Stochastic Control of Partially Observable Systems
Title | Stochastic Control of Partially Observable Systems PDF eBook |
Author | Alain Bensoussan |
Publisher | Cambridge University Press |
Pages | 364 |
Release | 1992-08-13 |
Genre | Mathematics |
ISBN | 052135403X |
These systems play an important role in many applications.
Stochastic Control of Partially Observable
Title | Stochastic Control of Partially Observable PDF eBook |
Author | Alain Bensoussan |
Publisher | |
Pages | 352 |
Release | 1992 |
Genre | |
ISBN |
Stochastic Control Theory
Title | Stochastic Control Theory PDF eBook |
Author | Makiko Nisio |
Publisher | Springer |
Pages | 263 |
Release | 2014-11-27 |
Genre | Mathematics |
ISBN | 4431551239 |
This book offers a systematic introduction to the optimal stochastic control theory via the dynamic programming principle, which is a powerful tool to analyze control problems. First we consider completely observable control problems with finite horizons. Using a time discretization we construct a nonlinear semigroup related to the dynamic programming principle (DPP), whose generator provides the Hamilton–Jacobi–Bellman (HJB) equation, and we characterize the value function via the nonlinear semigroup, besides the viscosity solution theory. When we control not only the dynamics of a system but also the terminal time of its evolution, control-stopping problems arise. This problem is treated in the same frameworks, via the nonlinear semigroup. Its results are applicable to the American option price problem. Zero-sum two-player time-homogeneous stochastic differential games and viscosity solutions of the Isaacs equations arising from such games are studied via a nonlinear semigroup related to DPP (the min-max principle, to be precise). Using semi-discretization arguments, we construct the nonlinear semigroups whose generators provide lower and upper Isaacs equations. Concerning partially observable control problems, we refer to stochastic parabolic equations driven by colored Wiener noises, in particular, the Zakai equation. The existence and uniqueness of solutions and regularities as well as Itô's formula are stated. A control problem for the Zakai equations has a nonlinear semigroup whose generator provides the HJB equation on a Banach space. The value function turns out to be a unique viscosity solution for the HJB equation under mild conditions. This edition provides a more generalized treatment of the topic than does the earlier book Lectures on Stochastic Control Theory (ISI Lecture Notes 9), where time-homogeneous cases are dealt with. Here, for finite time-horizon control problems, DPP was formulated as a one-parameter nonlinear semigroup, whose generator provides the HJB equation, by using a time-discretization method. The semigroup corresponds to the value function and is characterized as the envelope of Markovian transition semigroups of responses for constant control processes. Besides finite time-horizon controls, the book discusses control-stopping problems in the same frameworks.
On the Existence of Optimal Policies for Linear Partially Observable Stochastic Control
Title | On the Existence of Optimal Policies for Linear Partially Observable Stochastic Control PDF eBook |
Author | Masatoshi Fujisaki |
Publisher | |
Pages | 52 |
Release | 19?? |
Genre | Mathematical optimization |
ISBN |
Optimal Control of Partially Observable Stochastic Systems with an Exponential-of-integral Performance Index
Title | Optimal Control of Partially Observable Stochastic Systems with an Exponential-of-integral Performance Index PDF eBook |
Author | Alain Bensoussan |
Publisher | |
Pages | 23 |
Release | 1983 |
Genre | |
ISBN |
Measure-Valued Processes in the Control of Partially-Observable Stochastic Systems
Title | Measure-Valued Processes in the Control of Partially-Observable Stochastic Systems PDF eBook |
Author | Wendell H. Fleming |
Publisher | |
Pages | 30 |
Release | 1979 |
Genre | |
ISBN |
This paper is concerned with the optimal control of continuous-time Markov processes. The admissible control laws are based on white-noise corrupted observations of a function on the state processes. A 'separated' control problem is introduced, whose states are probability measures on the original state space. The original and separated control problems are related via the nonlinear filter equation. The existence of a minimum for the separated problem is established. Under more restrictive assumptions it is shown that the minimum expected cost for the separated problem equals the infimum of expected costs for the original problem with partially observed states.
Feedback Strategies for Partially Observable Stochastic Systems
Title | Feedback Strategies for Partially Observable Stochastic Systems PDF eBook |
Author | Yaakov Yavin |
Publisher | Springer |
Pages | 248 |
Release | 1983 |
Genre | Mathematics |
ISBN |