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@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}. roč.~24, č.~2, s.~333-354. ISSN~1877-0533. doi:10.1007/s11228-015-0345-4. 2016.
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