Primal–dual adaptive dynamic programming for finite-horizon optimal control of nonlinear systems with isoperimetric constraints

In this paper, a novel primal–dual adaptive dynamic programming (PDADP) method is developed to solve finite-horizon optimal control problems (OCPs) with isoperimetric constraints for continuous-time nonlinear systems. The OCP with isoperimetric constraints is approximated by a series of linear quadr...

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Veröffentlicht in:Automatica (Oxford) Jg. 173; S. 112029
Hauptverfasser: Wei, Qinglai, Li, Tao, Zhang, Jie, Wang, Fei-Yue
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Ltd 01.03.2025
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Abstract In this paper, a novel primal–dual adaptive dynamic programming (PDADP) method is developed to solve finite-horizon optimal control problems (OCPs) with isoperimetric constraints for continuous-time nonlinear systems. The OCP with isoperimetric constraints is approximated by a series of linear quadratic time-varying OCPs with isoperimetric quadratic constraints, which are solved by the primal–dual (PD) method. The convergence of the PDADP method is proven. Furthermore, the optimality of the solution is analyzed by deriving the necessary optimality conditions via Pontryagin’s principle and proving that the limiting values of the iterations satisfy the necessary optimality conditions. Finally, simulation experiments are provided to show the effectiveness of the present PDADP method.
AbstractList In this paper, a novel primal–dual adaptive dynamic programming (PDADP) method is developed to solve finite-horizon optimal control problems (OCPs) with isoperimetric constraints for continuous-time nonlinear systems. The OCP with isoperimetric constraints is approximated by a series of linear quadratic time-varying OCPs with isoperimetric quadratic constraints, which are solved by the primal–dual (PD) method. The convergence of the PDADP method is proven. Furthermore, the optimality of the solution is analyzed by deriving the necessary optimality conditions via Pontryagin’s principle and proving that the limiting values of the iterations satisfy the necessary optimality conditions. Finally, simulation experiments are provided to show the effectiveness of the present PDADP method.
ArticleNumber 112029
Author Wei, Qinglai
Li, Tao
Wang, Fei-Yue
Zhang, Jie
Author_xml – sequence: 1
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  surname: Wei
  fullname: Wei, Qinglai
  email: qinglai.wei@ia.ac.cn
  organization: State Key Laboratory of Multimodal Artificial Intelligence Systems, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China
– sequence: 2
  givenname: Tao
  surname: Li
  fullname: Li, Tao
  email: litao2019@ia.ac.cn
  organization: State Key Laboratory of Multimodal Artificial Intelligence Systems, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China
– sequence: 3
  givenname: Jie
  surname: Zhang
  fullname: Zhang, Jie
  email: jie.zhang@ia.ac.cn
  organization: State Key Laboratory of Multimodal Artificial Intelligence Systems, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China
– sequence: 4
  givenname: Fei-Yue
  surname: Wang
  fullname: Wang, Fei-Yue
  email: feiyue.wang@ia.ac.cn
  organization: State Key Laboratory of Multimodal Artificial Intelligence Systems, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China
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Cites_doi 10.1137/110853182
10.1137/0304013
10.1109/TAC.2018.2869462
10.1080/02331930701421061
10.1007/s10107-004-0559-y
10.1007/s00245-018-9532-7
10.1016/j.automatica.2014.07.012
10.1016/j.sysconle.2004.05.008
10.1109/TAC.2015.2414811
10.1016/j.automatica.2020.109421
10.1016/j.cherd.2019.10.027
10.1137/16M1062569
10.1109/TAC.2018.2790260
10.1007/s40819-022-01425-y
10.1109/TAC.1968.1098965
10.1109/TAC.1967.1098632
10.1016/j.automatica.2022.110564
10.1016/j.automatica.2022.110841
10.1090/S0002-9947-1983-0690039-8
10.1137/060661247
10.1016/j.automatica.2004.05.015
10.1007/BF00932663
10.4208/jcm.1003-m0015
10.1023/A:1019279617898
10.1016/j.automatica.2020.109433
10.1016/0022-0396(70)90005-7
10.1016/S0167-6911(00)00026-8
10.1109/TCT.1972.1083507
10.1016/j.automatica.2022.110347
10.1109/TAC.1967.1098488
10.1016/j.automatica.2020.109035
10.1109/TAC.2021.3087452
10.1002/(SICI)1099-1514(199903/04)20:2<79::AID-OCA647>3.0.CO;2-3
10.1016/j.automatica.2004.11.034
10.1109/9.774108
10.1016/j.automatica.2021.110058
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Keywords Isoperimetric constraints
Adaptive dynamic programming
Nonlinear systems
Optimal control
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References Tsiamis, Kalogerias, Chamon, Ribeiro, Pappas (b39) 2020
Zhou (b45) 2022; 142
Jiang, Jiang (b16) 2015; 60
Koenemann, Licitra, Alp, Diehl (b20) 2019
Pang, Jiang, Mareels (b33) 2020; 118
Schmitendorf (b34) 1976; 18
Lopez, Lewis (b26) 2018; 64
Boyd, Vandenberghe (b5) 2004
Soravia (b36) 2000; 40
Lee, Sutton (b23) 2021; 126
Jacobson (b15) 1970; 8
Moyalan, Choi, Chen, Vaidya (b32) 2023; 150
Sun (b37) 2021; 83
Lim, Zhou (b25) 1999; 44
He, Li, Du (b13) 2021; 125
Beard (b4) 1995
Kalman (b18) 1960; 5
Chyung (b6) 1967; 12
Miller, Sutton, Werbos (b31) 1995
Crandall, Lions (b9) 1983; 277
Malanowski (b28) 2007; 18
Cimen, Banks (b7) 2004; 53
Kumar, Vladimirsky (b21) 2010; 28
Lee (b22) 1967; 12
Grüne, Pannek, Grüne, Pannek (b12) 2017
Banks, Dinesh (b3) 2000; 98
Desoer, Haneda (b10) 1972; 19
Abu-Khalaf, Lewis (b1) 2005; 41
Zhang, Decardi-Nelson, Liu, Shen, Liu (b44) 2020; 153
Takei, Chen, Clawson, Kirov, Vladimirsky (b38) 2015; 53
Kelly (b19) 2017; 59
Mangasarian (b30) 1966; 4
Heydari (b14) 2018; 63
Govindarajan, de Visser, Krishnakumar (b11) 2014; 50
Sohrab (b35) 2003
Wei, Zhu, Li, Liu (b41) 2021; 67
Malanowski (b29) 2007; 56
Lim, Liu, Teo, Moore (b24) 1999; 20
Wächter, Biegler (b40) 2006; 106
Zouhri, El Baroudi, Saadi (b46) 2022; 8
Cimen, Banks (b8) 2004; 40
Banas, Vacroux (b2) 1968; 13
Luenberger (b27) 1997
Werbos (b42) 1977
Xie, Yu, Lan (b43) 2022; 146
Jiang, Zhou (b17) 2022; 136
Lim (10.1016/j.automatica.2024.112029_b24) 1999; 20
Takei (10.1016/j.automatica.2024.112029_b38) 2015; 53
Zouhri (10.1016/j.automatica.2024.112029_b46) 2022; 8
Sun (10.1016/j.automatica.2024.112029_b37) 2021; 83
Xie (10.1016/j.automatica.2024.112029_b43) 2022; 146
Wächter (10.1016/j.automatica.2024.112029_b40) 2006; 106
Pang (10.1016/j.automatica.2024.112029_b33) 2020; 118
Schmitendorf (10.1016/j.automatica.2024.112029_b34) 1976; 18
Malanowski (10.1016/j.automatica.2024.112029_b29) 2007; 56
Abu-Khalaf (10.1016/j.automatica.2024.112029_b1) 2005; 41
Kumar (10.1016/j.automatica.2024.112029_b21) 2010; 28
Miller (10.1016/j.automatica.2024.112029_b31) 1995
Desoer (10.1016/j.automatica.2024.112029_b10) 1972; 19
Werbos (10.1016/j.automatica.2024.112029_b42) 1977
Zhang (10.1016/j.automatica.2024.112029_b44) 2020; 153
Tsiamis (10.1016/j.automatica.2024.112029_b39) 2020
Grüne (10.1016/j.automatica.2024.112029_b12) 2017
Jiang (10.1016/j.automatica.2024.112029_b16) 2015; 60
Zhou (10.1016/j.automatica.2024.112029_b45) 2022; 142
Kalman (10.1016/j.automatica.2024.112029_b18) 1960; 5
Mangasarian (10.1016/j.automatica.2024.112029_b30) 1966; 4
Lee (10.1016/j.automatica.2024.112029_b23) 2021; 126
Chyung (10.1016/j.automatica.2024.112029_b6) 1967; 12
Govindarajan (10.1016/j.automatica.2024.112029_b11) 2014; 50
Lopez (10.1016/j.automatica.2024.112029_b26) 2018; 64
Luenberger (10.1016/j.automatica.2024.112029_b27) 1997
Sohrab (10.1016/j.automatica.2024.112029_b35) 2003
Soravia (10.1016/j.automatica.2024.112029_b36) 2000; 40
Banks (10.1016/j.automatica.2024.112029_b3) 2000; 98
Lim (10.1016/j.automatica.2024.112029_b25) 1999; 44
Crandall (10.1016/j.automatica.2024.112029_b9) 1983; 277
Cimen (10.1016/j.automatica.2024.112029_b8) 2004; 40
Moyalan (10.1016/j.automatica.2024.112029_b32) 2023; 150
Malanowski (10.1016/j.automatica.2024.112029_b28) 2007; 18
Cimen (10.1016/j.automatica.2024.112029_b7) 2004; 53
Kelly (10.1016/j.automatica.2024.112029_b19) 2017; 59
Heydari (10.1016/j.automatica.2024.112029_b14) 2018; 63
He (10.1016/j.automatica.2024.112029_b13) 2021; 125
Jacobson (10.1016/j.automatica.2024.112029_b15) 1970; 8
Boyd (10.1016/j.automatica.2024.112029_b5) 2004
Lee (10.1016/j.automatica.2024.112029_b22) 1967; 12
Wei (10.1016/j.automatica.2024.112029_b41) 2021; 67
Beard (10.1016/j.automatica.2024.112029_b4) 1995
Koenemann (10.1016/j.automatica.2024.112029_b20) 2019
Banas (10.1016/j.automatica.2024.112029_b2) 1968; 13
Jiang (10.1016/j.automatica.2024.112029_b17) 2022; 136
References_xml – volume: 277
  start-page: 1
  year: 1983
  end-page: 42
  ident: b9
  article-title: Viscosity solutions of Hamilton-Jacobi equations
  publication-title: Transactions of the American Mathematical Society
– year: 2003
  ident: b35
  article-title: Basic real analysis
– volume: 146
  year: 2022
  ident: b43
  article-title: Optimal output regulation for unknown continuous-time linear systems by internal model and adaptive dynamic programming
  publication-title: Automatica
– volume: 125
  year: 2021
  ident: b13
  article-title: Lexicographic multi-objective MPC for constrained nonlinear systems with changing objective prioritization
  publication-title: Automatica
– volume: 12
  start-page: 87
  year: 1967
  end-page: 90
  ident: b22
  article-title: Linear optimal control problems with isoperimetric constraints
  publication-title: IEEE Transactions on Automatic Control
– year: 1997
  ident: b27
  article-title: Optimization by vector space methods
– volume: 44
  start-page: 1359
  year: 1999
  end-page: 1369
  ident: b25
  article-title: Stochastic optimal LQR control with integral quadratic constraints and indefinite control weights
  publication-title: IEEE Transactions on Automatic Control
– volume: 40
  start-page: 325
  year: 2000
  end-page: 335
  ident: b36
  article-title: Viscosity solutions and optimal control problems with integral constraints
  publication-title: Systems & Control Letters
– year: 1995
  ident: b4
  article-title: Improving the closed-loop performance of nonlinear systems
– volume: 59
  start-page: 849
  year: 2017
  end-page: 904
  ident: b19
  article-title: An introduction to trajectory optimization: How to do your own direct collocation
  publication-title: SIAM Review
– volume: 20
  start-page: 79
  year: 1999
  end-page: 92
  ident: b24
  article-title: Linear-quadratic optimal control with integral quadratic constraints
  publication-title: Optimal Control Applications and Methods
– volume: 13
  start-page: 439
  year: 1968
  end-page: 440
  ident: b2
  article-title: On linear systems with a time-varying delay and isoperimetric constraints
  publication-title: IEEE Transactions on Automatic Control
– volume: 56
  start-page: 463
  year: 2007
  end-page: 478
  ident: b29
  article-title: Stability and sensitivity analysis for linear-quadratic optimal control subject to state constraints
  publication-title: Optimization
– volume: 53
  start-page: 712
  year: 2015
  end-page: 744
  ident: b38
  article-title: Optimal control with budget constraints and resets
  publication-title: SIAM Journal on Control and Optimization
– volume: 67
  start-page: 2610
  year: 2021
  end-page: 2617
  ident: b41
  article-title: A new approach to finite-horizon optimal control for discrete-time affine nonlinear systems via a pseudolinear method
  publication-title: IEEE Transactions on Automatic Control
– year: 2004
  ident: b5
  article-title: Convex optimization
– volume: 18
  start-page: 926
  year: 2007
  end-page: 945
  ident: b28
  article-title: Stability analysis for nonlinear optimal control problems subject to state constraints
  publication-title: SIAM Journal on Optimization
– volume: 136
  year: 2022
  ident: b17
  article-title: Bias-policy iteration based adaptive dynamic programming for unknown continuous-time linear systems
  publication-title: Automatica
– volume: 40
  start-page: 1845
  year: 2004
  end-page: 1863
  ident: b8
  article-title: Nonlinear optimal tracking control with application to super-tankers for autopilot design
  publication-title: Automatica
– volume: 50
  start-page: 2234
  year: 2014
  end-page: 2244
  ident: b11
  article-title: A sparse collocation method for solving time-dependent HJB equations using multivariate B-splines
  publication-title: Automatica
– volume: 64
  start-page: 2869
  year: 2018
  end-page: 2874
  ident: b26
  article-title: Dynamic multiobjective control for continuous-time systems using reinforcement learning
  publication-title: IEEE Transactions on Automatic Control
– volume: 4
  start-page: 139
  year: 1966
  end-page: 152
  ident: b30
  article-title: Sufficient conditions for the optimal control of nonlinear systems
  publication-title: SIAM Journal on Control
– volume: 8
  start-page: 258
  year: 1970
  end-page: 263
  ident: b15
  article-title: New conditions for boundedness of the solution of a matrix Riccati differential equation
  publication-title: Journal of Differential Equations
– start-page: 3040
  year: 2020
  end-page: 3047
  ident: b39
  article-title: Risk-constrained linear-quadratic regulators
  publication-title: IEEE conference on decision and control (CDC)
– volume: 60
  start-page: 2917
  year: 2015
  end-page: 2929
  ident: b16
  article-title: Global adaptive dynamic programming for continuous-time nonlinear systems
  publication-title: IEEE Transactions on Automatic Control
– volume: 19
  start-page: 480
  year: 1972
  end-page: 486
  ident: b10
  article-title: The measure of a matrix as a tool to analyze computer algorithms for circuit analysis
  publication-title: IEEE Transactions on Circuit Theory
– volume: 18
  start-page: 561
  year: 1976
  end-page: 567
  ident: b34
  article-title: Pontryagin’s principle for problems with isoperimetric constraints and for problems with inequality terminal constraints
  publication-title: Journal of Optimization Theory and Applications
– volume: 63
  start-page: 3119
  year: 2018
  end-page: 3126
  ident: b14
  article-title: Stability analysis of optimal adaptive control using value iteration with approximation errors
  publication-title: IEEE Transactions on Automatic Control
– volume: 98
  start-page: 19
  year: 2000
  end-page: 44
  ident: b3
  article-title: Approximate optimal control and stability of nonlinear finite-and infinite-dimensional systems
  publication-title: Annals of Operations Research
– volume: 142
  year: 2022
  ident: b45
  article-title: Viscosity solutions to first order path-dependent Hamilton–Jacobi–Bellman equations in Hilbert space
  publication-title: Automatica
– year: 1995
  ident: b31
  article-title: A menu of designs for reinforcement learning over time
– start-page: 1
  year: 2019
  end-page: 2
  ident: b20
  article-title: OpenOCL-Open optimal control library
  publication-title: Proceedings of the 2019 robotics: science and system conference
– volume: 153
  start-page: 246
  year: 2020
  end-page: 256
  ident: b44
  article-title: Zone economic model predictive control of a coal-fired boiler-turbine generating system
  publication-title: Chemical Engineering Research and Design
– volume: 12
  start-page: 434
  year: 1967
  end-page: 435
  ident: b6
  article-title: Linear time-lag systems with side constraints
  publication-title: IEEE Transactions on Automatic Control
– volume: 41
  start-page: 779
  year: 2005
  end-page: 791
  ident: b1
  article-title: Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach
  publication-title: Automatica
– year: 2017
  ident: b12
  article-title: Nonlinear model predictive control
– volume: 28
  start-page: 517
  year: 2010
  end-page: 551
  ident: b21
  article-title: An efficient method for multiobjective optimal control and optimal control subject to integral constraints
  publication-title: Journal of Computational Mathematics
– volume: 118
  year: 2020
  ident: b33
  article-title: Reinforcement learning for adaptive optimal control of continuous-time linear periodic systems
  publication-title: Automatica
– volume: 106
  start-page: 25
  year: 2006
  end-page: 57
  ident: b40
  article-title: On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
  publication-title: Mathematical Programming
– volume: 53
  start-page: 327
  year: 2004
  end-page: 346
  ident: b7
  article-title: Global optimal feedback control for general nonlinear systems with nonquadratic performance criteria
  publication-title: Systems & Control Letters
– volume: 126
  year: 2021
  ident: b23
  article-title: Policy iterations for reinforcement learning problems in continuous time and space—Fundamental theory and methods
  publication-title: Automatica
– volume: 150
  year: 2023
  ident: b32
  article-title: Data-driven optimal control via linear transfer operators: A convex approach
  publication-title: Automatica
– start-page: 25
  year: 1977
  end-page: 38
  ident: b42
  article-title: Advanced forecasting methods for global crisis warning and models of intelligence
  publication-title: General System Yearbook
– volume: 5
  start-page: 102
  year: 1960
  end-page: 119
  ident: b18
  article-title: Contributions to the theory of optimal control
  publication-title: Boletin de la Sociedad Matematica Mexicana
– volume: 83
  start-page: 251
  year: 2021
  end-page: 276
  ident: b37
  article-title: Linear quadratic optimal control problems with fixed terminal states and integral quadratic constraints
  publication-title: Applied Mathematics and Optimization
– volume: 8
  start-page: 215
  year: 2022
  ident: b46
  article-title: Optimal control with isoperimetric constraint for chemotherapy of tumors
  publication-title: International Journal of Applied and Computational Mathematics
– volume: 53
  start-page: 712
  issue: 2
  year: 2015
  ident: 10.1016/j.automatica.2024.112029_b38
  article-title: Optimal control with budget constraints and resets
  publication-title: SIAM Journal on Control and Optimization
  doi: 10.1137/110853182
– volume: 4
  start-page: 139
  issue: 1
  year: 1966
  ident: 10.1016/j.automatica.2024.112029_b30
  article-title: Sufficient conditions for the optimal control of nonlinear systems
  publication-title: SIAM Journal on Control
  doi: 10.1137/0304013
– volume: 64
  start-page: 2869
  issue: 7
  year: 2018
  ident: 10.1016/j.automatica.2024.112029_b26
  article-title: Dynamic multiobjective control for continuous-time systems using reinforcement learning
  publication-title: IEEE Transactions on Automatic Control
  doi: 10.1109/TAC.2018.2869462
– start-page: 3040
  year: 2020
  ident: 10.1016/j.automatica.2024.112029_b39
  article-title: Risk-constrained linear-quadratic regulators
– volume: 56
  start-page: 463
  issue: 4
  year: 2007
  ident: 10.1016/j.automatica.2024.112029_b29
  article-title: Stability and sensitivity analysis for linear-quadratic optimal control subject to state constraints
  publication-title: Optimization
  doi: 10.1080/02331930701421061
– volume: 106
  start-page: 25
  issue: 1
  year: 2006
  ident: 10.1016/j.automatica.2024.112029_b40
  article-title: On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
  publication-title: Mathematical Programming
  doi: 10.1007/s10107-004-0559-y
– volume: 83
  start-page: 251
  issue: 1
  year: 2021
  ident: 10.1016/j.automatica.2024.112029_b37
  article-title: Linear quadratic optimal control problems with fixed terminal states and integral quadratic constraints
  publication-title: Applied Mathematics and Optimization
  doi: 10.1007/s00245-018-9532-7
– volume: 50
  start-page: 2234
  issue: 9
  year: 2014
  ident: 10.1016/j.automatica.2024.112029_b11
  article-title: A sparse collocation method for solving time-dependent HJB equations using multivariate B-splines
  publication-title: Automatica
  doi: 10.1016/j.automatica.2014.07.012
– volume: 53
  start-page: 327
  issue: 5
  year: 2004
  ident: 10.1016/j.automatica.2024.112029_b7
  article-title: Global optimal feedback control for general nonlinear systems with nonquadratic performance criteria
  publication-title: Systems & Control Letters
  doi: 10.1016/j.sysconle.2004.05.008
– volume: 60
  start-page: 2917
  issue: 11
  year: 2015
  ident: 10.1016/j.automatica.2024.112029_b16
  article-title: Global adaptive dynamic programming for continuous-time nonlinear systems
  publication-title: IEEE Transactions on Automatic Control
  doi: 10.1109/TAC.2015.2414811
– volume: 126
  year: 2021
  ident: 10.1016/j.automatica.2024.112029_b23
  article-title: Policy iterations for reinforcement learning problems in continuous time and space—Fundamental theory and methods
  publication-title: Automatica
  doi: 10.1016/j.automatica.2020.109421
– volume: 153
  start-page: 246
  year: 2020
  ident: 10.1016/j.automatica.2024.112029_b44
  article-title: Zone economic model predictive control of a coal-fired boiler-turbine generating system
  publication-title: Chemical Engineering Research and Design
  doi: 10.1016/j.cherd.2019.10.027
– volume: 59
  start-page: 849
  issue: 4
  year: 2017
  ident: 10.1016/j.automatica.2024.112029_b19
  article-title: An introduction to trajectory optimization: How to do your own direct collocation
  publication-title: SIAM Review
  doi: 10.1137/16M1062569
– volume: 63
  start-page: 3119
  issue: 9
  year: 2018
  ident: 10.1016/j.automatica.2024.112029_b14
  article-title: Stability analysis of optimal adaptive control using value iteration with approximation errors
  publication-title: IEEE Transactions on Automatic Control
  doi: 10.1109/TAC.2018.2790260
– volume: 8
  start-page: 215
  issue: 4
  year: 2022
  ident: 10.1016/j.automatica.2024.112029_b46
  article-title: Optimal control with isoperimetric constraint for chemotherapy of tumors
  publication-title: International Journal of Applied and Computational Mathematics
  doi: 10.1007/s40819-022-01425-y
– volume: 13
  start-page: 439
  issue: 4
  year: 1968
  ident: 10.1016/j.automatica.2024.112029_b2
  article-title: On linear systems with a time-varying delay and isoperimetric constraints
  publication-title: IEEE Transactions on Automatic Control
  doi: 10.1109/TAC.1968.1098965
– volume: 12
  start-page: 434
  issue: 4
  year: 1967
  ident: 10.1016/j.automatica.2024.112029_b6
  article-title: Linear time-lag systems with side constraints
  publication-title: IEEE Transactions on Automatic Control
  doi: 10.1109/TAC.1967.1098632
– year: 2017
  ident: 10.1016/j.automatica.2024.112029_b12
– volume: 146
  year: 2022
  ident: 10.1016/j.automatica.2024.112029_b43
  article-title: Optimal output regulation for unknown continuous-time linear systems by internal model and adaptive dynamic programming
  publication-title: Automatica
  doi: 10.1016/j.automatica.2022.110564
– volume: 150
  year: 2023
  ident: 10.1016/j.automatica.2024.112029_b32
  article-title: Data-driven optimal control via linear transfer operators: A convex approach
  publication-title: Automatica
  doi: 10.1016/j.automatica.2022.110841
– volume: 277
  start-page: 1
  issue: 1
  year: 1983
  ident: 10.1016/j.automatica.2024.112029_b9
  article-title: Viscosity solutions of Hamilton-Jacobi equations
  publication-title: Transactions of the American Mathematical Society
  doi: 10.1090/S0002-9947-1983-0690039-8
– volume: 18
  start-page: 926
  issue: 3
  year: 2007
  ident: 10.1016/j.automatica.2024.112029_b28
  article-title: Stability analysis for nonlinear optimal control problems subject to state constraints
  publication-title: SIAM Journal on Optimization
  doi: 10.1137/060661247
– volume: 40
  start-page: 1845
  issue: 11
  year: 2004
  ident: 10.1016/j.automatica.2024.112029_b8
  article-title: Nonlinear optimal tracking control with application to super-tankers for autopilot design
  publication-title: Automatica
  doi: 10.1016/j.automatica.2004.05.015
– start-page: 25
  year: 1977
  ident: 10.1016/j.automatica.2024.112029_b42
  article-title: Advanced forecasting methods for global crisis warning and models of intelligence
  publication-title: General System Yearbook
– volume: 18
  start-page: 561
  issue: 4
  year: 1976
  ident: 10.1016/j.automatica.2024.112029_b34
  article-title: Pontryagin’s principle for problems with isoperimetric constraints and for problems with inequality terminal constraints
  publication-title: Journal of Optimization Theory and Applications
  doi: 10.1007/BF00932663
– year: 1995
  ident: 10.1016/j.automatica.2024.112029_b4
– year: 2004
  ident: 10.1016/j.automatica.2024.112029_b5
– volume: 28
  start-page: 517
  issue: 4
  year: 2010
  ident: 10.1016/j.automatica.2024.112029_b21
  article-title: An efficient method for multiobjective optimal control and optimal control subject to integral constraints
  publication-title: Journal of Computational Mathematics
  doi: 10.4208/jcm.1003-m0015
– volume: 98
  start-page: 19
  issue: 1
  year: 2000
  ident: 10.1016/j.automatica.2024.112029_b3
  article-title: Approximate optimal control and stability of nonlinear finite-and infinite-dimensional systems
  publication-title: Annals of Operations Research
  doi: 10.1023/A:1019279617898
– volume: 125
  year: 2021
  ident: 10.1016/j.automatica.2024.112029_b13
  article-title: Lexicographic multi-objective MPC for constrained nonlinear systems with changing objective prioritization
  publication-title: Automatica
  doi: 10.1016/j.automatica.2020.109433
– volume: 8
  start-page: 258
  issue: 2
  year: 1970
  ident: 10.1016/j.automatica.2024.112029_b15
  article-title: New conditions for boundedness of the solution of a matrix Riccati differential equation
  publication-title: Journal of Differential Equations
  doi: 10.1016/0022-0396(70)90005-7
– volume: 40
  start-page: 325
  issue: 5
  year: 2000
  ident: 10.1016/j.automatica.2024.112029_b36
  article-title: Viscosity solutions and optimal control problems with integral constraints
  publication-title: Systems & Control Letters
  doi: 10.1016/S0167-6911(00)00026-8
– volume: 19
  start-page: 480
  issue: 5
  year: 1972
  ident: 10.1016/j.automatica.2024.112029_b10
  article-title: The measure of a matrix as a tool to analyze computer algorithms for circuit analysis
  publication-title: IEEE Transactions on Circuit Theory
  doi: 10.1109/TCT.1972.1083507
– year: 1997
  ident: 10.1016/j.automatica.2024.112029_b27
– volume: 142
  year: 2022
  ident: 10.1016/j.automatica.2024.112029_b45
  article-title: Viscosity solutions to first order path-dependent Hamilton–Jacobi–Bellman equations in Hilbert space
  publication-title: Automatica
  doi: 10.1016/j.automatica.2022.110347
– volume: 12
  start-page: 87
  issue: 1
  year: 1967
  ident: 10.1016/j.automatica.2024.112029_b22
  article-title: Linear optimal control problems with isoperimetric constraints
  publication-title: IEEE Transactions on Automatic Control
  doi: 10.1109/TAC.1967.1098488
– volume: 118
  year: 2020
  ident: 10.1016/j.automatica.2024.112029_b33
  article-title: Reinforcement learning for adaptive optimal control of continuous-time linear periodic systems
  publication-title: Automatica
  doi: 10.1016/j.automatica.2020.109035
– volume: 67
  start-page: 2610
  issue: 5
  year: 2021
  ident: 10.1016/j.automatica.2024.112029_b41
  article-title: A new approach to finite-horizon optimal control for discrete-time affine nonlinear systems via a pseudolinear method
  publication-title: IEEE Transactions on Automatic Control
  doi: 10.1109/TAC.2021.3087452
– volume: 20
  start-page: 79
  issue: 2
  year: 1999
  ident: 10.1016/j.automatica.2024.112029_b24
  article-title: Linear-quadratic optimal control with integral quadratic constraints
  publication-title: Optimal Control Applications and Methods
  doi: 10.1002/(SICI)1099-1514(199903/04)20:2<79::AID-OCA647>3.0.CO;2-3
– volume: 41
  start-page: 779
  issue: 5
  year: 2005
  ident: 10.1016/j.automatica.2024.112029_b1
  article-title: Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach
  publication-title: Automatica
  doi: 10.1016/j.automatica.2004.11.034
– volume: 5
  start-page: 102
  issue: 2
  year: 1960
  ident: 10.1016/j.automatica.2024.112029_b18
  article-title: Contributions to the theory of optimal control
  publication-title: Boletin de la Sociedad Matematica Mexicana
– volume: 44
  start-page: 1359
  issue: 7
  year: 1999
  ident: 10.1016/j.automatica.2024.112029_b25
  article-title: Stochastic optimal LQR control with integral quadratic constraints and indefinite control weights
  publication-title: IEEE Transactions on Automatic Control
  doi: 10.1109/9.774108
– year: 1995
  ident: 10.1016/j.automatica.2024.112029_b31
– year: 2003
  ident: 10.1016/j.automatica.2024.112029_b35
– start-page: 1
  year: 2019
  ident: 10.1016/j.automatica.2024.112029_b20
  article-title: OpenOCL-Open optimal control library
– volume: 136
  year: 2022
  ident: 10.1016/j.automatica.2024.112029_b17
  article-title: Bias-policy iteration based adaptive dynamic programming for unknown continuous-time linear systems
  publication-title: Automatica
  doi: 10.1016/j.automatica.2021.110058
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Snippet In this paper, a novel primal–dual adaptive dynamic programming (PDADP) method is developed to solve finite-horizon optimal control problems (OCPs) with...
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SubjectTerms Adaptive dynamic programming
Isoperimetric constraints
Nonlinear systems
Optimal control
Title Primal–dual adaptive dynamic programming for finite-horizon optimal control of nonlinear systems with isoperimetric constraints
URI https://dx.doi.org/10.1016/j.automatica.2024.112029
Volume 173
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