Advanced Mathematical Tools for Automatic Control Engineers: Volume 2: Stochastic Systems

Advanced 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 analysisProvides practical examples of modern optimization methods that can be effectively used in variety of real-world applicationsContains worked proofs of all theorems and propositions presented

Preface; Introduction; Probability Space; Random Variables; Mathematical Expectation; Random Sequences; Conditional Mathematical Expectation; Discrete Martingales; Large Number Laws; Characteristic Functions and the Central Limit Theorem; Iterative Logarithmic Law; Stochastic Differential Equations; Wiener and Kalman Filtering; Parametric Identification under Stochastic Measurements; Stochastic Optimization; Finite Markov Chains, Discrete Events and Elements of Queering Theory