Accession Number:

AD0275944

Title:

LIAPOUNOV'S THEOREM ON THE RANGE OF A VECTOR MEASURE AND PONTRYAGIN'S MAXIMUM PRINCIPLE

Descriptive Note:

Corporate Author:

STANFORD UNIV CALIF APPLIED MATHEMATICS AND STATISTICS LABS

Personal Author(s):

• HALKIN,HUBERT

Report Date:

1962-05-07

Pagination or Media Count:

1.0

Abstract:

The necessary condition for the optimal control of a non-linear dynamical system is studied. The system under consideration is described by a canonical system of ordinary differential equations for the state variables. The differential equations depend also on certain parameters called control variables. The problem is to choose the value of these control variables, which can be time dependent, in order to satisfy given initialAND END POINTS CONDITIONS AND TO MAXIMIZE A GIVEN FUNCTIONAL. When there are no restrictions on the values which can be taken by the control variables the problem is relatively simple and equivalent to the Problem of Bolza of the calculus of variations. Such situation however is very unlikely to occur in practice because of the physical limitations of the control devices. Autho

Descriptors:

• *CALCULUS OF VARIATIONS
• *FUNCTIONAL ANALYSIS
• *TOPOLOGY
• MEASURE THEORY
• PARTIAL DIFFERENTIAL EQUATIONS
• TRANSFORMATIONS(MATHEMATICS)
• VECTOR ANALYSIS

Subject Categories:

Distribution Statement:

APPROVED FOR PUBLIC RELEASE