Estimation and control of dynamical systems. (2018)

• Record Type: Book
• Further Information: Note: Alain Bensoussan.
• Authors: Bensoussan, Alain
• Contents: Intro; Contents; 1 Introduction; 2 State Representation of Linear Dynamical Systems; 2.1 General Description; 2.1.1 The Model: Internal Representation; 2.1.2 Fundamental Matrix; 2.1.3 External Representation; 2.1.4 Stationary Case; 2.2 Controllability; 2.3 Stability; 2.3.1 Definition; 2.3.2 Stabilizability; 2.4 Observability; 2.4.1 Definition; 2.4.2 Observers; 3 Optimal Control of Linear Dynamical Systems; 3.1 Finite Horizon Problem; 3.1.1 Solution of the Problem; 3.1.2 Proof of Theorem; 3.2 Infinite Horizon Problem; 3.3 Positivity; 3.3.1 Positive Real Lemma; 3.3.2 Characterization of P 4 Estimation Theory4.1 Deterministic Approach; 4.2 Bayesian Approach; 4.2.1 Definition; 4.2.2 Examples; 4.3 Good Estimators; 4.3.1 Properties; 4.3.2 The Cramér-Rao Inequality; 4.4 Minimum Mean Square Estimator; 4.4.1 Definition; 4.4.2 Properties; 4.4.3 MMSE for Gaussian Variables; 4.5 Minimum Variance Linear Estimator; 4.5.1 Definition; 4.5.2 Necessary and Sufficient Condition; 4.5.3 Least Squares Estimator; 4.5.4 A Particular Structure; 4.6 The Maximum Likelihood Method; 4.6.1 Definition; 4.6.2 Properties; 4.6.3 Maximum Posterior Probability Estimators; 4.7 Dynamic Models 4.7.1 Fixed Parameter4.7.2 Recursive Formulas; 4.7.3 Dual Formulation; 4.7.4 The Gaussian Case; 4.7.5 The Kalman Filter in Discrete Time; 4.8 Appendix; 4.8.1 Preliminaries; 4.8.2 Consistency; 4.8.3 Asymptotic Normality; 5 Further Techniques of Estimation; 5.1 Generalized Linear Models; 5.2 Examples; 5.2.1 The Gaussian Distribution; 5.2.2 The Exponential Distribution; 5.2.3 The Poisson Distribution; 5.2.4 The Binomial Distribution; 5.2.5 The Gamma Distribution; 5.2.6 The Weibull Distribution; 5.2.7 Nonlinear Gaussian Model; 5.2.8 Canonical Links; 5.3 MLE for Generalized Linear Models 5.3.1 Statement of the Problem and Notation5.3.2 Examples; 5.3.3 Consistency; 5.3.4 Further Consistency Estimates; 5.3.5 Asymptotic Normality; 5.4 The Vector Case; 5.4.1 Notation and Preliminaries; 5.4.2 MLE Estimate; 5.4.3 The Gaussian Case; 5.4.4 Recursivity; 5.4.5 Examples; 5.4.5.1 The Binomial Distribution; 5.4.5.2 The Poisson Distribution; 5.4.5.3 The Gamma Distribution; 5.5 Dynamic Models; 5.5.1 General Bayesian Approach; 5.5.1.1 Preliminaries; 5.5.1.2 Recurrence Formulas; 5.5.2 Dynamic GLM; 5.5.2.1 Conditional Probability; 5.5.2.2 The First Two Moments; 5.5.3 Applications 5.5.3.1 Kalman Filter5.5.3.2 The Poisson Distribution; 5.5.3.3 The Kalman Filter Revisited; 5.5.4 First Two Moments Revisited; 5.5.4.1 General Ideas; 5.5.4.2 Model and Approximation; 5.5.4.3 Further Approximation; 5.5.5 Example of a Beta Model; 5.6 Seasonal Factors; 5.6.1 Setting of the Problem; 5.6.2 Moving Averages; 5.6.3 Exponential Smoothing; 5.6.4 Estimation of the Trend; 5.6.5 Holt-Winters Formulas with Seasonality; 6 Complements on Probability Theory; 6.1 Probability Concepts; 6.1.1 Review of Basic Probability Concepts; 6.1.2 Conditional Expectation; 6.2 Stochastic Processes
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2018
• Extent: 1 online resource (xii, 547 pages)
• Subjects: 515/.39; Mathematics; Dynamics; MATHEMATICS / Calculus; MATHEMATICS / Mathematical Analysis; Dynamics; Mathematics -- Calculus; Mathematics -- Probability & Statistics -- General; Calculus of variations; Probability & statistics; Differentiable dynamical systems; Mathematical optimization; Distribution (Probability theory); Mathematics -- Mathematical Analysis; Nonlinear science; Electronic books
• Languages: English
• ISBNs: 9783319754567; 3319754564
• Related ISBNs: 9783319754550; 3319754556
• Notes: Note: Includes bibliographical references.; Note: Online resource; title from PDF title page (SpringerLink, viewed May 30, 2018).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.