Well-posedness and sliding mode control
ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 2, pp. 219-228.

Sliding mode control of ordinary differential equations is considered. A key robustness property, called approximability, is studied from an optimization point of view. It is proved that Tikhonov well-posedness of a suitably defined optimization problem is intimately related to approximability. Making use of this link, new approximability criteria are obtained for nonlinear sliding mode control systems.

DOI : 10.1051/cocv:2005003
Classification : 49K40, 93B12
Mots clés : sliding mode control, Tikhonov well-posedness, approximability
@article{COCV_2005__11_2_219_0,
     author = {Zolezzi, Tullio},
     title = {Well-posedness and sliding mode control},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {219--228},
     publisher = {EDP-Sciences},
     volume = {11},
     number = {2},
     year = {2005},
     doi = {10.1051/cocv:2005003},
     mrnumber = {2141887},
     zbl = {1125.93011},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/cocv:2005003/}
}
TY  - JOUR
AU  - Zolezzi, Tullio
TI  - Well-posedness and sliding mode control
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2005
SP  - 219
EP  - 228
VL  - 11
IS  - 2
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/cocv:2005003/
DO  - 10.1051/cocv:2005003
LA  - en
ID  - COCV_2005__11_2_219_0
ER  - 
%0 Journal Article
%A Zolezzi, Tullio
%T Well-posedness and sliding mode control
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2005
%P 219-228
%V 11
%N 2
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/cocv:2005003/
%R 10.1051/cocv:2005003
%G en
%F COCV_2005__11_2_219_0
Zolezzi, Tullio. Well-posedness and sliding mode control. ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 2, pp. 219-228. doi : 10.1051/cocv:2005003. http://www.numdam.org/articles/10.1051/cocv:2005003/

[1] J.-P. Aubin and H. Frankowska, Set-valued analysis. Birkhäuser (1990). | MR | Zbl

[2] G. Bartolini, A. Levant, A. Pisano and E. Usai, Higher-order sliding modes for the output-feedback control of nonlinear uncertain systems. Sliding mode control in engineering, W. Perruquetti and J.P. Barbot Eds., Dekker (2002). | MR | Zbl

[3] G. Bartolini and T. Zolezzi, Control of nonlinear variable structure systems. J. Math. Anal. Appl. 118 (1986) 42-62. | Zbl

[4] G. Bartolini and T. Zolezzi, Behavior of variable-structure control systems near the sliding manifold. Syst. Control Lett. 21 (1993) 43-48. | Zbl

[5] F.H. Clarke, Optimization and nonsmooth analysis. Wiley-Interscience (1983). | MR | Zbl

[6] R.A. Decarlo, S.H. Zak and G.P. Matthews, Variable structure control of non linear systems: a tutorial. Proc. IEEE 76 (1988) 212-232.

[7] K. Deimling, Multivalued differential equations. De Gruyter (1992). | MR | Zbl

[8] A. Dontchev and T. Zolezzi, Well-posed optimization problems, Springer. Lect. Notes Math. 1543 (1993). | MR | Zbl

[9] C. Edwards and S. Spurgeon, Sliding mode control: theory and applications. Taylor and Francis (1988).

[10] A.F. Filippov, Differential equations with discontinuous right-hand side. Amer. Math. Soc. Transl. 42 (1964) 199-231. | Zbl

[11] A.F. Filippov, Differential equations with discontinuous righthand sides. Kluwer (1988). | MR | Zbl

[12] W. Perruquetti and J.P. Barbot Eds., Sliding mode control in engineering. Dekker (2002).

[13] R.T. Rockafellar, Integral functionals, normal integrands and measurable selections, Springer. Lect. Notes Math. 543 (1976) 157-207. | Zbl

[14] V. Utkin, Sliding modes in control and optimization. Springer (1992). | MR | Zbl

Cité par Sources :