Accession Number : AD0602143

Title :   ROLE OF THE GENERALIZED LIPSCHITZ CONDITION IN FINITE-TIME STABILITY AND IN THE DERIVATION OF THE MAXIMUM PRINCIPLE,

Corporate Author : ILLINOIS UNIV URBANA COORDINATED SCIENCE LAB

Personal Author(s) : Agashe,S. D.

Report Date : JUN 1964

Pagination or Media Count : 28

Abstract : The main purpose of the report was to show how important the generalized Lipschitz condition is in proving certain properties of varied solutions of differential equations. These are particularly useful in consideration of finite-time stability and in deriving the Pontryagin Maximum Principle. It was shown that if a system satisfies a generalized Lipschitz condition in the state variables, it is finite-time stable with respect to the initial state. If it satisifies a generalized Lipschitz condition in the control, it is finite-time stable with respect to the control. In deriving the Maximum Principle using the Calculus of Variations approach, an implicit assumption was made that for sufficiently small variations of the optimum control, the terminal conditions of the problem can still be met. This assumption was shown to be valid if a generalized Lipschitz condition is satisfied. (Author)

Descriptors :   (*DIFFERENTIAL EQUATIONS, CALCULUS OF VARIATIONS), (*CALCULUS OF VARIATIONS, DIFFERENTIAL EQUATIONS), (*CONTROL, THEORY), TIME, STABILITY, THEOREMS, OPTIMIZATION, CONTROL SYSTEMS, THEOREMS, FUNCTIONS(MATHEMATICS), REAL VARIABLES, VECTOR ANALYSIS

Distribution Statement : APPROVED FOR PUBLIC RELEASE