Conditional Markov processes and Their Application to the Theory of Optimal Control

Alternate Titles

• Uslovnye markovskie prot͡s︡essy

Description

The adoption of the state space description of systems has led to substantial advances in optimal control and filtering theory in recent years. This volume, will be appreciated only by those specialists who are working in the domain of applied statistics and control engineering and by a few advanced graduate students with mathematical background. Nevertheless the problems considered are mathematically rigorous, interesting and practically important, and this book shall reward the perseverance of any reader with the necessary mathematical background. Stratonovich has been a major influence in the development of the subject.

Description

Using this description the statex(j, w) of the system and the (noisy) observation y{j, w) of thestate are Markov Processes. The basic problem in optimalfiltering becomes the derivation of equations describing theevolution of the probability distribution of x(j) conditionalin the available observations y{j), re[t0, t], or the evolutionof some risk function determined by the posterior distribution.The optimal control problem becomes the determination ofa realisable control (function of t and the available observa-tions) to minimise an expected risk. To deal rigorouslywith these continuous-time conditional Markov processesrequires the development of mathematical tools of the samekind as those available for Markov processes, and this is oneof the main intentions of the present volume.

Subjects

Series Statement

• Modern analytic and computational methods in science and mathematics

Other Editions

• Conditional Markov processes and Their Application to the Theory of Optimal ControlHardcoverAmerican Elsevier Pub. Co.1968-01-01
• Conditional Markov Processes and Their Application to the Theory of Optimal ControlAmerican Elsevier Pub. Co.1968-01-01
• Conditional Markov processes and their application to the theory of optimal controlElsevier1968-01-01