A remark on the Bellman principle of optimality

✍ Scribed by K.G. Garaev

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 341 KB
• Volume: 335
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/s0016-0032(96)00125-1

✦ Synopsis

The group-theoretical approach bused on joint use of the Lie-Ovsyannikor injinitesimul upparatus (l-3) und the Noether theory ofinvariant variation problems ( 4) is suggestedfbr the problem of synthesis of optimum control. Up to now the ideas qf the Noether theory were used on the theory of optimum control,for the problems of programmed control only and considered in (I small number of publications ; as for the problem of synthesis, this paper is the first in this area In this paper a corollary of the Bellman equation is obtained in the.form of a linear partial d@rentiul equation. The use of' the equation simpl$es the problem of construction qf synthesizing controls (note, that the equation is correct both in the case when no restrictions are imposed on the vector qf'control, and in the case when the values qf the vector belong to a bounded closed domain. An example illustrating the technique of use qf the Lie-Ovsyannikov inJinitesimul upparutus ,for reduction of the corresponding Bellman equation is presented.