9780521611978

Stochastic Control of Partially Observable Systems

by
  • ISBN13:

    9780521611978

  • ISBN10:

    0521611970

  • Format: Paperback
  • Copyright: 2004-11-11
  • Publisher: Cambridge University Press
  • Purchase Benefits
  • Free Shipping On Orders Over $35!
    Your order must be $35 or more to qualify for free economy shipping. Bulk sales, PO's, Marketplace items, eBooks and apparel do not qualify for this offer.
  • Get Rewarded for Ordering Your Textbooks! Enroll Now
List Price: $62.00 Save up to $1.86
  • Buy New
    $60.14
    Add to Cart Free Shipping

    SPECIAL ORDER: 1-2 WEEKS

Supplemental Materials

What is included with this book?

  • The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

Summary

The problem of stochastic control of partially observable systems plays an important role in many applications. All real problems are in fact of this type, and deterministic control as well as stochastic control with full observation can only be approximations to the real world. This justifies the importance of having a theory as complete as possible, which can be used for numerical implementation. This book first presents those problems under the linear theory that may be dealt with algebraically. Later chapters discuss the nonlinear filtering theory, in which the statistics are infinite dimensional and thus, approximations and perturbation methods are developed.

Table of Contents

Preface vii
Linear filtering theory
1(18)
Filtering theory in discrete time
2(9)
Filtering theory in continuous time
11(8)
Optimal stochastic control for linear dynamic systems with quadratic payoff
19(34)
A brief review of the deterministic systems
20(3)
Optimal stochastic control with complete observation
23(6)
Optimal stochastic control with partial information: simplified approach
29(7)
Complete solution of the optimal stochastic control problem with partial information
36(17)
Optimal control of linear stochastic systems with an exponential-of-integral performance index
53(21)
The full observation case
54(5)
The partial observation case
59(13)
Additional remarks to the partial information case
72(2)
Non linear filtering theory
74(62)
Non linear filtering equation
76(13)
Uniqueness theorem
89(5)
Equation of the conditional probability
94(7)
An explicit solution
101(4)
Correlation between the signal noise and the observation noise
105(9)
Some representation formulas for the conditional probability
114(12)
Study of stochastic PDEs
126(9)
Concluding remarks
135(1)
Perturbation methods in non linear filtering
136(54)
Linear systems with small noise in the observation
138(8)
Non linear systems with small noise in the observation
146(21)
Dynamic systems with small noise and small signal to noise ratio
167(10)
Non linear filtering for dynamic systems with singular perturbations
177(13)
Some explicit solutions of the Zakai equation
190(32)
Non gaussian initial condition
192(5)
Explicit solution in the case of a non linear drift
197(7)
The conditionally gaussian case
204(18)
Some explicit controls for systems with partial observation
222(46)
The separation principle
223(4)
The Bellman equation for the separated problem when Uad is bounded
227(6)
Solution of the stochastic control problem with partial information when Uad is bounded
233(5)
Solution of the Bellman equation in some particular cases, with bounded controls
238(8)
Solution of the predicted-miss and minimum distance problems
246(7)
An extension of the concept of solution
253(15)
Stochastic maximum principle and dynamic programming for systems with partial observation
268(58)
Setting of the problem
270(6)
Stochastic maximum principle
276(13)
Applications of the stochastic maximum principle
289(8)
Preliminaries to dynamic programming
297(8)
Stationary dynamic programming
305(9)
Non stationary dynamic programming
314(9)
Non linear semigroup
323(3)
Existence results for stochastic control problems with partial information
326(14)
Notation: setting of the problem
327(3)
Stochastic optimal control
330(6)
Existence of a solution
336(4)
References 340(11)
Index 351

Rewards Program

Write a Review