Small-Time Reachable Sets of Linear Systems with Integral Control Constraints: Birth of the Shape of a Reachable Set

被引：10

作者：

Goncharova, Elena ^{[1
]}

Ovseevich, Alexander ^{[2
]}

机构：

[1] Russian Acad Sci, Siberian Branch, Inst Syst Dynam & Control Theory, Irkutsk 664003, Russia

[2] Russian Acad Sci, Inst Problems Mech, Moscow, Russia

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2016年 / 168卷 / 02期

基金：

俄罗斯基础研究基金会;

关键词：

Linear control systems; Reachable sets; Shapes of convex bodies; APPROXIMATIONS;

D O I：

10.1007/s10957-015-0754-4

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

The paper is concerned with small-time reachable sets of a linear dynamical system under integral constraints on control. The main result is the existence of a limit shape of the reachable sets as time tends to zero. A precise estimate for the rate of convergence is given.

引用

页码：615 / 624

页数：10

共 17 条

[1]

Agrachev A. A., 2004, Control Theory and Optimization, V87

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

AGRACHEV, AA ;

GAMKRELIDZE, RV ;

SARYCHEV, AV .

ACTA APPLICANDAE MATHEMATICAE, 1989, 14 (03) :191-237

[3] Bounded Feedback Controls for Linear Dynamic Systems by Using Common Lyapunov Functions [J].

Anan'evskii, I. M. ;

Anokhin, N. V. ;

Ovseevich, A. I. .

DOKLADY MATHEMATICS, 2010, 82 (02) :831-834

[4]

[Anonymous], KYBERNETICA

[5]

[Anonymous], 1994, PROGR MATH

[6] GRADED APPROXIMATIONS AND CONTROLLABILITY ALONG A TRAJECTORY [J].

BIANCHINI, RM ;

STEFANI, G .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1990, 28 (04) :903-924

[7] Comparative analysis of the asymptotic dynamics of reachable sets to linear systems [J].

Goncharova, E. V. ;

Ovseevich, A. I. .

JOURNAL OF COMPUTER AND SYSTEMS SCIENCES INTERNATIONAL, 2007, 46 (04) :505-513

[8] Birth of the shape of a reachable set [J].

Goncharova, E. V. ;

Ovseevich, A. I. .

DOKLADY MATHEMATICS, 2013, 88 (02) :605-607

[9] Limit Behavior of Reachable Sets of Linear Time-Invariant Systems with Integral Bounds on Control [J].

Goncharova, Elena ;

Ovseevich, Alexander .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2013, 157 (02) :400-415

[10]

Gromov M., 1996, Carnot-Caratheodory spaces seen from within, V144, P79

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