Optimal control problems with delays in state and control variables subject to mixed control-state constraints

Optimal control problems with delays in state and control variables are studied. Constraints are imposed as mixed control–state inequality constraints. Necessary optimality conditions in the form of Pontryagin's minimum principle are established. The proof proceeds by augmenting the delayed con...

Full description

Saved in:

Bibliographic Details
Published in:	Optimal control applications & methods Vol. 30; no. 4; pp. 341 - 365
Main Authors:	Göllmann, L., Kern, D., Maurer, H.
Format:	Journal Article
Language:	English
Published:	Chichester, UK John Wiley & Sons, Ltd 01.07.2009
Subjects:	Chemical engineering Delay delays in state and control Discretization discretization methods Mathematical analysis Mathematical models mixed control-state inequality constraints Nonlinear programming Optimal control optimal control of a CSTR reactor optimal fishing Pontryagin's minimum principle retarded optimal control problems Terminals
ISSN:	0143-2087, 1099-1514
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Abstract	Optimal control problems with delays in state and control variables are studied. Constraints are imposed as mixed control–state inequality constraints. Necessary optimality conditions in the form of Pontryagin's minimum principle are established. The proof proceeds by augmenting the delayed control problem to a nondelayed problem with mixed terminal boundary conditions to which Pontryagin's minimum principle is applicable. Discretization methods are discussed by which the delayed optimal control problem is transformed into a large‐scale nonlinear programming problem. It is shown that the Lagrange multipliers associated with the programming problem provide a consistent discretization of the advanced adjoint equation for the delayed control problem. An analytical example and numerical examples from chemical engineering and economics illustrate the results. Copyright © 2008 John Wiley & Sons, Ltd.
AbstractList	Optimal control problems with delays in state and control variables are studied. Constraints are imposed as mixed control-state inequality constraints. Necessary optimality conditions in the form of Pontryagin's minimum principle are established. The proof proceeds by augmenting the delayed control problem to a nondelayed problem with mixed terminal boundary conditions to which Pontryagin's minimum principle is applicable. Discretization methods are discussed by which the delayed optimal control problem is transformed into a large-scale nonlinear programming problem. It is shown that the Lagrange multipliers associated with the programming problem provide a consistent discretization of the advanced adjoint equation for the delayed control problem. An analytical example and numerical examples from chemical engineering and economics illustrate the results. Optimal control problems with delays in state and control variables are studied. Constraints are imposed as mixed control–state inequality constraints. Necessary optimality conditions in the form of Pontryagin's minimum principle are established. The proof proceeds by augmenting the delayed control problem to a nondelayed problem with mixed terminal boundary conditions to which Pontryagin's minimum principle is applicable. Discretization methods are discussed by which the delayed optimal control problem is transformed into a large‐scale nonlinear programming problem. It is shown that the Lagrange multipliers associated with the programming problem provide a consistent discretization of the advanced adjoint equation for the delayed control problem. An analytical example and numerical examples from chemical engineering and economics illustrate the results. Copyright © 2008 John Wiley & Sons, Ltd.
Author	Kern, D. Maurer, H. Göllmann, L.
Author_xml	– sequence: 1 givenname: L. surname: Göllmann fullname: Göllmann, L. email: goellmann@fh-muenster.de organization: Department of Mechanical Engineering, Münster University of Applied Sciences, Münster, Germany – sequence: 2 givenname: D. surname: Kern fullname: Kern, D. organization: Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Berlin, Germany – sequence: 3 givenname: H. surname: Maurer fullname: Maurer, H. organization: Department of Numerical Analysis and Applied Mathematics, University of Münster, Münster, Germany
BookMark	eNp10E1PAjEQBuDGaCKg8S_05sEsttv9PBIiaILiQaO3ZrbMxmLZxbYo_HtL1uBFT5NOnk5m3j45btoGCbngbMgZi69bBcMiEUekx1lZRjzlyTHpMZ6IKGZFfkr6zi0ZYzkXcY8087XXKzBUtY23raFr21YGV45-af9GF2hg56huqPPgkUKzOMhPsBqCddRtqiUqT31LV3qLBxJ1n8LLeQu68e6MnNRgHJ7_1AF5ntw8jW-j2Xx6Nx7NIiUEFxEUKRcizxYQJ1UqFlUNAuskK2NUdVLWAnldFGVSFZDFGJpYKVHEJatiUAyZGJDLbm4452ODzsuVdgqNgQbbjZN5KrIyy0IoAxJ1UtnWOYu1VDpsrfcXgDaSM7mPVYZYZYj1d_LBr20I0O7-kFed_NIGd_8xOR-POv2zh3YetwcN9l1muchT-fIwlU-z15fZYzaR9-IbPOOaBQ
CitedBy_id	crossref_primary_10_1016_j_matcom_2018_08_009 crossref_primary_10_1177_0142331218819048 crossref_primary_10_1002_oca_2087 crossref_primary_10_1002_oca_2482 crossref_primary_10_1093_imamci_dnw018 crossref_primary_10_3390_math11194025 crossref_primary_10_1016_j_automatica_2021_109981 crossref_primary_10_1007_s10441_015_9244_1 crossref_primary_10_1016_j_amc_2019_02_002 crossref_primary_10_1016_j_neucom_2014_08_060 crossref_primary_10_1007_s12190_022_01766_3 crossref_primary_10_12677_AAM_2023_122081 crossref_primary_10_3390_math11092113 crossref_primary_10_1002_oca_70005 crossref_primary_10_1016_j_nonrwa_2012_10_017 crossref_primary_10_1080_1726037X_2011_10698595 crossref_primary_10_1093_imamci_dnw020 crossref_primary_10_1017_S1446181114000352 crossref_primary_10_1016_j_chaos_2021_110869 crossref_primary_10_1155_2019_9596253 crossref_primary_10_1016_j_apm_2017_08_025 crossref_primary_10_1016_j_cam_2023_115106 crossref_primary_10_1080_17513758_2019_1629031 crossref_primary_10_1002_mma_70046 crossref_primary_10_1016_j_apm_2021_08_024 crossref_primary_10_1002_oca_2351 crossref_primary_10_1080_00036811_2020_1820995 crossref_primary_10_1109_TMC_2013_96 crossref_primary_10_1140_epjs_s11734_024_01221_3 crossref_primary_10_1007_s40314_014_0184_1 crossref_primary_10_1007_s40435_016_0231_4 crossref_primary_10_3389_fncom_2022_931121 crossref_primary_10_1137_17M1143563 crossref_primary_10_1007_s10957_015_0783_z crossref_primary_10_1007_s12190_024_02053_z crossref_primary_10_1007_s40435_016_0287_1 crossref_primary_10_1080_0954898X_2022_2059117 crossref_primary_10_1080_02331934_2020_1786568 crossref_primary_10_1115_1_4023060 crossref_primary_10_1016_j_euroecorev_2020_103439 crossref_primary_10_1093_imamci_dnv044 crossref_primary_10_1007_s12591_022_00593_z crossref_primary_10_1007_s40435_015_0221_y crossref_primary_10_1016_j_compbiomed_2024_108682 crossref_primary_10_1016_j_matcom_2015_03_002 crossref_primary_10_1140_epjp_s13360_024_04911_y crossref_primary_10_1016_j_automatica_2018_12_036 crossref_primary_10_1155_2024_3253724 crossref_primary_10_3390_pr10102070 crossref_primary_10_1140_epjs_s11734_024_01294_0 crossref_primary_10_1016_j_jedc_2025_105122 crossref_primary_10_1007_s11786_018_0333_9 crossref_primary_10_1016_j_ejcon_2023_100824 crossref_primary_10_1007_s13278_020_00685_0 crossref_primary_10_1007_s40435_016_0270_x crossref_primary_10_1093_imamci_dnw044 crossref_primary_10_1155_2014_250419 crossref_primary_10_1007_s40313_020_00586_9 crossref_primary_10_1016_j_rico_2025_100528 crossref_primary_10_1155_2014_982978 crossref_primary_10_1080_00207721_2024_2392822 crossref_primary_10_1007_s12190_022_01776_1 crossref_primary_10_1016_j_ifacol_2018_07_208 crossref_primary_10_3390_fractalfract3030046 crossref_primary_10_1049_iet_syb_2013_0012 crossref_primary_10_1080_00207179_2011_641158 crossref_primary_10_1002_oca_2407 crossref_primary_10_1016_j_jprocont_2019_04_013 crossref_primary_10_1016_j_jprocont_2024_103234 crossref_primary_10_1155_2014_602641 crossref_primary_10_1016_j_jfranklin_2020_09_002 crossref_primary_10_1155_2013_403549 crossref_primary_10_1002_oca_2163 crossref_primary_10_1002_mma_10351 crossref_primary_10_1007_s12064_016_0234_x crossref_primary_10_1007_s10640_017_0204_x crossref_primary_10_1080_17513758_2017_1381280 crossref_primary_10_1007_s11071_019_05304_y crossref_primary_10_1016_j_rineng_2025_104450 crossref_primary_10_1007_s40819_015_0051_9 crossref_primary_10_1155_2021_8673020 crossref_primary_10_1007_s10957_023_02288_z crossref_primary_10_1016_j_amc_2022_127448 crossref_primary_10_1080_00036811_2012_762090 crossref_primary_10_1080_00036811_2016_1192136 crossref_primary_10_1080_00207179_2018_1463456 crossref_primary_10_1109_TAC_2022_3207865 crossref_primary_10_1016_j_jfranklin_2020_02_051 crossref_primary_10_1016_j_physa_2019_121544 crossref_primary_10_1186_s13662_025_03947_3 crossref_primary_10_1016_j_jfranklin_2013_09_027 crossref_primary_10_1016_j_jfranklin_2018_08_003 crossref_primary_10_3390_math10132188 crossref_primary_10_1016_j_amc_2010_03_075 crossref_primary_10_1016_j_biosystems_2020_104321 crossref_primary_10_1016_j_cnsns_2023_107500 crossref_primary_10_1155_2014_945158 crossref_primary_10_1002_oca_2549 crossref_primary_10_1007_s40314_013_0089_4 crossref_primary_10_1016_j_sysconle_2014_07_001 crossref_primary_10_1088_1751_8121_aa8a92 crossref_primary_10_1137_18M119121X crossref_primary_10_1007_s10957_016_0957_3 crossref_primary_10_1002_rnc_4003 crossref_primary_10_1093_imamci_dnw057 crossref_primary_10_1002_mma_4926 crossref_primary_10_1002_aic_17777 crossref_primary_10_1155_2021_5525857 crossref_primary_10_1016_j_amc_2016_07_009 crossref_primary_10_1093_imamci_dnu058 crossref_primary_10_1093_imamci_dnv025 crossref_primary_10_1002_oca_2187 crossref_primary_10_1080_00036811_2018_1538500 crossref_primary_10_1109_TWC_2014_2366136 crossref_primary_10_5402_2012_215124 crossref_primary_10_1016_j_cnsns_2023_107615 crossref_primary_10_1080_00207179_2012_715752 crossref_primary_10_1016_j_apm_2020_07_051 crossref_primary_10_1080_00207160_2024_2366908 crossref_primary_10_1155_ijmm_3238188 crossref_primary_10_1016_j_apm_2018_09_039 crossref_primary_10_1007_s12190_020_01369_w crossref_primary_10_1177_1077546314550698 crossref_primary_10_1155_2018_6710575 crossref_primary_10_1016_j_apnum_2015_12_008 crossref_primary_10_1016_j_ins_2014_08_020 crossref_primary_10_1016_j_heliyon_2022_e12274 crossref_primary_10_1155_2014_940819 crossref_primary_10_1007_s12190_024_02335_6 crossref_primary_10_1093_imamci_dnv032 crossref_primary_10_1002_oca_2572 crossref_primary_10_1177_09596518211067476 crossref_primary_10_1002_oca_2295 crossref_primary_10_1155_2021_5545551 crossref_primary_10_1177_10775463211053182 crossref_primary_10_1007_s10957_022_02046_7 crossref_primary_10_1080_01630563_2018_1489415 crossref_primary_10_3390_app6080219 crossref_primary_10_3390_fractalfract7070533 crossref_primary_10_1109_TAC_2020_2982862 crossref_primary_10_1016_j_cnsns_2024_108156 crossref_primary_10_1016_j_ins_2021_02_047 crossref_primary_10_1007_s12591_021_00570_y crossref_primary_10_1007_s11071_021_06841_1 crossref_primary_10_1016_j_ifacol_2018_09_235 crossref_primary_10_1016_j_ecosta_2022_03_004
Cites_doi	10.1007/s10107-004-0559-y 10.1007/BF00933818 10.1007/s002110000178 10.1002/oca.4660130103 10.1080/00207177208932327 10.1016/0005-1098(71)90006-9 10.1137/0306016 10.1137/0316060 10.1007/BF01447323 10.1137/0306002 10.1090/mmono/180 10.2307/1934339 10.1007/BF00952825 10.1016/0009-2509(70)87009-9 10.1023/A:1008677427361 10.1002/aic.690220117 10.1137/0329063
ContentType	Journal Article
Copyright	Copyright © 2008 John Wiley & Sons, Ltd.
Copyright_xml	– notice: Copyright © 2008 John Wiley & Sons, Ltd.
DBID	BSCLL AAYXX CITATION 7SP 8FD L7M
DOI	10.1002/oca.843
DatabaseName	Istex CrossRef Electronics & Communications Abstracts Technology Research Database Advanced Technologies Database with Aerospace
DatabaseTitle	CrossRef Technology Research Database Advanced Technologies Database with Aerospace Electronics & Communications Abstracts
DatabaseTitleList	Technology Research Database CrossRef
DeliveryMethod	fulltext_linktorsrc
Discipline	Engineering
EISSN	1099-1514
EndPage	365
ExternalDocumentID	10_1002_oca_843 OCA843 ark_67375_WNG_TLXWLP6F_M
Genre	article
GroupedDBID	-~X .3N .GA .Y3 05W 0R~ 10A 123 1L6 1OB 1OC 31~ 33P 3SF 3WU 4.4 50Y 50Z 51W 51X 52M 52N 52O 52P 52S 52T 52U 52W 52X 5VS 66C 702 7PT 8-0 8-1 8-3 8-4 8-5 8UM 930 A03 AAESR AAEVG AAHQN AAMMB AAMNL AANHP AANLZ AAONW AASGY AAXRX AAYCA AAZKR ABCQN ABCUV ABEML ABIJN ABJNI ABPVW ACAHQ ACBWZ ACCZN ACGFS ACPOU ACRPL ACSCC ACXBN ACXQS ACYXJ ADBBV ADEOM ADIZJ ADKYN ADMGS ADNMO ADOZA ADXAS ADZMN AEFGJ AEIGN AEIMD AENEX AEUYR AEYWJ AFBPY AFFPM AFGKR AFWVQ AFZJQ AGHNM AGQPQ AGXDD AGYGG AHBTC AIDQK AIDYY AIQQE AITYG AIURR AJXKR ALAGY ALMA_UNASSIGNED_HOLDINGS ALVPJ AMBMR AMVHM AMYDB ASPBG ATUGU AUFTA AVWKF AZBYB AZFZN AZVAB BAFTC BDRZF BFHJK BHBCM BMNLL BMXJE BNHUX BROTX BRXPI BSCLL BY8 CMOOK CS3 D-E D-F DCZOG DPXWK DR2 DRFUL DRSTM DU5 EBS EJD F00 F01 F04 FEDTE G-S G.N GNP GODZA H.T H.X HBH HF~ HGLYW HHY HVGLF HZ~ I-F IX1 J0M JPC KQQ LATKE LAW LC2 LC3 LEEKS LH4 LITHE LOXES LP6 LP7 LUTES LW6 LYRES M59 MEWTI MK4 MRFUL MRSTM MSFUL MSSTM MXFUL MXSTM N04 N05 N9A NF~ NNB O66 O9- OIG P2P P2W P2X P4D PALCI Q.N Q11 QB0 QRW R.K RIWAO RJQFR ROL RX1 SAMSI SUPJJ TN5 TUS UB1 V2E W8V W99 WBKPD WH7 WIH WIK WLBEL WOHZO WQJ WXSBR WYISQ XG1 XPP XV2 ZZTAW ~IA ~WT AEUQT AFPWT ALUQN RWI UCJ WRC WWI AAYXX CITATION O8X 7SP 8FD L7M
ID	FETCH-LOGICAL-c3313-a8513376da24b53dbfa3ef4692ecf49f3e1f8894b8a62e2ecebc38290b2ac0e03
IEDL.DBID	DRFUL
ISICitedReferencesCount	204
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000268706700001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	0143-2087
IngestDate	Thu Jul 10 23:49:06 EDT 2025 Sat Nov 29 04:09:48 EST 2025 Tue Nov 18 22:22:52 EST 2025 Wed Jan 22 16:19:20 EST 2025 Tue Nov 11 03:32:28 EST 2025
IsPeerReviewed	true
IsScholarly	true
Issue	4
Language	English
License	http://onlinelibrary.wiley.com/termsAndConditions#vor
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c3313-a8513376da24b53dbfa3ef4692ecf49f3e1f8894b8a62e2ecebc38290b2ac0e03
Notes	ArticleID:OCA843 ark:/67375/WNG-TLXWLP6F-M istex:9438DBB367800C0EA4083C2D025DCD0B3C52B56E ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
PQID	753696614
PQPubID	23500
PageCount	25
ParticipantIDs	proquest_miscellaneous_753696614 crossref_citationtrail_10_1002_oca_843 crossref_primary_10_1002_oca_843 wiley_primary_10_1002_oca_843_OCA843 istex_primary_ark_67375_WNG_TLXWLP6F_M
PublicationCentury	2000
PublicationDate	2009-07 July/August 2009 2009-07-00 20090701
PublicationDateYYYYMMDD	2009-07-01
PublicationDate_xml	– month: 07 year: 2009 text: 2009-07
PublicationDecade	2000
PublicationPlace	Chichester, UK
PublicationPlace_xml	– name: Chichester, UK
PublicationTitle	Optimal control applications & methods
PublicationTitleAlternate	Optim. Control Appl. Meth
PublicationYear	2009
Publisher	John Wiley & Sons, Ltd
Publisher_xml	– name: John Wiley & Sons, Ltd
References	Halanay A. Optimal controls for systems with time lag. SIAM Journal on Control 1968; 6:215-234. Hestenes MR. Calculus of Variations and Optimal Control Theory. Wiley: New York, 1966. Colonius F, Hinrichsen D. Optimal control of functional differential systems. SIAM Journal on Control and Optimization 1978; 16(6):861-879. Vanderbei RJ, Shanno DF. An interior-point algorithm for nonconvex nonlinear programming. Computational Optimization and Applications 1999; 13:231-252. Angell TS, Kirsch A. On the necessary conditions for optimal control of retarded systems. Applied Mathematics and Optimization 1990; 22:117-145. Kharatishvili GL. Maximum principle in the theory of optimal time-delay processes. Doklady Akademii Nauk USSR 1961; 136:39-42. Fourer R, Gay DM, Kernighan BW. AMPL: A Modeling Language for Mathematical Programming. The Scientific Press: South San Francisco, CA, 1993. Hager W. Runge-Kutta methods in optimal control and the transformed adjoint system. Numerische Mathematik 2000; 87:247-282. Kharatishvili GL. A Maximum Principle in External Problems with Delays. Mathematical Theory on Control. Academic Press: New York, 1967. Banks HT. Necessary conditions for control problems with variable time lags. SIAM Journal on Control 1968; 8(1):9-47. Soliman MA, Ray WH. Optimal control of multivariable systems with pure time delays. Automatica 1971; 7:681-689. Guinn T. Reduction of delayed optimal control problems to nondelayed problems. Journal of Optimization Theory and Applications 1976; 18:371-377. May RM. Time-delay versus stability in population models with two and three tropic levels. Ecology 1973; 54:315-325. May RM. Stability and Complexity in Model Ecosystems (2nd edn). Princeton University Press: Princeton, NJ, 1975. Neustadt LW. Optimization-A Theory of Necessary Conditions. Princeton University Press: Princeton, NJ, 1976. Ray WH, Soliman MA. The optimal control of processes containing pure time delays-I, necessary conditions for an optimum. Chemical Engineering Science 1970; 25:1911-1925. Soliman MA, Ray WH. On the optimal control of systems having pure time delays and singular arcs. International Journal of Control 1972; 16(5):963-976. Oh SH, Luus R. Optimal feedback control of time-delay systems. AIChE Journal 1976; 22(1):140-147. Oğuztöreli MN. Time-Lag Control Systems. Academic Press: New York, 1966. Chan WL, Yung SP. Sufficient conditions for variational problems with delayed argument. Journal of Optimization Theory and Applications 1993; 76:131-144. Milyutin AA, Osmolovskii NP. Calculus of Variations and Optimal Control. Translations of Mathematical Monographs, vol. 180. American Mathematical Society: Providence, RI, 1998. Clarke FH, Wolenski PR. The sensitivity of optimal control problems to time delay. SIAM Journal on Control and Optimization 1991; 29(5):1176-1215. Dadebo S, Luus R. Optimal control of time-delay systems by dynamic programming. Optimal Control Applications and Methods 1992; 13:29-41. Wächter A, Biegler LT. On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Mathematical Programming 2006; 106:25-57. 1968; 8 1976; 22 1973; 54 2000; 87 1968; 6 1998 1976 1975 1996 1961; 136 1978; 16 1992; 13 2005 1993 2002 1991; 29 1971; 7 1990; 22 1993; 76 1999; 13 1983 1976; 18 2006; 106 1967 1972; 16 1970; 25 1966 May RM (e_1_2_1_28_2) 1975 Kharatishvili GL (e_1_2_1_4_2) 1967 e_1_2_1_22_2 e_1_2_1_23_2 e_1_2_1_21_2 e_1_2_1_26_2 e_1_2_1_27_2 e_1_2_1_24_2 e_1_2_1_25_2 Oğuztöreli MN (e_1_2_1_2_2) 1966 e_1_2_1_29_2 Hestenes MR (e_1_2_1_18_2) 1966 Neustadt LW (e_1_2_1_19_2) 1976 e_1_2_1_6_2 e_1_2_1_30_2 e_1_2_1_7_2 Fourer R (e_1_2_1_20_2) 1993 e_1_2_1_5_2 e_1_2_1_11_2 e_1_2_1_12_2 e_1_2_1_32_2 e_1_2_1_10_2 e_1_2_1_31_2 e_1_2_1_15_2 Kharatishvili GL (e_1_2_1_3_2) 1961; 136 e_1_2_1_16_2 e_1_2_1_13_2 e_1_2_1_14_2 e_1_2_1_8_2 e_1_2_1_9_2 Milyutin AA (e_1_2_1_17_2) 1998
References_xml	– reference: Oğuztöreli MN. Time-Lag Control Systems. Academic Press: New York, 1966. – reference: Colonius F, Hinrichsen D. Optimal control of functional differential systems. SIAM Journal on Control and Optimization 1978; 16(6):861-879. – reference: Ray WH, Soliman MA. The optimal control of processes containing pure time delays-I, necessary conditions for an optimum. Chemical Engineering Science 1970; 25:1911-1925. – reference: Clarke FH, Wolenski PR. The sensitivity of optimal control problems to time delay. SIAM Journal on Control and Optimization 1991; 29(5):1176-1215. – reference: Hager W. Runge-Kutta methods in optimal control and the transformed adjoint system. Numerische Mathematik 2000; 87:247-282. – reference: May RM. Time-delay versus stability in population models with two and three tropic levels. Ecology 1973; 54:315-325. – reference: Halanay A. Optimal controls for systems with time lag. SIAM Journal on Control 1968; 6:215-234. – reference: Soliman MA, Ray WH. Optimal control of multivariable systems with pure time delays. Automatica 1971; 7:681-689. – reference: Angell TS, Kirsch A. On the necessary conditions for optimal control of retarded systems. Applied Mathematics and Optimization 1990; 22:117-145. – reference: Oh SH, Luus R. Optimal feedback control of time-delay systems. AIChE Journal 1976; 22(1):140-147. – reference: Soliman MA, Ray WH. On the optimal control of systems having pure time delays and singular arcs. International Journal of Control 1972; 16(5):963-976. – reference: Guinn T. Reduction of delayed optimal control problems to nondelayed problems. Journal of Optimization Theory and Applications 1976; 18:371-377. – reference: Chan WL, Yung SP. Sufficient conditions for variational problems with delayed argument. Journal of Optimization Theory and Applications 1993; 76:131-144. – reference: Kharatishvili GL. A Maximum Principle in External Problems with Delays. Mathematical Theory on Control. Academic Press: New York, 1967. – reference: May RM. Stability and Complexity in Model Ecosystems (2nd edn). Princeton University Press: Princeton, NJ, 1975. – reference: Kharatishvili GL. Maximum principle in the theory of optimal time-delay processes. Doklady Akademii Nauk USSR 1961; 136:39-42. – reference: Hestenes MR. Calculus of Variations and Optimal Control Theory. Wiley: New York, 1966. – reference: Dadebo S, Luus R. Optimal control of time-delay systems by dynamic programming. Optimal Control Applications and Methods 1992; 13:29-41. – reference: Wächter A, Biegler LT. On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Mathematical Programming 2006; 106:25-57. – reference: Fourer R, Gay DM, Kernighan BW. AMPL: A Modeling Language for Mathematical Programming. The Scientific Press: South San Francisco, CA, 1993. – reference: Banks HT. Necessary conditions for control problems with variable time lags. SIAM Journal on Control 1968; 8(1):9-47. – reference: Milyutin AA, Osmolovskii NP. Calculus of Variations and Optimal Control. Translations of Mathematical Monographs, vol. 180. American Mathematical Society: Providence, RI, 1998. – reference: Neustadt LW. Optimization-A Theory of Necessary Conditions. Princeton University Press: Princeton, NJ, 1976. – reference: Vanderbei RJ, Shanno DF. An interior-point algorithm for nonconvex nonlinear programming. Computational Optimization and Applications 1999; 13:231-252. – year: 1983 – volume: 136 start-page: 39 year: 1961 end-page: 42 article-title: Maximum principle in the theory of optimal time‐delay processes publication-title: Doklady Akademii Nauk USSR – year: 1966 – volume: 22 start-page: 117 year: 1990 end-page: 145 article-title: On the necessary conditions for optimal control of retarded systems publication-title: Applied Mathematics and Optimization – year: 2005 – volume: 8 start-page: 9 issue: 1 year: 1968 end-page: 47 article-title: Necessary conditions for control problems with variable time lags publication-title: SIAM Journal on Control – volume: 87 start-page: 247 year: 2000 end-page: 282 article-title: Runge–Kutta methods in optimal control and the transformed adjoint system publication-title: Numerische Mathematik – year: 1996 – year: 1975 – volume: 29 start-page: 1176 issue: 5 year: 1991 end-page: 1215 article-title: The sensitivity of optimal control problems to time delay publication-title: SIAM Journal on Control and Optimization – year: 1998 – volume: 13 start-page: 231 year: 1999 end-page: 252 article-title: An interior–point algorithm for nonconvex nonlinear programming publication-title: Computational Optimization and Applications – volume: 54 start-page: 315 year: 1973 end-page: 325 article-title: Time‐delay versus stability in population models with two and three tropic levels publication-title: Ecology – volume: 18 start-page: 371 year: 1976 end-page: 377 article-title: Reduction of delayed optimal control problems to nondelayed problems publication-title: Journal of Optimization Theory and Applications – volume: 25 start-page: 1911 year: 1970 end-page: 1925 article-title: The optimal control of processes containing pure time delays—I, necessary conditions for an optimum publication-title: Chemical Engineering Science – volume: 6 start-page: 215 year: 1968 end-page: 234 article-title: Optimal controls for systems with time lag publication-title: SIAM Journal on Control – volume: 22 start-page: 140 issue: 1 year: 1976 end-page: 147 article-title: Optimal feedback control of time‐delay systems publication-title: AIChE Journal – year: 1967 – year: 2002 – volume: 106 start-page: 25 year: 2006 end-page: 57 article-title: On the implementation of an interior–point filter line‐search algorithm for large‐scale nonlinear programming publication-title: Mathematical Programming – volume: 76 start-page: 131 year: 1993 end-page: 144 article-title: Sufficient conditions for variational problems with delayed argument publication-title: Journal of Optimization Theory and Applications – volume: 16 start-page: 963 issue: 5 year: 1972 end-page: 976 article-title: On the optimal control of systems having pure time delays and singular arcs publication-title: International Journal of Control – volume: 16 start-page: 861 issue: 6 year: 1978 end-page: 879 article-title: Optimal control of functional differential systems publication-title: SIAM Journal on Control and Optimization – volume: 13 start-page: 29 year: 1992 end-page: 41 article-title: Optimal control of time‐delay systems by dynamic programming publication-title: Optimal Control Applications and Methods – year: 1976 – year: 1993 – volume: 7 start-page: 681 year: 1971 end-page: 689 article-title: Optimal control of multivariable systems with pure time delays publication-title: Automatica – ident: e_1_2_1_11_2 – ident: e_1_2_1_23_2 doi: 10.1007/s10107-004-0559-y – volume-title: Time‐Lag Control Systems year: 1966 ident: e_1_2_1_2_2 – volume-title: AMPL: A Modeling Language for Mathematical Programming year: 1993 ident: e_1_2_1_20_2 – ident: e_1_2_1_7_2 doi: 10.1007/BF00933818 – volume-title: Optimization—A Theory of Necessary Conditions year: 1976 ident: e_1_2_1_19_2 – ident: e_1_2_1_22_2 – ident: e_1_2_1_25_2 doi: 10.1007/s002110000178 – volume-title: Stability and Complexity in Model Ecosystems year: 1975 ident: e_1_2_1_28_2 – volume-title: Calculus of Variations and Optimal Control Theory year: 1966 ident: e_1_2_1_18_2 – ident: e_1_2_1_14_2 doi: 10.1002/oca.4660130103 – ident: e_1_2_1_6_2 doi: 10.1080/00207177208932327 – ident: e_1_2_1_12_2 doi: 10.1016/0005-1098(71)90006-9 – ident: e_1_2_1_5_2 doi: 10.1137/0306016 – volume: 136 start-page: 39 year: 1961 ident: e_1_2_1_3_2 article-title: Maximum principle in the theory of optimal time‐delay processes publication-title: Doklady Akademii Nauk USSR – ident: e_1_2_1_9_2 doi: 10.1137/0316060 – ident: e_1_2_1_10_2 doi: 10.1007/BF01447323 – ident: e_1_2_1_8_2 doi: 10.1137/0306002 – volume-title: Calculus of Variations and Optimal Control year: 1998 ident: e_1_2_1_17_2 doi: 10.1090/mmono/180 – ident: e_1_2_1_21_2 – ident: e_1_2_1_27_2 doi: 10.2307/1934339 – ident: e_1_2_1_24_2 – ident: e_1_2_1_32_2 doi: 10.1007/BF00952825 – ident: e_1_2_1_16_2 – ident: e_1_2_1_26_2 doi: 10.1016/0009-2509(70)87009-9 – ident: e_1_2_1_29_2 – ident: e_1_2_1_31_2 doi: 10.1023/A:1008677427361 – volume-title: A Maximum Principle in External Problems with Delays year: 1967 ident: e_1_2_1_4_2 – ident: e_1_2_1_15_2 – ident: e_1_2_1_13_2 doi: 10.1002/aic.690220117 – ident: e_1_2_1_30_2 doi: 10.1137/0329063
SSID	ssj0007132
Score	2.2990172
Snippet	Optimal control problems with delays in state and control variables are studied. Constraints are imposed as mixed control–state inequality constraints.... Optimal control problems with delays in state and control variables are studied. Constraints are imposed as mixed control-state inequality constraints....
SourceID	proquest crossref wiley istex
SourceType	Aggregation Database Enrichment Source Index Database Publisher
StartPage	341
SubjectTerms	Chemical engineering Delay delays in state and control Discretization discretization methods Mathematical analysis Mathematical models mixed control-state inequality constraints Nonlinear programming Optimal control optimal control of a CSTR reactor optimal fishing Pontryagin's minimum principle retarded optimal control problems Terminals
Title	Optimal control problems with delays in state and control variables subject to mixed control-state constraints
URI	https://api.istex.fr/ark:/67375/WNG-TLXWLP6F-M/fulltext.pdf https://onlinelibrary.wiley.com/doi/abs/10.1002%2Foca.843 https://www.proquest.com/docview/753696614
Volume	30
WOSCitedRecordID	wos000268706700001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVWIB databaseName: Wiley Online Library customDbUrl: eissn: 1099-1514 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0007132 issn: 0143-2087 databaseCode: DRFUL dateStart: 19960101 isFulltext: true titleUrlDefault: https://onlinelibrary.wiley.com providerName: Wiley-Blackwell
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3NTuMwEB6xLYflwM_uIgrsygfELUsbp4l9RECXQyloBaI3y3ZsqQJS1LQIbrwDb8iTMJOEUIRWQtpTJGcmsTzj8Yw9_gZgx7gkxGXCBF4mPIhSHQcy9SawBNQSeWvbXV8Um0gGAzEcyrO5Ul8lPkS94UYzo7DXNMG1yffeQEPR1P8WEf8CzRC1NmpA8_Bv76Jfm2GMvsIyf5GjKoikvDFLzHsV67ulqEmjev_Oz5z3VovlprfyHx1dheXKx2T7pVKswYLLvsHSHPLgd7g9RVNxg0RVqjqrCsvkjDZmGUFHPuRslLHiwhHTWVpT3mF0TfetcpbPDO3isOmY3YzuXU3y_PhUsllyPqkGxTT_ARe9o_OD46AqvhBYzjs80IIqvyRxqsPIdHlqvObOYzAdOusj6bnreCFkZISOQ4eNzlhOp7Im1Lbt2nwdGtk4cxvAkJOLWMeOext1pJepk1RAT0vbllqYFuy-ykHZCpmcOnetSkzlUOEQKhzCFrCa8LYE4_hIslsIsn6vJ1eUu5Z01eXgjzrvDy_7Z3FPneC3XiWtcEbRMYnO3HiWKwzgYkluSwt2Crn-61_q9GAfH5ufI9uCr-VJFKX6bkNjOpm5n7Bo76ajfPKr0t4XLYL4Pg
linkProvider	Wiley-Blackwell
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1fb9MwED9BiwQ8jL8ThQF-mPYW1sZpYj9O28oQWVuhVu2bZTu2VLGlU9NO423fYd-QT8JdkoVNCAmJp0jJXRL5zufz-e53ALvGJSEuEybwMuFBlOk4kJk3gSWglshb2-37stlEMhyK-VyO66xKqoWp8CGagBvNjNJe0wSngPT-b9RQtPWfRMQfQjtCJeq3oH30bTBNGzuM26-wSmDkqAsiqUpmiXm_Zr23FrVpWK_uOZp33dVyvRk8-58_fQ5btZfJDiq1eAEPXP4Snt7BHnwFFyM0FudIVCers7q1TMEoNMsIPPJHwRY5K0uOmM6zhvIS99dUcVWwYmMojsPWS3a-uHINyc_rm4rNkvtJXSjWxWuYDo4nhydB3X4hsJz3eKAF9X5J4kyHkenzzHjNncftdOisj6TnrueFkJEROg4d3nTGcjqXNaG2Xdfl29DKl7l7Aww5uYh17Li3UU96mTlJLfS0tF2phenA3q0glK2xyennzlSFqhwqHEKFQ9gB1hBeVHAcf5LslZJsnuvVd8peS_pqNvysJul8lo7jgTrFd92KWuGcooMSnbvlplC4hYslOS4d2C0F-7dvqdHhAV7e_hvZR3h8MjlNVfpl-PUdPKnOpSjxdwda69XGvYdH9nK9KFYfalX-Bfbg_C4
linkToPdf	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1fT9swED8NitB42AZjovuHHxBvgTZOE_sRwbJNdKVCIPpm2Y4tVRtp1bQI3vgO-4b7JLtLQgZCk5B4ipTcJZHPd76z734HsGNcEuIyYQIvEx5EmY4DmXkTWAJqiby1nZ4vm00kg4EYjeSwzqqkWpgKH6LZcCPNKO01KbibZn7_H2oo2vo9EfElaEU9GaNSto5O0_N-Y4cx_AqrBEaOc0EkVcksMe_XrA_WohYN6_UDR_O-u1quN-nr5_zpG3hVe5nsoJoW6_DC5Ruwdg978C1MT9BYXCJRnazO6tYyBaOtWUbgkTcFG-esLDliOs8ayiuMr6niqmDFwtA-DptP2OX42jUkf25_V2yW3E_qQjEvNuE8_XJ2-C2o2y8ElvMuD7Sg3i9JnOkwMj2eGa-58xhOh876SHruul4IGRmh49DhTWcsp3NZE2rbcR3-DpbzSe62gCEnF7GOHfc26kovMyephZ6WtiO1MG3YvROEsjU2Of3cL1WhKocKh1DhELaBNYTTCo7jMcluKcnmuZ79pOy1pKcuBl_VWX900R_GqfqB77oTtUKdooMSnbvJolAYwsWSHJc27JSC_d-31MnhAV7eP41sG1aHR6nqfx8cf4CX1bEU5f1-hOX5bOE-wYq9mo-L2ed6Jv8Fip_7qQ
openUrl	ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Optimal+control+problems+with+delays+in+state+and+control+variables+subject+to+mixed+control%E2%80%93state+constraints&rft.jtitle=Optimal+control+applications+%26+methods&rft.au=G%C3%B6llmann%2C+L.&rft.au=Kern%2C+D.&rft.au=Maurer%2C+H.&rft.date=2009-07-01&rft.pub=John+Wiley+%26+Sons%2C+Ltd&rft.issn=0143-2087&rft.eissn=1099-1514&rft.volume=30&rft.issue=4&rft.spage=341&rft.epage=365&rft_id=info:doi/10.1002%2Foca.843&rft.externalDBID=10.1002%252Foca.843&rft.externalDocID=OCA843
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0143-2087&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0143-2087&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0143-2087&client=summon