear Filtering and Stochastic Mechanics.- 7.3. Pathwise Non-linear Filtering.- 7.4. Non-linear Filtering, Prediction and Smoothing.- 7.5. Estimation Problems with Low Dimensional Filters.- 7.6. Group Invariance Methods in Nonlinear Filtering of Diffusion Processes.- 7.7. Asymptotic Bounds on the Minimal Error of Non-linear Filtering.- 7.8. An Approximation to Optical Nonlinear Filtering with Discontinuous Observations.- 7.9. Some Results and Speculations on the Role of Lie Algebras in Filtering.- 7.10. Deterministic Estimation and Asymptotic Stochastic Estimation.- 7.11. Non-linear Filtering Equation and a Problem of Parametric Estimation.- 7.12. Regularity of Conditional Laws in Non-linear Filtering Theory and Stochastic Calculus of Variations.- 7.13. Finite Dimensional Estimation Algebras in Nonlinear Filtering.- 7.14. Rigorous Results on the Cubic Sensor Problem.- 7.15. A Footnote to the Papers which Prove the Non-Existence of Finite Dimensional Filters.- List of Other Contributed Papers.- List of Participants.

Hazewinkel, Michiel

Hazewinkel, Michiel

Williams, J.C.

[Book]

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