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 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
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Discrete Time Processes
Continuous Time Processes
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absolutely continuous Applying assumption asymptotically Borel characteristic function Cl.S completes the proof conditional mathematical expectation Consider convergence Corollary corresponding defined Definition density deterministic distribution function equivalently estimate example exists finite formula function f Gaussian given hence holds implies independent random variables inequality Itó Lebesgue integral Lemma is proven lim sup linear Markov process Markov property martingale matrix mean-square monotonically n-CO noise nonlinear nonnegative o-algebras optimal control parameter Poznyak probability space problem procedure proves random process random vectors relation result right-hand side robust optimal robust optimal control satisfying scalar sequence sigma-algebra solution stochastic differential equations stochastic integral stochastic process Stratonovich submartingale taking into account Theorem is proven uniform integrability Wiener process xn+1