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Advanced Mathematical Tools for Automatic Control Engineers: Volume 2
Stochastic Systems
- 1st Edition - August 13, 2009
- Author: Alexander S. Poznyak
- Language: English
- Hardback ISBN:9 7 8 - 0 - 0 8 - 0 4 4 6 7 3 - 8
- eBook ISBN:9 7 8 - 0 - 0 8 - 0 9 1 4 0 3 - 9
Advanced Mathematical Tools for Automatic Control Engineers, Volume 2: Stochastic Techniques provides comprehensive discussions on statistical tools for control engineers… Read more
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Request a sales quoteAdvanced Mathematical Tools for Automatic Control Engineers, Volume 2: Stochastic Techniques provides comprehensive discussions on statistical tools for control engineers.
The book is divided into four main parts. Part I discusses the fundamentals of probability theory, covering probability spaces, random variables, mathematical expectation, inequalities, and characteristic functions. Part II addresses discrete time processes, including the concepts of random sequences, martingales, and limit theorems. Part III covers continuous time stochastic processes, namely Markov processes, stochastic integrals, and stochastic differential equations. Part IV presents applications of stochastic techniques for dynamic models and filtering, prediction, and smoothing problems. It also discusses the stochastic approximation method and the robust stochastic maximum principle.
- Provides comprehensive theory of matrices, real, complex and functional analysis
- Provides practical examples of modern optimization methods that can be effectively used in variety of real-world applications
- Contains worked proofs of all theorems and propositions presented
Undergraduate, graduate, research students of automotive control engineering, aerospace engineering, mechanical engineering and control in Chemical engineering.
Preface
Notations and Symbols
List of Figures
List of Tables
Part I Basics of Probability
Chapter 1 Probability Space
1.1 Set operations, algebras and sigma-algebras
1.2 Measurable and probability spaces
1.3 Borel algebra and probability measures
1.4 Independence and conditional probability
Chapter 2 Random Variables
2.1 Measurable functions and random variables
2.2 Transformation of distributions
2.3 Continuous random variables
Chapter 3 Mathematical Expectation
3.1 Definition of mathematical expectation
3.2 Calculation of mathematical expectation
3.3 Covariance, correlation and independence
Chapter 4 Basic Probabilistic Inequalities
4.1 Moment-type inequalities
4.2 Probability inequalities for maxima of Partial sums
4.3 Inequalities between moments of sums and summands
Chapter 5 Characteristic Functions
5.1 Definitions and examples
5.2 Basic properties of characteristic functions
5.3 Uniqueness and inversion
Part II Discrete Time Processes
Chapter 6 Random Sequences
6.1 Random process in discrete and continuous time
6.2 Infinitely often events
6.3 Properties of Lebesgue integral with probabilistic measure
6.4 Convergence
Chapter 7 Martingales
7.1 Conditional expectation relative to a sigma-algebra
7.2 Martingales and related concepts
7.3 Main martingale inequalities
7.4 Convergence
Chapter 8 Limit Theorems as Invariant Laws
8.1 Characteristics of dependence
8.2 Law of large numbers
8.3 Central limit theorem
8.4 Logarithmic iterative law
Part III Continuous Time Processes
Chapter 9 Basic Properties of Continuous Time Processes
9.1 Main definitions
9.2 Second-order processes
9.3 Processes with orthogonal and independent increments
Chapter 10 Markov Processes
10.1 Definition of Markov property
10.2 Chapman–Kolmogorov equation and transition function
10.3 Diffusion processes
10.4 Markov chains
Chapter 11 Stochastic Integrals
11.1 Time-integral of a sample-path
11.2 λ-stochastic integrals
11.3 The Itô stochastic integral
11.4 The Stratonovich stochastic integral
Chapter 12 Stochastic Differential Equations
12.1 Solution as a stochastic process
12.2 Solutions as diffusion processes
12.3 Reducing by change of variables
12.4 Linear stochastic differential equations
Part IV Applications
Chapter 13 Parametric Identification
13.1 Introduction
13.2 Some models of dynamic processes
13.3 LSM estimating
13.4 Convergence analysis
13.5 Information bounds for identification methods
13.6 Efficient estimates
13.7 Robustification of identification procedures
Chapter 14 Filtering, Prediction and Smoothing
14.1 Estimation of random vectors
14.2 State-estimating of linear discrete-time processes
14.3 State-estimating of linear continuous-time processes
Chapter 15 Stochastic Approximation
15.1 Outline of chapter
15.2 Stochastic nonlinear regression
15.3 Stochastic optimization
Chapter 16 Robust Stochastic Control
16.1 Introduction
16.2 Problem setting
16.3 Robust stochastic maximum principle
16.4 Proof of Theorem 16.1
16.5 Discussion
16.6 Finite uncertainty set
16.7 Min-Max LQ-control
16.8 Conclusion
Bibliography
Index
- No. of pages: 567
- Language: English
- Edition: 1
- Published: August 13, 2009
- Imprint: Elsevier Science
- Hardback ISBN: 9780080446738
- eBook ISBN: 9780080914039
AP
Alexander S. Poznyak
Alexander Poznyak is Professor and Department Head of Automatic Control at CINESTAV of IPN in Mexico. He graduated from Moscow Physical Technical Institute in 1970, and earned Ph.D. and Doctoral Degrees from the Institute of Control Sciences of Russian Academy of Sciences in 1978 and 1989, respectively. He has directed 43 Ph.D. theses, and published more than 260 papers and 14 books.
Affiliations and expertise
Professor and Department Head of Automatic Control, CINESTAV of IPN, MexicoRead Advanced Mathematical Tools for Automatic Control Engineers: Volume 2 on ScienceDirect