Partial Differential Equation for Evolution of Star-Shaped
Reachability Domains of Differential Inclusions

J 2016

Partial Differential Equation for Evolution of Star-Shaped Reachability Domains of Differential Inclusions

MAZURENKO, Stanislav

Basic information

Original name

Partial Differential Equation for Evolution of Star-Shaped Reachability Domains of Differential Inclusions

Authors

MAZURENKO, Stanislav (643 Russian Federation, guarantor, belonging to the institution)

Edition

SET-VALUED AND VARIATIONAL ANALYSIS, 2016, 1877-0533

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

Netherlands

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL

Impact factor

Impact factor: 0.886

RIV identification code

RIV/00216224:14310/16:00092840

Organization unit

Faculty of Science

DOI

http://dx.doi.org/10.1007/s11228-015-0345-4

UT WoS

000375418300009

Keywords in English

Reachability sets; Differential inclusion; Star-shaped sets; Radial (gauge) function; Viability; Optimal control synthesis

Abstract

V originále

The problem of reachability for differential inclusions is an active topic in the recent control theory. Its solution provides an insight into the dynamics of an investigated system and also enables one to design synthesizing control strategies under a given optimality criterion. The primary results on reachability were mostly applicable to convex sets, whose dynamics is described through that of their support functions. Those results were further extended to the viability problem and some types of nonlinear systems. However, non-convex sets can arise even in simple bilinear systems. Hence, the issue of nonconvexity in reachability problems requires a more detailed investigation. The present article follows an alternative approach for this cause. It deals with star-shaped reachability sets, describing the evolution of these sets in terms of radial (Minkowski gauge) functions. The derived partial differential equation is then modified to cope with additional state constraints due to on-line measurement observations. Finally, the last section is on designing optimal closed-loop control strategies using radial functions.

Links

LO1214, research and development project

Name: Centrum pro výzkum toxických látek v prostředí (Acronym: RECETOX)

Investor: Ministry of Education, Youth and Sports of the CR

Citovat

MAZURENKO, Stanislav. Partial Differential Equation for Evolution of Star-Shaped Reachability Domains of Differential Inclusions. SET-VALUED AND VARIATIONAL ANALYSIS. 2016, vol. 24, No 2, p. 333-354. ISSN 1877-0533. Available from: https://dx.doi.org/10.1007/s11228-015-0345-4.

@article{1367560,
   author = {Mazurenko, Stanislav},
   article_number = {2},
   doi = {http://dx.doi.org/10.1007/s11228-015-0345-4},
   keywords = {Reachability sets; Differential inclusion; Star-shaped sets; Radial (gauge) function; Viability; Optimal control synthesis},
   language = {eng},
   issn = {1877-0533},
   journal = {SET-VALUED AND VARIATIONAL ANALYSIS},
   title = {Partial Differential Equation for Evolution of Star-Shaped Reachability Domains of Differential Inclusions},
   url = {https://loschmidt.chemi.muni.cz/peg/wp-content/uploads/2016/01/Mazurenko_2016SVVA.pdf},
   volume = {24},
   year = {2016}
}

TY  - JOUR
ID  - 1367560
AU  - Mazurenko, Stanislav
PY  - 2016
TI  - Partial Differential Equation for Evolution of Star-Shaped Reachability Domains of Differential Inclusions
JF  - SET-VALUED AND VARIATIONAL ANALYSIS
VL  - 24
IS  - 2
SP  - 333-354
EP  - 333-354
SN  - 18770533
KW  - Reachability sets
KW  - Differential inclusion
KW  - Star-shaped sets
KW  - Radial (gauge) function
KW  - Viability
KW  - Optimal control synthesis
UR  - https://loschmidt.chemi.muni.cz/peg/wp-content/uploads/2016/01/Mazurenko_2016SVVA.pdf
N2  - The problem of reachability for differential inclusions is an active topic in the recent control theory. Its solution provides an insight into the dynamics of an investigated system and also enables one to design synthesizing control strategies under a given optimality criterion. The primary results on reachability were mostly applicable to convex sets, whose dynamics is described through that of their support functions. Those results were further extended to the viability problem and some types of nonlinear systems. However, non-convex sets can arise even in simple bilinear systems. Hence, the issue of nonconvexity in reachability problems requires a more detailed investigation. The present article follows an alternative approach for this cause. It deals with star-shaped reachability sets, describing the evolution of these sets in terms of radial (Minkowski gauge) functions. The derived partial differential equation is then modified to cope with additional state constraints due to on-line measurement observations. Finally, the last section is on designing optimal closed-loop control strategies using radial functions.
ER  -

MAZURENKO, Stanislav. Partial Differential Equation for Evolution of Star-Shaped Reachability Domains of Differential Inclusions. \textit{SET-VALUED AND VARIATIONAL ANALYSIS}. 2016, vol.~24, No~2, p.~333-354. ISSN~1877-0533. Available from: https://dx.doi.org/10.1007/s11228-015-0345-4.

Detailed Information on Publication Record