On the local structure of optimal trajectories in R3

被引：28
作者：
Agrachev, AA
Sigalotti, M
机构：
[1] SISSA, ISAS, I-34014 Trieste, Italy
[2] VA Steklov Math Inst, Moscow 117333, Russia
来源：
SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2003年 / 42卷 / 02期
关键词：
optimal control; Lie brackets;
D O I：
10.1137/S0363012902409246
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
We analyze the structure of a control function u(t) corresponding to an optimal trajectory for the system (q) over dot = f(q) + ug(q) in a three-dimensional manifold, near a point where some nondegeneracy conditions are satisfied. The kind of optimality which is studied includes time-optimality. The control turns out to be the concatenation of some bang and some singular arcs. Studying the index of the second variation of the switching times, the number of such arcs is bounded by four.
引用
收藏
页码：513 / 531
页数：19
相关论文
共 23 条
[1]   2ND ORDER OPTIMALITY PRINCIPLE FOR A TIME-OPTIMAL PROBLEM [J].
AGRACEV, AA ;
GAMKRELIDZE, RV .
MATHEMATICS OF THE USSR-SBORNIK, 1976, 29 (04) :547-576
[2]  
Agrachev A, 1995, J DYN CONTROL SYST, V1, P319
[3]   Strong optimality or a bang-bang trajectory [J].
Agrachev, AA ;
Stefani, G ;
Zezza, P .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2002, 41 (04) :991-1014
[4]  
AGRACHEV AA, 1990, NONLINEAR CONTROLLAB, V133, P263
[5]   TOWARD A GEOMETRIC-THEORY IN THE TIME-MINIMAL CONTROL OF CHEMICAL BATCH REACTORS [J].
BONNARD, B ;
DEMORANT, J .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1995, 33 (05) :1279-1311
[6]   THE GENERIC LOCAL TIME-OPTIMAL STABILIZING CONTROLS IN DIMENSION-3 [J].
BRESSAN, A .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1986, 24 (02) :177-190
[7]  
Fuller A. T., 1963, J ELECTRON CONTR, V15, P63, DOI DOI 10.1080/00207216308937555
[8]  
Kelley H. J., 1967, TOPICS OPTIMIZATION, P63
[9]   THE STRUCTURE OF SMALL-TIME REACHABLE SETS IN LOW DIMENSIONS [J].
KRENER, AJ ;
SCHATTLER, H .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1989, 27 (01) :120-147
[10]  
Piccoli B., 1996, REND SEM MAT UNIV P, V95, P59
123