Extension principle and controller design for systems with distributed time-delay

Altuğ İftar

Kybernetika (2017)

  • Volume: 53, Issue: 4, page 630-652
  • ISSN: 0023-5954

Abstract

top
Extension principle is defined for systems with distributed time-delay and the necessary and sufficient conditions for one system being an extension of the other are presented. Preservation of stability properties between two systems, one of which is an extension of the other is also discussed and it is shown that when the expanded system is an extension of the original system, (i) the original system is bounded-input bounded-output stable if and only if the expanded system is bounded-input bounded-output stable and (ii) the original system is exponentially stable if the expanded system is exponentially stable. Controller design using the extension principle is then considered. It is shown that, if the expanded system is an extension of the original system, then any controller designed for the expanded system can be contracted for implementation on the original system. Furthermore, if the controller designed for the expanded system stabilizes the expanded system and satisfies certain performance requirements, then the contracted controller stabilizes the original system and satisfies corresponding performance requirements for the original system. Finally, overlapping decompositions and controller design using overlapping decompositions are demonstrated. A highway traffic congestion control problem is then considered to demonstrate a possible application of the presented controller design approach.

How to cite

top

İftar, Altuğ. "Extension principle and controller design for systems with distributed time-delay." Kybernetika 53.4 (2017): 630-652. <http://eudml.org/doc/294690>.

@article{İftar2017,
abstract = {Extension principle is defined for systems with distributed time-delay and the necessary and sufficient conditions for one system being an extension of the other are presented. Preservation of stability properties between two systems, one of which is an extension of the other is also discussed and it is shown that when the expanded system is an extension of the original system, (i) the original system is bounded-input bounded-output stable if and only if the expanded system is bounded-input bounded-output stable and (ii) the original system is exponentially stable if the expanded system is exponentially stable. Controller design using the extension principle is then considered. It is shown that, if the expanded system is an extension of the original system, then any controller designed for the expanded system can be contracted for implementation on the original system. Furthermore, if the controller designed for the expanded system stabilizes the expanded system and satisfies certain performance requirements, then the contracted controller stabilizes the original system and satisfies corresponding performance requirements for the original system. Finally, overlapping decompositions and controller design using overlapping decompositions are demonstrated. A highway traffic congestion control problem is then considered to demonstrate a possible application of the presented controller design approach.},
author = {İftar, Altuğ},
journal = {Kybernetika},
keywords = {large-scale systems; time-delay systems; distributed time-delay; overlapping decompositions; decentralized control; controller design},
language = {eng},
number = {4},
pages = {630-652},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Extension principle and controller design for systems with distributed time-delay},
url = {http://eudml.org/doc/294690},
volume = {53},
year = {2017},
}

TY - JOUR
AU - İftar, Altuğ
TI - Extension principle and controller design for systems with distributed time-delay
JO - Kybernetika
PY - 2017
PB - Institute of Information Theory and Automation AS CR
VL - 53
IS - 4
SP - 630
EP - 652
AB - Extension principle is defined for systems with distributed time-delay and the necessary and sufficient conditions for one system being an extension of the other are presented. Preservation of stability properties between two systems, one of which is an extension of the other is also discussed and it is shown that when the expanded system is an extension of the original system, (i) the original system is bounded-input bounded-output stable if and only if the expanded system is bounded-input bounded-output stable and (ii) the original system is exponentially stable if the expanded system is exponentially stable. Controller design using the extension principle is then considered. It is shown that, if the expanded system is an extension of the original system, then any controller designed for the expanded system can be contracted for implementation on the original system. Furthermore, if the controller designed for the expanded system stabilizes the expanded system and satisfies certain performance requirements, then the contracted controller stabilizes the original system and satisfies corresponding performance requirements for the original system. Finally, overlapping decompositions and controller design using overlapping decompositions are demonstrated. A highway traffic congestion control problem is then considered to demonstrate a possible application of the presented controller design approach.
LA - eng
KW - large-scale systems; time-delay systems; distributed time-delay; overlapping decompositions; decentralized control; controller design
UR - http://eudml.org/doc/294690
ER -

References

top
  1. Ataşlar, B., İftar, A., 10.1080/002071799220335, Int. J. Control 72 (1999), 1175-1192. MR1717872DOI10.1080/002071799220335
  2. Atay, F. M., Hutt, A., 10.1137/050629367, SIAM J. Appl. Dynam. Systems 5 (2006), 670-698. MR2274494DOI10.1137/050629367
  3. Aybar, A., İftar, A., 10.1109/9.989151, IEEE Trans. Automat. Control 47 (2002), 511-515. MR1891337DOI10.1109/9.989151
  4. Bakule, L., 10.1016/j.arcontrol.2008.03.004, Ann. Rev. Control 32 (2008), 87-98. DOI10.1016/j.arcontrol.2008.03.004
  5. Bakule, L., Rodellar, J., Rossell, J. M., 10.3182/20050703-6-cz-1902.01547, In: Proc. 16th IFAC World Congress, Prague 2005. DOI10.3182/20050703-6-cz-1902.01547
  6. Bakule, L., Rodellar, J., Rossell, J. M., 10.1109/cdc.2005.1582503, In: Proc. IEEE Conference on Decision and Control, Seville 2005, pp. 2290-2295. DOI10.1109/cdc.2005.1582503
  7. Bakule, L., Rossell, J. M., Overlapping controllers for uncertain delay continuous-time systems., Kybernetika 44 (2008), 17-34. MR2405052
  8. Berezansky, L., Braverman, E., 10.1016/s1468-1218(02)00010-x, Nonlinear Analysis: Real World Applications 4 (2003), 1-19. MR1932138DOI10.1016/s1468-1218(02)00010-x
  9. Cooke, K. L., Grossman, Z., 10.1016/0022-247x(82)90243-8, J. Math. Anal. Appl. 86 (1082), 592-627. MR0652197DOI10.1016/0022-247x(82)90243-8
  10. Ding, Z., Decentralized output regulation of large scale nonlinear systems with delay., Kybernetika 45 (2009), 33-48. Zbl1158.93303MR2489579
  11. Erol, H. E., İftar, A., 10.1016/j.automatica.2015.11.022, Automatica 64 (2016), 262-269. MR3433104DOI10.1016/j.automatica.2015.11.022
  12. Hale, J. K., Verduyn-Lunel, S. M., Introduction to Functional Differential Equations., Springer-Verlag, New York 1993. MR1243878
  13. İftar, A., 10.1016/0005-1098(93)90148-m, Automatica 29 (1993), 511-516. MR1211311DOI10.1016/0005-1098(93)90148-m
  14. İftar, A., 10.1080/00207179308922997, Int. J. Control 58 (1993), 187-209. MR1222143DOI10.1080/00207179308922997
  15. İftar, A., 10.1016/s1474-6670(17)31673-7, In: Preprints 10th IFAC Symposium on Large Scale Systems, Osaka 2004, pp. 605-609. DOI10.1016/s1474-6670(17)31673-7
  16. İftar, A., 10.3182/20080706-5-kr-1001.01577, In: Proc. 17th IFAC Word Congress, Seoul 2008, pp. 9332-9337. DOI10.3182/20080706-5-kr-1001.01577
  17. İftar, A., 10.3182/20140824-6-za-1003.00565, In: Proc. 19th IFAC World Congress, Cape Town 2014, pp. 5796-5801. DOI10.3182/20140824-6-za-1003.00565
  18. İftar, A., 10.1109/cdc.2014.7039424, In: Proc. IEEE Conference on Decision and Control, Los Angeles 2014, pp. 463-468. DOI10.1109/cdc.2014.7039424
  19. İftar, A., Khorrami, F., 10.1109/21.44051, IEEE Trans. Systems, Man, Cybernet. 19 (1989), 1296-1300. DOI10.1109/21.44051
  20. İftar, A., Özgüner, Ü., Decentralized LQG/LTR controller design for interconnected systems., In: Proc. American Control Conference, Minneapolis 1987, pp. 1682-1687. 
  21. İftar, A., Özgüner, Ü., 10.1109/tac.1987.1104451, IEEE Trans. Automat. Control 32 (1987), 926-930. DOI10.1109/tac.1987.1104451
  22. İftar, A., Özgüner, Ü., 10.1016/0005-1098(90)90031-c, Automatica 26 (1990), 593-597. MR1056141DOI10.1016/0005-1098(90)90031-c
  23. İftar, A., Özgüner, Ü., 10.1109/9.704976, IEEE Trans. Automat. Control 43 (1998), 1040-1055. MR1636494DOI10.1109/9.704976
  24. Ikeda, M., Šiljak, D. D., Overlapping decompositions, expansions, and contractions of dynamic systems., Large Scale Systems 1 (1980), 29-38. MR0617153
  25. Ikeda, M., Šiljak, D. D., Overlapping decentralized control with input, state, and output inclusion., Control Theory Advanced Technol. 2 (1986), 155-172. 
  26. Ikeda, M., Šiljak, D. D., White, D. E., 10.1007/bf00935477, J. Optim. Theory Appl. 34 (1981), 279-310. MR0625231DOI10.1007/bf00935477
  27. Ikeda, M., Šiljak, D. D., White, D. E., 10.1109/tac.1984.1103486, IEEE Trans. Automat. Control 29 (1984), 244-249. MR0739610DOI10.1109/tac.1984.1103486
  28. Liu, S., Yu, W., Zhang, F., 10.14736/kyb-2015-5-0874, Kybernetika 51 (2015), 874-889. MR3445989DOI10.14736/kyb-2015-5-0874
  29. Ma, L., Xu, M., Jia, R., Ye, H., 10.14736/kyb-2014-4-0491, Kybernetika 50 (2014), 491-511. MR3275081DOI10.14736/kyb-2014-4-0491
  30. Michiels, W., Morărescu, C.-I., Niculescu, S.-I., 10.1137/060671425, SIAM J. Control Optim. 48 (2009), 77-101. MR2480127DOI10.1137/060671425
  31. Niculescu, S.-I., Delay Effects on Stability: A Robust Control Approach., Lect. Notes Control Inform. Sci. 269, Springer-Verlag, London 2001. MR1880658
  32. Özbay, H., Bonnet, C., Clairambault, J., 10.1109/cdc.2008.4738654, In: Proc. {IEEE} Conference on Decision and Control, Cancun 2008, pp. 2050-2055. DOI10.1109/cdc.2008.4738654
  33. Özer, S. M., Gülmez, G., İftar, A., 10.1109/cacsd.2016.7602548, In: Proc. 2016 IEEE Conference on Computer Aided Control System Design, Buenos Aires 2016, pp. 868-873. DOI10.1109/cacsd.2016.7602548
  34. Özer, S. M., İftar, A., 10.1016/j.ifacol.2015.09.422, In: Preprints 12th IFAC Workshop on Time-delay Systems Ann Arbor 2015, pp. 462-467. DOI10.1016/j.ifacol.2015.09.422
  35. Özgüner, Ü., Hatipoğlu, C., İftar, A., Redmill, K., 10.1007/bfb0031566, In: Hybrid Systems IV, Lecture Notes in Computer Science, 1273, (P. J. Antsaklis, ed.), pp. 294-328, Springer Verlag, 1997. MR1636494DOI10.1007/bfb0031566
  36. Papageorgiou, M., Blosseville, J., Hadj-Salem, H., 10.1016/0191-2615(89)90021-0, Transport. Res., Part B 23 (1989), 29-47. DOI10.1016/0191-2615(89)90021-0
  37. Papageorgiou, M., Blosseville, J., Hadj-Salem, H., Modeling and real-time control of traffic flow on the southern part of Boulevard Peripherique in Paris: Part I: Modelling., Transport. Res. Part A 24 (1990), 345-359. 
  38. Papageorgiou, M., Blosseville, J., Hadj-Salem, H., Modeling and real-time control of traffic flow on the southern part of Boulevard Peripherique in Paris: Part II: Coordinated on-ramp metering., Transport. Res., Part A 24 (1990), 361-370. 
  39. Penrose, R., Todd, J. A., 10.1017/s0305004100030929, Math. Proc. Cambridge Philosoph. Soc. 52 (1956), 17-19. MR0074092DOI10.1017/s0305004100030929
  40. Rahman, B., Blyuss, K. B., Kyrychko, Y. N., 10.1137/15m1006398, SIAM J. Applied Dynamical Systems 14 (2015), 2069-2095. MR3432142DOI10.1137/15m1006398
  41. Rao, V. S. H., Rao, P. R. S., 10.1016/s1468-1218(03)00022-1, Nonlinear Analysis: Real World Appl. 5 (2004), 141-158. MR2004091DOI10.1016/s1468-1218(03)00022-1
  42. Richard, J.-P., 10.1016/s0005-1098(03)00167-5, Automatica 39 (2003), 1667-1694. MR2141765DOI10.1016/s0005-1098(03)00167-5
  43. Šiljak, D. D., 10.1016/s0076-5392(08)x6200-9, Academic Press, Inc., San Diego 1991. MR1086632DOI10.1016/s0076-5392(08)x6200-9
  44. Sipahi, R., Atay, F. M., Niculescu, S.-I., 10.1137/060673813, SIAM J. Appl. Math. 68 (2008), 738-759. MR2375293DOI10.1137/060673813
  45. Stanković, S. S., Stanojević, M. J., Šiljak, D. D., 10.1109/87.865854, IEEE Trans. Control Systems Technol. 8 (2000), 816-832. DOI10.1109/87.865854
  46. Vanbiervliet, J., Verheyden, K., Michiels, W., Vandewalle, S., 10.1051/cocv:2007060, ESAIM: Control, Optimisation and Calculus of Variations 14 (2008), 3, 478-493. MR2434062DOI10.1051/cocv:2007060
  47. Xie, L., Fridman, E., Shaked, U., 10.1109/9.975483, IEEE Trans. Automat Control 46 (2001), 1930-1935. MR1878215DOI10.1109/9.975483

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.