Stochastic systems: estimation, identification, and adaptive control.

*(English)*Zbl 0706.93057
Pentice-Hall Information and System Sciences Series. Englewood Cliffs, New Jersey, 07632: Prentice Hall, Inc. XII, 358 p.; $ 62.10 (1986).

The book deals with modeling, identification, estimation and control theory for discrete-time stochastic systems. These topics are treated in a unified decision-theoretic setting and the book naturally leads to a level of knowledge of the subject that allows the study of the most recent research works in the field.

The book provides detailed and rigorous proofs of all important results and devotes special emphasis to some methodological questions often neglected in other books, e.g. dual effects of control, effects of nonlinear control laws and so on.

The usefulness of the book as a text (also for self study) is increased by the large amount of exercises that allow to check that the material is sufficiently understood. It should be also appreciated by people involved in applications in the fields of control, signal processing and operations research.

The book is organized as follows. The first five chapters introduce the problems of decision making under uncertainty and the models to be used in the sequel such as state space models, input-output models and controlled Markov chains models. Finite and infinite horizon dynamic programming are treated in a rigorous form in Chapters 6 and 8 respectively in the case of both complete and incomplete information. Linear systems estimation and control is treated in Chapter 7 while identification of such systems is developed in Chapter 10, following a general introduction to identification given in Chapter 9. The last three chapters are devoted to adaptive control problems treated both in a bayesian setting (mainly bandit problems) and in a nonbayesian one.

The book provides detailed and rigorous proofs of all important results and devotes special emphasis to some methodological questions often neglected in other books, e.g. dual effects of control, effects of nonlinear control laws and so on.

The usefulness of the book as a text (also for self study) is increased by the large amount of exercises that allow to check that the material is sufficiently understood. It should be also appreciated by people involved in applications in the fields of control, signal processing and operations research.

The book is organized as follows. The first five chapters introduce the problems of decision making under uncertainty and the models to be used in the sequel such as state space models, input-output models and controlled Markov chains models. Finite and infinite horizon dynamic programming are treated in a rigorous form in Chapters 6 and 8 respectively in the case of both complete and incomplete information. Linear systems estimation and control is treated in Chapter 7 while identification of such systems is developed in Chapter 10, following a general introduction to identification given in Chapter 9. The last three chapters are devoted to adaptive control problems treated both in a bayesian setting (mainly bandit problems) and in a nonbayesian one.

Reviewer: G.Di Masi

##### MSC:

93E03 | Stochastic systems in control theory (general) |

93-02 | Research exposition (monographs, survey articles) pertaining to systems and control theory |

93E11 | Filtering in stochastic control theory |

93E12 | Identification in stochastic control theory |

93E20 | Optimal stochastic control |

93C55 | Discrete-time control/observation systems |

90C40 | Markov and semi-Markov decision processes |

90C39 | Dynamic programming |

49L20 | Dynamic programming in optimal control and differential games |