Optimal control of random sequences in problems with constraints.

*(English)*Zbl 0894.93001
Mathematics and its Applications (Dordrecht). 410. Dordrecht: Kluwer Academic Publishers. xi, 345 p. (1997).

This is a book on constrained optimal control of random sequences. In the first chapter, formulations of some problems with known solutions that can be obtained by the type of techniques presented later are given.

The second chapter introduces theoretical methods used to handle constraint-optimal control problems for general stochastic models. The methods are based on the Kuhn-Tucker theorem.

The third chapter deals with the existence and the form of solutions.

Previous development is specialized, in the fourth chapter, to linear models, quadratic loss, and linear and/or quadratic constraints.

The fifth chapter includes possible applications to several models from economics, engineering, etc.

Some results from Borel spaces, convex analysis, and the Kuhn-Tucker theorem are placed in the Appendix for self-contained reading.

Although, this book may be a useful addition to the stochastic control expert’s library, it would be hard to read for a novice because of the verbose language used.

The second chapter introduces theoretical methods used to handle constraint-optimal control problems for general stochastic models. The methods are based on the Kuhn-Tucker theorem.

The third chapter deals with the existence and the form of solutions.

Previous development is specialized, in the fourth chapter, to linear models, quadratic loss, and linear and/or quadratic constraints.

The fifth chapter includes possible applications to several models from economics, engineering, etc.

Some results from Borel spaces, convex analysis, and the Kuhn-Tucker theorem are placed in the Appendix for self-contained reading.

Although, this book may be a useful addition to the stochastic control expert’s library, it would be hard to read for a novice because of the verbose language used.

Reviewer: E.Yaz (Fayetteville)

##### MSC:

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

93E20 | Optimal stochastic control |

93C55 | Discrete-time control/observation systems |