Optimality conditions and duality for a non-linear time-delay control problem

Various types of sufficient conditions of optimality for non‐linear optimal control problems with delays in state and control variables are formulated. The involved functions are not required to be convex. A second‐order sufficient condition is shown to be related to the existence of solutions of a...

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Published inOptimal control applications & methods Vol. 18; no. 5; pp. 327 - 340
Main Authors Lee, Richard C. H., Yung, S. P.
Format Journal Article
LanguageEnglish
Published Chichester Wiley Subscription Services, Inc., A Wiley Company 01.09.1997
Wiley
Subjects
Applied sciences
Computer science; control theory; systems
Control theory. Systems
delay in control
delay in state
dual problem
Exact sciences and technology
Optimal control
optimal control problem
Riccati differential inequality
sufficient conditions
Second order
Optimal control
Non linear control
Optimality condition
Duality
Delay time
Riccati equation
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Abstract Various types of sufficient conditions of optimality for non‐linear optimal control problems with delays in state and control variables are formulated. The involved functions are not required to be convex. A second‐order sufficient condition is shown to be related to the existence of solutions of a Riccati‐type matrix differential inequality. Under certain concavity and convexity assumptions, dual problems are constructed without using convex conjugates. © 1997 John Wiley & Sons, Ltd.
AbstractList Various types of sufficient conditions of optimality for non‐linear optimal control problems with delays in state and control variables are formulated. The involved functions are not required to be convex. A second‐order sufficient condition is shown to be related to the existence of solutions of a Riccati‐type matrix differential inequality. Under certain concavity and convexity assumptions, dual problems are constructed without using convex conjugates. © 1997 John Wiley & Sons, Ltd.
Author Lee, Richard C. H.
Yung, S. P.
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10.1016/0362-546X(86)90057-X
10.1137/0324053
10.1137/0331026
10.1007/BF00952825
10.1137/0316060
10.1137/0306016
10.1109/TAC.1974.1100631
10.1007/BF02192046
10.1093/imamci/4.3.251
10.1093/imamci/5.2.125
10.1080/00207178308933097
10.1093/imamat/9.2.123-a
10.1007/BF02192027
10.1137/0320048
10.1007/BF01442179
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Issue 5
Keywords Second order
Optimal control
Non linear control
Optimality condition
Duality
Delay time
Riccati equation
Language English
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References Colonius, F. and D. Hinrichsen, 'Optimal control of functional differential systems', SIAM J. Control Optim., 16, 861-879 (1978).
Bien, Z. and S. H. Hwang, 'Sufficient conditions for optimal time-delay systems with applications to functionally constrained control problems', Int. J. Control, 38, 607-620 (1983).
Tsoutsinos, G. I. and R. B. Vinter, 'Duality theorems for convex problems with time delay', J. Optim. Theory Appl., 87, 167-195 (1995).
Chan, W. L. and S. P. Yung, 'Duality theory for the linear-convex optimal control problem with delays', IMA J. Math. Control Inform., 4, 251-262 (1987).
Zeidan, V., 'First and second-order sufficient conditions for optimal control and the calculus of variations', Appl. Math. Optim., 11, 209-226 (1984).
Clarke, F. H., Optimization and Nonsmooth Analysis, Wiley-Interscience, New York, 1983.
Kharatishvili, G. L., 'Maximum principle in the theory of optimum time delay processes', Dokl. Akad. Nauk USSR, 136, 39-42 (1961).
Banks, H. T. and A. Manitius, 'Applications of abstract variational theory to hereditary systems - a survey', IEEE Trans. Automat. Control, AC-19, 524-533 (1974).
Banks, H. T. and G. A. Kent, 'Control of functional differential equations of retarded and neutral type with target sets m function space', SIAM J. Control, 10, 567-593 (1972).
Clarke, F. H. and G. G. Watkins, 'Necessary conditions, controllability and the value function for differential difference inclusions', Nonlinear Anal. - Theory, Methods Appl., 10, 1155-1179 (1986).
Barbu, V. and Th. Precupanu, Convexity and Optimization in Branch Spaces, Editura Academiei, Bucuresti/Sijthoff and Noordhoff, Groningen, 1978.
Halanay, A., 'Optimal control for systems with time lag,' SIAM J. Control, 6, 215-234 (1968).
Ichikawa, A., 'Quadratic control of evolution equations with delay in control', SIAM J. Control Optim., 20, 645-668 (1982).
Delfour, M. C., 'The linear-quadratic optimal control problem with delays in state and control variables: a state space approach', SIAM J. Control Optim., 24, 835-883 (1986).
Chan W. L. and S. P. Yung, 'Sufficient conditions for variational problems with delayed argument', J. Optim Theory Appl., 76, 131-144 (1993).
Noble, B. and M. J. Sewell, 'One dual extremum principles in applied mathematics', J. Inst. Math. Appl. 9, 124-193 (1972).
Lee, C. H. and S. P. Yung, 'Sufficient conditions for optimal control problems with time delay', J. Optim. Theory Appl., 88, 157-176 (1996).
Rosenblueth, J. F., 'Systems with time delay in the calculus of variations: a variational approach', IMA J. Math. Control Inform., 5, 125-145 (1988).
Dontchev, A. L. and W. W. Hager, 'Lipschitzian stability in nonlinear control and optimization', SIAM J. Control Optim., 31, 569-603 (1993).
1972; 9
1974; AC‐19
1986; 10
1987; 4
1982; 20
1986; 24
1993; 76
1988; 5
1984; 11
1993; 31
1968; 6
1995; 87
1974
1995
1961; 136
1972; 10
1978; 16
1983
1983; 38
1978
1996; 88
Halanay (10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB2) 1968; 6
Büskens (10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB19) 1995
Chan (10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB21) 1987; 4
Colonius (10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB12) 1978; 16
Clarke (10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB22) 1983
Lee (10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB16) 1996; 88
Zeidan (10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB14) 1983
Dontchev (10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB20) 1993; 31
Manitius (10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB3) 1974
Banks (10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB9) 1972; 10
Noble (10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB18) 1972; 9
Kharatishvili (10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB1) 1961; 136
Chan (10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB7) 1993; 76
Bien (10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB11) 1983; 38
Rosenblueth (10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB8) 1988; 5
Zeidan (10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB15) 1984; 11
Ichikawa (10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB5) 1982; 20
Delfour (10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB6) 1986; 24
Barbu (10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB10) 1978
Tsoutsinos (10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB13) 1995; 87
Banks (10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB4) 1974; AC-19
Clarke (10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB17) 1986; 10
References_xml – volume: 10
  start-page: 567
  year: 1972
  end-page: 593
  article-title: Control of functional differential equations of retarded and neutral type with target sets m function space
  publication-title: SIAM J. Control
– year: 1983
– volume: 10
  start-page: 1155
  year: 1986
  end-page: 1179
  article-title: Necessary conditions, controllability and the value function for differential difference inclusions
  publication-title: Nonlinear Anal. ‐ Theory, Methods Appl.
– volume: 11
  start-page: 209
  year: 1984
  end-page: 226
  article-title: First and second‐order sufficient conditions for optimal control and the calculus of variations
  publication-title: Appl. Math. Optim.
– volume: 9
  start-page: 124
  year: 1972
  end-page: 193
  article-title: One dual extremum principles in applied mathematics
  publication-title: J. Inst. Math. Appl.
– volume: 4
  start-page: 251
  year: 1987
  end-page: 262
  article-title: Duality theory for the linear‐convex optimal control problem with delays
  publication-title: IMA J. Math. Control Inform.
– volume: 88
  start-page: 157
  year: 1996
  end-page: 176
  article-title: Sufficient conditions for optimal control problems with time delay
  publication-title: J. Optim. Theory Appl.
– volume: 31
  start-page: 569
  year: 1993
  end-page: 603
  article-title: Lipschitzian stability in nonlinear control and optimization
  publication-title: SIAM J. Control Optim.
– volume: 16
  start-page: 861
  year: 1978
  end-page: 879
  article-title: Optimal control of functional differential systems
  publication-title: SIAM J. Control Optim.
– volume: 20
  start-page: 645
  year: 1982
  end-page: 668
  article-title: Quadratic control of evolution equations with delay in control
  publication-title: SIAM J. Control Optim.
– volume: 87
  start-page: 167
  year: 1995
  end-page: 195
  article-title: Duality theorems for convex problems with time delay
  publication-title: J. Optim. Theory Appl.
– year: 1974
– year: 1995
– volume: 136
  start-page: 39
  year: 1961
  end-page: 42
  article-title: Maximum principle in the theory of optimum time delay processes
  publication-title: Dokl. Akad. Nauk USSR
– volume: 24
  start-page: 835
  year: 1986
  end-page: 883
  article-title: The linear‐quadratic optimal control problem with delays in state and control variables: a state space approach
  publication-title: SIAM J. Control Optim.
– year: 1978
– volume: 38
  start-page: 607
  year: 1983
  end-page: 620
  article-title: Sufficient conditions for optimal time‐delay systems with applications to functionally constrained control problems
  publication-title: Int. J. Control
– volume: 6
  start-page: 215
  year: 1968
  end-page: 234
  article-title: Optimal control for systems with time lag
  publication-title: SIAM J. Control
– volume: 5
  start-page: 125
  year: 1988
  end-page: 145
  article-title: Systems with time delay in the calculus of variations: a variational approach
  publication-title: IMA J. Math. Control Inform.
– volume: AC‐19
  start-page: 524
  year: 1974
  end-page: 533
  article-title: Applications of abstract variational theory to hereditary systems – a survey
  publication-title: IEEE Trans. Automat. Control
– volume: 76
  start-page: 131
  year: 1993
  end-page: 144
  article-title: Sufficient conditions for variational problems with delayed argument
  publication-title: J. Optim Theory Appl.
– volume: 10
  start-page: 567
  year: 1972
  ident: 10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB9
  publication-title: SIAM J. Control
  doi: 10.1137/0310043
  contributor:
    fullname: Banks
– volume-title: Convexity and Optimization in Branch Spaces
  year: 1978
  ident: 10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB10
  contributor:
    fullname: Barbu
– volume: 10
  start-page: 1155
  year: 1986
  ident: 10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB17
  publication-title: Nonlinear Anal. - Theory, Methods Appl.
  doi: 10.1016/0362-546X(86)90057-X
  contributor:
    fullname: Clarke
– volume: 24
  start-page: 835
  year: 1986
  ident: 10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB6
  publication-title: SIAM J. Control Optim.
  doi: 10.1137/0324053
  contributor:
    fullname: Delfour
– volume: 31
  start-page: 569
  year: 1993
  ident: 10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB20
  publication-title: SIAM J. Control Optim.
  doi: 10.1137/0331026
  contributor:
    fullname: Dontchev
– year: 1983
  ident: 10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB14
  contributor:
    fullname: Zeidan
– volume: 76
  start-page: 131
  year: 1993
  ident: 10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB7
  publication-title: J. Optim Theory Appl.
  doi: 10.1007/BF00952825
  contributor:
    fullname: Chan
– year: 1995
  ident: 10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB19
  contributor:
    fullname: Büskens
– volume-title: Optimization and Nonsmooth Analysis
  year: 1983
  ident: 10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB22
  contributor:
    fullname: Clarke
– volume: 16
  start-page: 861
  year: 1978
  ident: 10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB12
  publication-title: SIAM J. Control Optim.
  doi: 10.1137/0316060
  contributor:
    fullname: Colonius
– volume: 6
  start-page: 215
  year: 1968
  ident: 10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB2
  publication-title: SIAM J. Control
  doi: 10.1137/0306016
  contributor:
    fullname: Halanay
– year: 1974
  ident: 10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB3
  contributor:
    fullname: Manitius
– volume: AC-19
  start-page: 524
  year: 1974
  ident: 10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB4
  publication-title: IEEE Trans. Automat. Control
  doi: 10.1109/TAC.1974.1100631
  contributor:
    fullname: Banks
– volume: 87
  start-page: 167
  year: 1995
  ident: 10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB13
  publication-title: J. Optim. Theory Appl.
  doi: 10.1007/BF02192046
  contributor:
    fullname: Tsoutsinos
– volume: 4
  start-page: 251
  year: 1987
  ident: 10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB21
  publication-title: IMA J. Math. Control Inform.
  doi: 10.1093/imamci/4.3.251
  contributor:
    fullname: Chan
– volume: 5
  start-page: 125
  year: 1988
  ident: 10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB8
  publication-title: IMA J. Math. Control Inform.
  doi: 10.1093/imamci/5.2.125
  contributor:
    fullname: Rosenblueth
– volume: 38
  start-page: 607
  year: 1983
  ident: 10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB11
  publication-title: Int. J. Control
  doi: 10.1080/00207178308933097
  contributor:
    fullname: Bien
– volume: 9
  start-page: 124
  year: 1972
  ident: 10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB18
  publication-title: J. Inst. Math. Appl.
  doi: 10.1093/imamat/9.2.123-a
  contributor:
    fullname: Noble
– volume: 88
  start-page: 157
  year: 1996
  ident: 10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB16
  publication-title: J. Optim. Theory Appl.
  doi: 10.1007/BF02192027
  contributor:
    fullname: Lee
– volume: 136
  start-page: 39
  year: 1961
  ident: 10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB1
  publication-title: Dokl. Akad. Nauk USSR
  contributor:
    fullname: Kharatishvili
– volume: 20
  start-page: 645
  year: 1982
  ident: 10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB5
  publication-title: SIAM J. Control Optim.
  doi: 10.1137/0320048
  contributor:
    fullname: Ichikawa
– volume: 11
  start-page: 209
  year: 1984
  ident: 10.1002/(SICI)1099-1514(199709/10)18:5<327::AID-OCA614>3.0.CO;2-9-BIB15
  publication-title: Appl. Math. Optim.
  doi: 10.1007/BF01442179
  contributor:
    fullname: Zeidan
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Snippet Various types of sufficient conditions of optimality for non‐linear optimal control problems with delays in state and control variables are formulated. The...
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SubjectTerms Applied sciences
Computer science; control theory; systems
Control theory. Systems
delay in control
delay in state
dual problem
Exact sciences and technology
Optimal control
optimal control problem
Riccati differential inequality
sufficient conditions
Title Optimality conditions and duality for a non-linear time-delay control problem
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Volume 18
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