| Title:
|
Optimal control of nonlinear delay systems with implicit derivative and quadratic performance (English) |
| Author:
|
Balachandran, K. |
| Author:
|
Rajagopal, N. |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
35 |
| Issue:
|
2 |
| Year:
|
1999 |
| Pages:
|
[225]-233 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
optimal control |
| Keyword:
|
nonlinear delay system |
| Keyword:
|
Darboux’s fixed-point theorem |
| MSC:
|
47N20 |
| MSC:
|
49J15 |
| MSC:
|
49J25 |
| MSC:
|
49K25 |
| MSC:
|
93C10 |
| idZBL:
|
Zbl 1274.49002 |
| idMR:
|
MR1690948 |
| . |
| Date available:
|
2009-09-24T19:25:11Z |
| Last updated:
|
2015-03-27 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135283 |
| . |
| Reference:
|
[1] Athans M., Falb P. L.: Optimal Control.McGraw–Hill, New York 1966 Zbl 0186.22501, MR 0204181 |
| Reference:
|
[2] Balachandran K.: Global relative controllability of nonlinear systems with time varying multiple delays in control.Internat. J. Control 46 (1987), 1, 193–200 Zbl 0629.93010, MR 0895702, 10.1080/00207178708933892 |
| Reference:
|
[3] Balachandran K.: Existence of optimal control for nonlinear multiple–delay systems.Internat. J. Control 49 (1989), 3, 769–775 Zbl 0681.49001, MR 0990313, 10.1080/00207178908559666 |
| Reference:
|
[4] Balachandran K., Dauer J. P.: Controllability of nonlinear systems via fixed point theorems.J. Optim. Theory Appl. 53 (1987), 1, 345–352 Zbl 0596.93010, MR 0891093, 10.1007/BF00938943 |
| Reference:
|
[5] Balachandran K., Ramaswamy R. S.: Optimal control for nonlinear multiple delay systems with quadratic performance.Journal A 27 (1986), 1, 37–40 Zbl 0583.93027 |
| Reference:
|
[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 Zbl 0623.49002, MR 0905808, 10.1017/S0334270000005750 |
| Reference:
|
[7] Dacka C.: On the controllability of a class of nonlinear systems.IEEE Trans. Automat. Control 25 (1980), 3, 263–266 Zbl 0439.93006, MR 0567386, 10.1109/TAC.1980.1102287 |
| Reference:
|
[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 MR 1228381, 10.1002/oca.4660140206 |
| Reference:
|
[9] Malek–Zavarei M.: Suboptimal control systems with multiple delays.J. Optim. Theory Appl. 30 (1980), 4, 621–633 MR 0572160, 10.1007/BF01686725 |
| Reference:
|
[10] Sadovskii B. J.: Limit compact and condensing operators.Russian Math. Surveys 27 (1972), 1, 85–155 MR 0428132, 10.1070/RM1972v027n01ABEH001364 |
| Reference:
|
[11] Yamamoto Y.: Optimal control for nonlinear systems with quadratic performance.J. Math. Anal. Appl. 64 (1978), 2, 348–353 Zbl 0378.49024, MR 0479536, 10.1016/0022-247X(78)90042-2 |
| . |
