SUFFICIENT OPTIMALITY CONDITIONS FOR PONTRYAGIN EXTREMALS

被引：5

作者：

SARYCHEV, AV

机构：

[1] ACAD SCI,INST CONTROL SCI,MOSCOW 117342,USSR

[2] UNIV WURZBURG,INST MATH,W-8700 WURZBURG,GERMANY

来源：

SYSTEMS & CONTROL LETTERS | 1992年 / 19卷 / 06期

关键词：

OPTIMAL CONTROL; PONTRYAGIN EXTREMALS; THEORY OF 2ND VARIATION; INDEX AND NULLITY THEOREMS; SUFFICIENT OPTIMALITY CONDITIONS;

D O I：

10.1016/0167-6911(92)90076-5

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

L1-local optimality of a given control u(.) in an optimal control problem for an affine control system with bounded controls is investigated. Starting from the Pontryagin Maximum Principle, which is a first-order necessary optimality condition, we develop it in two directions: (1) "tending the notions of lst and 2nd variations of the system along u(.), we obtain 1st and 2nd-order sufficient optimality conditions for bang-bang Pontryagin extremals; (2) developing Legendre-Jacobi-Morse-type results for the extended second variation we obtain 2nd-order sufficient optimality conditions for general (bang-bang-singular) type of Pontryagin extremals.

引用

页码：451 / 460

页数：10

共 12 条

[1]

AGRACHEV AA, 1990, PURE A MATH, V133, P263

[2] LOCAL INVARIANTS OF SMOOTH CONTROL-SYSTEMS [J].