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## Details

Genre/Form: | Electronic books |
---|---|

Additional Physical Format: | Print version: Costa, Oswaldo Luiz do Valle. Continuous average control of piecewise deterministic Markov processes. New York : Springer, [2013] (DLC) 2013934018 (OCoLC)828487890 |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
Oswaldo Luiz do Valle Costa; François Dufour, (Mathematician) |

ISBN: | 9781461469834 146146983X |

OCLC Number: | 840605078 |

Description: | 1 online resource (xii, 116 pages) : illustrations. |

Contents: | Introduction -- Average Continuous Control of PDMPs -- Optimality Equation for the Average Control of PDMPs -- The Vanishing Discount Approach for PDMPs -- The Policy Iteration Algorithm for PDMPs -- Examples. |

Series Title: | SpringerBriefs in mathematics. |

Responsibility: | Oswaldo Luiz do Valle Costa, Francois Dufour. |

### Abstract:

"The intent of this book is to present recent results in the control theory for the long run average continuous control problem of piecewise deterministic Markov processes (PDMPs). The book focuses mainly on the long run average cost criteria and extends to the PDMPs some well-known techniques related to discrete-time and continuous-time Markov decision processes, including the so-called "average inequality approach'', "vanishing discount technique'' and "policy iteration algorithm''. We believe that what is unique about our approach is that, by using the special features of the PDMPs, we trace a parallel with the general theory for discrete-time Markov Decision Processes rather than the continuous-time case. The two main reasons for doing that is to use the powerful tools developed in the discrete-time framework and to avoid working with the infinitesimal generator associated to a PDMP, which in most cases has its domain of definition difficult to be characterized. Although the book is mainly intended to be a theoretically oriented text, it also contains some motivational examples. The book is targeted primarily for advanced students and practitioners of control theory. The book will be a valuable source for experts in the field of Markov decision processes. Moreover, the book should be suitable for certain advanced courses or seminars. As background, one needs an acquaintance with the theory of Markov decision processes and some knowledge of stochastic processes and modern analysis."--Publisher's website.

## Reviews

*Editorial reviews*

Publisher Synopsis

From the reviews: "This book is a successful attempt to present a recent progress in some control problems for the class of Piecewise Deterministic Markov Processes (PDMP). ... The book is addressed to readers who are well prepared. ... The detailed description of problems, results, proofs and numerical illustrations makes the book a valuable source for many people working in stochastic control." (Jordan M. Stoyanov, zbMATH, Vol. 1272, 2013) Read more...

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## Similar Items

### Related Subjects:(11)

- Control theory -- Mathematical models.
- Markov processes.
- MATHEMATICS -- Calculus.
- MATHEMATICS -- Mathematical Analysis.
- Mathematics.
- Distribution (Probability theory)
- Probability Theory and Stochastic Processes.
- Continuous Optimization.
- Systems Theory, Control.
- Operations Research, Management Science.
- Complex Systems.