Sufficient conditions for local controllability and high-order necessary conditions for optimality. A differential-geometric approach

1997 ◽  
Vol 85 (3) ◽  
pp. 1899-2001 ◽  
Author(s):  
A. I. Tretiyak
Keyword(s):  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Geometric Approach ◽  
High Order ◽  
Local Controllability ◽  
Necessary Conditions For Optimality

scholarly journals 2-regularity and 2-normality conditions for systems with impulsive controls

2007 ◽  
Vol 17 (2) ◽  
pp. 149-164
Author(s):  
Natal'ya Pavlova
Keyword(s):  
Necessary Conditions ◽  
Dimensional Space ◽  
Sufficient Conditions ◽  
Local Controllability ◽  
Finite Dimensional Space ◽  
Borel Set ◽  
Finite Dimensional ◽  
Second Order Necessary Conditions ◽  
Impulsive Controls ◽  
The Given

In this paper a controlled system with impulsive controls in the neighborhood of an abnormal point is investigated. The set of pairs (u,?) is considered as a class of admissible controls, where u is a measurable essentially bounded function and ? is a finite-dimensional Borel measure, such that for any Borel set B, ?(B) is a subset of the given convex closed pointed cone. In this article the concepts of 2-regularity and 2-normality for the abstract mapping ?, operating from the given Banach space into a finite-dimensional space, are introduced. The concepts of 2-regularity and 2-normality play a great role in the course of derivation of the first and the second order necessary conditions for the optimal control problem, consisting of the minimization of a certain functional on the set of the admissible processes. These concepts are also important for obtaining the sufficient conditions for the local controllability of the nonlinear systems. The convenient criterion for 2-regularity along the prescribed direction and necessary conditions for 2-normality of systems, linear in control, are introduced in this article as well.

High Order Necessary Conditions for Optimality

1972 ◽  
Vol 10 (1) ◽  
pp. 127-168 ◽  
Author(s):  
R. Gabasov ◽  
F. M. Kirillova
Keyword(s):  
Necessary Conditions ◽  
High Order ◽  
Necessary Conditions For Optimality

scholarly journals High-order optimality conditions for degenerate variational problems

2014 ◽  
Vol 30 (3) ◽  
pp. 387-394
Author(s):  
AGNIESZKA PRUSINSKA ◽  
◽  
EWA SZCZEPANIK ◽  
ALEXEY A. TRETYAKOV ◽  
◽  
...  
Keyword(s):  
Optimality Conditions ◽  
Calculus Of Variations ◽  
Necessary Conditions ◽  
Regularity Theory ◽  
Variational Problems ◽  
High Order ◽  
Singular Problems ◽  
Necessary Conditions For Optimality ◽  
Solution Point

The paper is devoted to the class of singular calculus of variations problems with constraints which are not regular mappings at the solution point. Methods of the p-regularity theory are used for investigation of isoperimetric and Lagrange singular problems. Necessary conditions for optimality in p-regular calculus of variations problem are presented.

Sign in / Sign up

Export Citation Format

Share Document