A control system describing the dynamic behavior of a car thermostat is considered. The cooling power of the car’s radiator is allowed to depend on the ambient temperature. This physically natural assumption presents some challenges to mathematical investigation of the model. The existence and some properties of solutions of the control system are established.
Accepté le :
DOI : 10.1051/cocv/2017064
Mots clés : Evolution system, time delay, hysteresis, thermostat, bang-bang controls
@article{COCV_2018__24_2_709_0,
author = {Timoshin, Sergey A.},
title = {Bang-bang control of a thermostat with nonconstant cooling power},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {709--719},
publisher = {EDP-Sciences},
volume = {24},
number = {2},
year = {2018},
doi = {10.1051/cocv/2017064},
zbl = {06974825},
mrnumber = {3816411},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv/2017064/}
}
TY - JOUR AU - Timoshin, Sergey A. TI - Bang-bang control of a thermostat with nonconstant cooling power JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2018 SP - 709 EP - 719 VL - 24 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2017064/ DO - 10.1051/cocv/2017064 LA - en ID - COCV_2018__24_2_709_0 ER -
%0 Journal Article %A Timoshin, Sergey A. %T Bang-bang control of a thermostat with nonconstant cooling power %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %P 709-719 %V 24 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2017064/ %R 10.1051/cocv/2017064 %G en %F COCV_2018__24_2_709_0
Timoshin, Sergey A. Bang-bang control of a thermostat with nonconstant cooling power. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 2, pp. 709-719. doi : 10.1051/cocv/2017064. http://archive.numdam.org/articles/10.1051/cocv/2017064/
[1] , Variational Convergence for Functions and Operators. Pitman Adv. Publishing Program. Boston-London-Melbourne (1984) | MR | Zbl
[2] , Integrals of set-valued functions. J. Math. Anal. Appl. 12 (1965) 1–12 | DOI | MR | Zbl
[3] , , and , Analysis of thermostat models. Eur. J. Appl. Math. 8 (1997) 437–455 | DOI | MR | Zbl
[4] , and , An introduction to nonlinear analysis. Theory. Dordrecht: Kluwer Academic/Plenum Publishers (2003) | DOI | MR | Zbl
[5] and , Differential equations, hysteresis, and time delay. Z. Angew. Math. Phys. 53 (2002) 676–691 | DOI | MR | Zbl
[6] , and , A class of differential-delay systems with hysteresis: Asymptotic behaviour of solutions. Nonl. Anal. 69 (2008) 363–391 | DOI | MR | Zbl
[7] , Topological equivalence in the space of integrable vector-valued functions. Proc. Am. Math. Soc. 93 (1985) 40–42 | DOI | MR | Zbl
[8] , and , Mathematical models for hysteresis. SIAM Rev. 35 (1993) 94–123 | DOI | MR | Zbl
[9] , Convergence of convex sets and of solutions of variational inequalities. Adv. Math. 3 (1969) 510–585 | DOI | MR | Zbl
[10] , Control system with hysteresis and delay. Syst. Control Lett. 91 (2016) 43–47 | DOI | MR | Zbl
[11] and , Existence and properties of solutions of a control system with hysteresis effect. Nonlinear Anal. 74 (2011) 4433–4447 | DOI | MR | Zbl
[12] , Mosco convergence of integral functionals and its applications. Sb. Math. 200 (2009) 429–454 | DOI | MR | Zbl
[13] and , Lp-continuous extreme selectors of multifunctions with decomposable values: Existence theorems. Set-Valued Anal. 4 (1996) 173–203 | DOI | MR | Zbl
[14] , Differential Models of Hysteresis. Appl. Math. Sci. Springer Verlag, Berlin 111 (1994) | MR | Zbl
[15] , and , A dynamic model for a thermostat. J. Eng. Math. 36 (1999) 291–310 | DOI | MR | Zbl
Cité par Sources :
