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

Základní údaje

Originální název

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

Autoři

MAZURENKO, Stanislav (643 Rusko, garant, domácí)

Vydání

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

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Nizozemské království

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 0.886

Kód RIV

RIV/00216224:14310/16:00092840

Organizační jednotka

Přírodovědecká fakulta

DOI

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

UT WoS

000375418300009

Klíčová slova anglicky

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

Štítky

AKR, rivok

Změněno: 9. 4. 2017 10:57, Ing. Andrea Mikešková

Anotace

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.

Návaznosti

LO1214, projekt VaV

Název: Centrum pro výzkum toxických látek v prostředí (Akronym: RECETOX)

Investor: Ministerstvo školství, mládeže a tělovýchovy ČR, Centrum pro výzkum toxických látek v prostředí

Citovat

MAZURENKO, Stanislav. Partial Differential Equation for Evolution of Star-Shaped Reachability Domains of Differential Inclusions. SET-VALUED AND VARIATIONAL ANALYSIS. 2016, roč. 24, č. 2, s. 333-354. ISSN 1877-0533. Dostupné z: 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, roč.~24, č.~2, s.~333-354. ISSN~1877-0533. Dostupné z: https://dx.doi.org/10.1007/s11228-015-0345-4.

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