Optimal control of nonlinear delay systems with implicit derivative and quadratic performance
Kybernetika, Tome 35 (1999) no. 2, pp. 225-233 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

The existence of optimal control for nonlinear delay systems having an implicit derivative with quadratic performance criteria is proved. The results are established by an iterative technique and using the Darbo fixed point theorem.
The existence of optimal control for nonlinear delay systems having an implicit derivative with quadratic performance criteria is proved. The results are established by an iterative technique and using the Darbo fixed point theorem.
Classification : 47N20, 49J15, 49J25, 49K25, 93C10
Keywords: optimal control; nonlinear delay system; Darboux’s fixed-point theorem
@article{KYB_1999_35_2_a6,
     author = {Balachandran, K. and Rajagopal, N.},
     title = {Optimal control of nonlinear delay systems with implicit derivative and quadratic performance},
     journal = {Kybernetika},
     pages = {225--233},
     year = {1999},
     volume = {35},
     number = {2},
     mrnumber = {1690948},
     zbl = {1274.49002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_1999_35_2_a6/}
}
TY  - JOUR
AU  - Balachandran, K.
AU  - Rajagopal, N.
TI  - Optimal control of nonlinear delay systems with implicit derivative and quadratic performance
JO  - Kybernetika
PY  - 1999
SP  - 225
EP  - 233
VL  - 35
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/KYB_1999_35_2_a6/
LA  - en
ID  - KYB_1999_35_2_a6
ER  - 
%0 Journal Article
%A Balachandran, K.
%A Rajagopal, N.
%T Optimal control of nonlinear delay systems with implicit derivative and quadratic performance
%J Kybernetika
%D 1999
%P 225-233
%V 35
%N 2
%U http://geodesic.mathdoc.fr/item/KYB_1999_35_2_a6/
%G en
%F KYB_1999_35_2_a6
Balachandran, K.; Rajagopal, N. Optimal control of nonlinear delay systems with implicit derivative and quadratic performance. Kybernetika, Tome 35 (1999) no. 2, pp. 225-233. http://geodesic.mathdoc.fr/item/KYB_1999_35_2_a6/

[1] Athans M., Falb P. L.: Optimal Control. McGraw–Hill, New York 1966 | MR | Zbl

[2] Balachandran K.: Global relative controllability of nonlinear systems with time varying multiple delays in control. Internat. J. Control 46 (1987), 1, 193–200 | DOI | MR | Zbl

[3] Balachandran K.: Existence of optimal control for nonlinear multiple–delay systems. Internat. J. Control 49 (1989), 3, 769–775 | DOI | MR | Zbl

[4] Balachandran K., Dauer J. P.: Controllability of nonlinear systems via fixed point theorems. J. Optim. Theory Appl. 53 (1987), 1, 345–352 | DOI | MR | Zbl

[5] Balachandran K., Ramaswamy R. S.: Optimal control for nonlinear multiple delay systems with quadratic performance. Journal A 27 (1986), 1, 37–40 | Zbl

[6] Balachandran K., Somasundaram D.: Existence of optimal control for nonlinear systems with quadratic performance. J. Austral. Math. Soc. Ser. B 29 (1987), 249–255 | DOI | MR | Zbl

[7] Dacka C.: On the controllability of a class of nonlinear systems. IEEE Trans. Automat. Control 25 (1980), 3, 263–266 | DOI | MR | Zbl

[8] Dauer J. P., Balachandran K.: Existence of optimal control for nonlinear systems with an implicit derivative. Optimal Control Appl. Methods 24 (1993), 1, 145–152 | DOI | MR

[9] Malek–Zavarei M.: Suboptimal control systems with multiple delays. J. Optim. Theory Appl. 30 (1980), 4, 621–633 | DOI | MR

[10] Sadovskii B. J.: Limit compact and condensing operators. Russian Math. Surveys 27 (1972), 1, 85–155 | DOI | MR

[11] Yamamoto Y.: Optimal control for nonlinear systems with quadratic performance. J. Math. Anal. Appl. 64 (1978), 2, 348–353 | DOI | MR | Zbl