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Volumn 25, Issue 3, 2014, Pages 621-634

Policy iteration adaptive dynamic programming algorithm for discrete-time nonlinear systems

Author keywords

Adaptive critic designs; adaptive dynamic programming (ADP); approximate dynamic programming; discrete time policy iteration; neural networks; neurodynamic programming; nonlinear systems; optimal control; reinforcement learning

Indexed keywords

ADAPTIVE CRITIC DESIGNS; ADAPTIVE DYNAMIC PROGRAMMING; APPROXIMATE DYNAMIC PROGRAMMING; NEURO DYNAMIC PROGRAMMING; OPTIMAL CONTROLS; POLICY ITERATION;

EID: 84897594646     PISSN: 2162237X     EISSN: 21622388     Source Type: Journal    
DOI: 10.1109/TNNLS.2013.2281663     Document Type: Article
Times cited : (646)

References (50)
  • 1
    • 85012688561 scopus 로고
    • Princeton NJ USA: Princeton Univ. Press
    • R. E. Bellman, Dynamic Programming. Princeton, NJ, USA: Princeton Univ. Press, 1957.
    • (1957) Dynamic Programming
    • Bellman, R.E.1
  • 2
    • 0002557583 scopus 로고
    • Advanced forecasting methods for global crisis warning and models of intelligence
    • Jan.
    • P. J. Werbos, "Advanced forecasting methods for global crisis warning and models of intelligence," General Syst. Yearbook, vol. 22, pp. 25-38, Jan. 1977.
    • (1977) General Syst. Yearbook , vol.22 , pp. 25-38
    • Werbos, P.J.1
  • 3
    • 0002011091 scopus 로고
    • A menu of designs for reinforcement learning over time
    • W. T. Miller, R. S. Sutton, and P. J. Werbos, Ed., Cambridge, MA, USA: MIT Press
    • P. J. Werbos, "A menu of designs for reinforcement learning over time," in Neural Networks for Control, W. T. Miller, R. S. Sutton, and P. J. Werbos, Ed., Cambridge, MA, USA: MIT Press, 1991, pp. 67-95.
    • (1991) Neural Networks for Control , pp. 67-95
    • Werbos, P.J.1
  • 4
    • 84875270081 scopus 로고    scopus 로고
    • Online optimal control of affine nonlinear discrete-time systems with unknown internal dynamics by using timebased policy update
    • Jul.
    • T. Dierks and S. Jagannathan, "Online optimal control of affine nonlinear discrete-time systems with unknown internal dynamics by using timebased policy update," IEEE Trans. Neurl Netw. Learn. Syst., vol. 23, no. 7, pp. 1118-1129, Jul. 2012.
    • (2012) IEEE Trans. Neurl Netw. Learn. Syst. , vol.23 , Issue.7 , pp. 1118-1129
    • Dierks, T.1    Jagannathan, S.2
  • 5
    • 84876158475 scopus 로고    scopus 로고
    • Simple and fast calculation of the second-order gradients for globalized dual heuristic dynamic programming in neural networks
    • Oct.
    • M. Fairbank, E. Alonso, and D. Prokhorov, "Simple and fast calculation of the second-order gradients for globalized dual heuristic dynamic programming in neural networks," IEEE Trans. Neural Netw. Learn. Syst., vol. 23, no. 10, pp. 1671-1676, Oct. 2012.
    • (2012) IEEE Trans. Neural Netw. Learn. Syst. , vol.23 , Issue.10 , pp. 1671-1676
    • Fairbank, M.1    Alonso, E.2    Prokhorov, D.3
  • 6
    • 84877914583 scopus 로고    scopus 로고
    • Robust adaptive dynamic programming with an application to power systems
    • Jul.
    • Y. Jiang and Z. P. Jiang, "Robust adaptive dynamic programming with an application to power systems," IEEE Trans. Neural Netw. Learn. Syst., vol. 24, no. 7, pp. 1150-1156, Jul. 2013.
    • (2013) IEEE Trans. Neural Netw. Learn. Syst. , vol.24 , Issue.7 , pp. 1150-1156
    • Jiang, Y.1    Jiang, Z.P.2
  • 7
    • 26844483839 scopus 로고    scopus 로고
    • A self-learning call admission control scheme for CDMA cellular networks
    • DOI 10.1109/TNN.2005.853408
    • D. Liu, Y. Zhang, and H. Zhang, "A self-learning call admission control scheme for CDMA cellular networks," IEEE Trans. Neural Netw., vol. 16, no. 5, pp. 1219-1228, Sep. 2005. (Pubitemid 41444623)
    • (2005) IEEE Transactions on Neural Networks , vol.16 , Issue.5 , pp. 1219-1228
    • Liu, D.1    Zhang, Y.2    Zhang, H.3
  • 8
    • 84876149222 scopus 로고    scopus 로고
    • Adaptive learning in tracking control based on the dual critic network design
    • Jun.
    • Z. Ni, H. He, and J. Wen, "Adaptive learning in tracking control based on the dual critic network design," IEEE Trans. Neural Netw. Learn. Syst., vol. 24, no. 6, pp. 913-928, Jun. 2013.
    • (2013) IEEE Trans. Neural Netw. Learn. Syst. , vol.24 , Issue.6 , pp. 913-928
    • Ni, Z.1    He, H.2    Wen, J.3
  • 9
    • 84877928110 scopus 로고    scopus 로고
    • Neural networkbased optimal adaptive output feedback control of a helicopter UAV
    • Jul.
    • D. Nodland, H. Zargarzadeh, and S. Jagannathan, "Neural networkbased optimal adaptive output feedback control of a helicopter UAV," IEEE Trans. Neural Netw. Learn. Syst., vol. 24, no. 7, pp. 1061-1073, Jul. 2013.
    • (2013) IEEE Trans. Neural Netw. Learn. Syst. , vol.24 , Issue.7 , pp. 1061-1073
    • Nodland, D.1    Zargarzadeh, H.2    Jagannathan, S.3
  • 10
    • 84872617336 scopus 로고    scopus 로고
    • A neuralnetwork-based iterative GDHP approach for solving a class of nonlinear optimal control problems with control constraints
    • Feb.
    • D. Wang, D. Liu, D. Zhao, Y. Huang, and D. Zhang, "A neuralnetwork-based iterative GDHP approach for solving a class of nonlinear optimal control problems with control constraints," Neural Comput. Appl., vol. 22, no. 2, pp. 219-227, Feb. 2013.
    • (2013) Neural Comput. Appl. , vol.22 , Issue.2 , pp. 219-227
    • Wang, D.1    Liu, D.2    Zhao, D.3    Huang, Y.4    Zhang, D.5
  • 11
    • 84862815087 scopus 로고    scopus 로고
    • Stochastic optimal control of unknown linear networked control system in the presence of random delays and packet losses
    • Jun.
    • H. Xu, S. Jagannathan, and F. L. Lewis, "Stochastic optimal control of unknown linear networked control system in the presence of random delays and packet losses," Automatica, vol. 48, no. 6, pp. 1017-1030, Jun. 2012.
    • (2012) Automatica , vol.48 , Issue.6 , pp. 1017-1030
    • Xu, H.1    Jagannathan, S.2    Lewis, F.L.3
  • 12
    • 84884958993 scopus 로고    scopus 로고
    • Stochastic optimal controller design for uncertain nonlinear networked control system via neuro dynamic programming
    • Mar.
    • H. Xu and S. Jagannathan, "Stochastic optimal controller design for uncertain nonlinear networked control system via neuro dynamic programming," IEEE Trans. Neural Netw. Learn. Syst., vol. 24, no. 3, pp. 471-484, Mar. 2013.
    • (2013) IEEE Trans. Neural Netw. Learn. Syst. , vol.24 , Issue.3 , pp. 471-484
    • Xu, H.1    Jagannathan, S.2
  • 13
    • 84857646134 scopus 로고    scopus 로고
    • Wide-area measurement based dynamic stochastic optimal power flow control for smart grids with high variability and uncertainty
    • Mar.
    • J. Liang, G. K. Venayagamoorthy, and R. G. Harley, "Wide-area measurement based dynamic stochastic optimal power flow control for smart grids with high variability and uncertainty," IEEE Trans. Smart Grid, vol. 3, no. 1, pp. 59-69, Mar. 2012.
    • (2012) IEEE Trans. Smart Grid , vol.3 , Issue.1 , pp. 59-69
    • Liang, J.1    Venayagamoorthy, G.K.2    Harley, R.G.3
  • 15
    • 84884922436 scopus 로고    scopus 로고
    • Online learning control using adaptive critic designs with sparse kernel machines
    • May
    • X. Xu, Z. Hou, C. Lian, and H. He, "Online learning control using adaptive critic designs with sparse kernel machines," IEEE Trans. Neural Netw. Learn. Syst., vol. 24, no. 5, pp. 762-775, May 2013.
    • (2013) IEEE Trans. Neural Netw. Learn. Syst. , vol.24 , Issue.5 , pp. 762-775
    • Xu, X.1    Hou, Z.2    Lian, C.3    He, H.4
  • 16
    • 84863467146 scopus 로고    scopus 로고
    • Neural-network-based optimal control for a class of unknown discrete-time nonlinear systems using globalized dual heuristic programming
    • Jul.
    • D. Liu, D. Wang, D. Zhao, Q. Wei, and N. Jin, "Neural-network-based optimal control for a class of unknown discrete-time nonlinear systems using globalized dual heuristic programming," IEEE Trans. Autom. Sci. Eng., vol. 9, no. 3, pp. 628-634, Jul. 2012.
    • (2012) IEEE Trans. Autom. Sci. Eng. , vol.9 , Issue.3 , pp. 628-634
    • Liu, D.1    Wang, D.2    Zhao, D.3    Wei, Q.4    Jin, N.5
  • 18
    • 84864489666 scopus 로고    scopus 로고
    • Optimal control of unknown nonaffine nonlinear discrete-time systems based on adaptive dynamic programming
    • Aug.
    • D. Wang, D. Liu, Q. Wei, D. Zhao, and N. Jin, "Optimal control of unknown nonaffine nonlinear discrete-time systems based on adaptive dynamic programming," Automatica, vol. 48, no. 8, pp. 1825-1832, Aug. 2012.
    • (2012) Automatica , vol.48 , Issue.8 , pp. 1825-1832
    • Wang, D.1    Liu, D.2    Wei, Q.3    Zhao, D.4    Jin, N.5
  • 19
    • 84862811062 scopus 로고    scopus 로고
    • An iterative optimal control scheme for a class of discrete time nonlinear systems with unfixed initial state
    • Aug.
    • Q. Wei and D. Liu, "An iterative optimal control scheme for a class of discrete-time nonlinear systems with unfixed initial state," Neural Netw., vol. 32, pp. 236-244, Aug. 2012.
    • (2012) Neural Netw. , vol.32 , pp. 236-244
    • Wei, Q.1    Liu, D.2
  • 20
    • 83655167263 scopus 로고    scopus 로고
    • Approximate dynamic programming for optimal stationary control with control-dependent noise
    • Dec.
    • Y. Jiang and Z. P. Jiang, "Approximate dynamic programming for optimal stationary control with control-dependent noise," IEEE Trans. Neurl Netw., vol. 22, no. 12, pp. 2392-2398, Dec. 2011.
    • (2011) IEEE Trans. Neurl Netw. , vol.22 , Issue.12 , pp. 2392-2398
    • Jiang, Y.1    Jiang, Z.P.2
  • 21
    • 0002031779 scopus 로고
    • Approximate dynamic programming for real-time control and neural modeling
    • D. A. White and D. A. Sofge, Ed., New York, NY, USA: Van Nostrand Reinhold ch. 13
    • P. J. Werbos, "Approximate dynamic programming for real-time control and neural modeling," in Handbook of Intelligent Control: Neural, Fuzzy, and Adaptive Approaches, D. A. White and D. A. Sofge, Ed., New York, NY, USA: Van Nostrand Reinhold, 1992, ch. 13.
    • (1992) Handbook of Intelligent Control: Neural, Fuzzy, and Adaptive Approaches
    • Werbos, P.J.1
  • 22
    • 0043026775 scopus 로고    scopus 로고
    • Helicopter trimming and tracking control using direct neural dynamic programming
    • Aug.
    • R. Enns and J. Si, "Helicopter trimming and tracking control using direct neural dynamic programming," IEEE Trans. Neural Netw., vol. 14, no. 4, pp. 929-939, Aug. 2003.
    • (2003) IEEE Trans. Neural Netw. , vol.14 , Issue.4 , pp. 929-939
    • Enns, R.1    Si, J.2
  • 24
    • 0035273403 scopus 로고    scopus 로고
    • On-line learning control by association and reinforcement
    • DOI 10.1109/72.914523, PII S1045922701014047
    • J. Si and Y.-T. Wang, "On-line learning control by association and reinforcement," IEEE Trans. Neural Netw., vol. 12, no. 2, pp. 264-276, Mar. 2001. (Pubitemid 32371483)
    • (2001) IEEE Transactions on Neural Networks , vol.12 , Issue.2 , pp. 264-276
    • Si, J.1    Wang, Y.-T.2
  • 25
    • 84876108223 scopus 로고    scopus 로고
    • Algorithmic survey of parametric value function approximation
    • Jun.
    • M. Geist and O. Pietquin, "Algorithmic survey of parametric value function approximation," IEEE Trans. Neural Netw. Learn. Syst., vol. 24, no. 6, pp. 845-867, Jun. 2013.
    • (2013) IEEE Trans. Neural Netw. Learn. Syst. , vol.24 , Issue.6 , pp. 845-867
    • Geist, M.1    Pietquin, O.2
  • 26
    • 84884963190 scopus 로고    scopus 로고
    • Policy improvement by a model-free Dyna architecture
    • May
    • K. S. Hwang and C. Y. Lo, "Policy improvement by a model-free Dyna architecture," IEEE Trans. Neural Netw. Learn. Syst., vol. 24, no. 5, pp. 776-788, May 2013.
    • (2013) IEEE Trans. Neural Netw. Learn. Syst. , vol.24 , Issue.5 , pp. 776-788
    • Hwang, K.S.1    Lo, C.Y.2
  • 27
    • 0004049893 scopus 로고
    • Ph.D. dissertation Dept. Comput. Sci., Cambridge Univ., Cambridge, U.K.
    • C. Watkins, "Learning from delayed rewards," Ph.D. dissertation, Dept. Comput. Sci., Cambridge Univ., Cambridge, U.K., 1989.
    • (1989) Learning from Delayed Rewards
    • Watkins, C.1
  • 28
    • 84872594962 scopus 로고    scopus 로고
    • A self-learning scheme for residential energy system control and management
    • Feb.
    • T. Huang and D. Liu, "A self-learning scheme for residential energy system control and management," Neural Comput. Appl., vol. 22, no. 2, pp. 259-269, Feb. 2013.
    • (2013) Neural Comput. Appl. , vol.22 , Issue.2 , pp. 259-269
    • Huang, T.1    Liu, D.2
  • 29
    • 84878421441 scopus 로고    scopus 로고
    • Optimal control for discrete-time affine nonlinear systems using general value iteration
    • Dec.
    • H. Li and D. Liu, "Optimal control for discrete-time affine nonlinear systems using general value iteration," IET Control Theory Appl., vol. 6, no. 18, pp. 2725-2736, Dec. 2012.
    • (2012) IET Control Theory Appl. , vol.6 , Issue.18 , pp. 2725-2736
    • Li, H.1    Liu, D.2
  • 30
    • 84881555023 scopus 로고    scopus 로고
    • Finite-approximation-error-based optimal control approach for discrete-time nonlinear systems
    • Apr.
    • D. Liu and Q. Wei, "Finite-approximation-error-based optimal control approach for discrete-time nonlinear systems," IEEE Trans. Cybern., vol. 43, no. 2, pp. 779-789, Apr. 2013.
    • (2013) IEEE Trans. Cybern. , vol.43 , Issue.2 , pp. 779-789
    • Liu, D.1    Wei, Q.2
  • 31
    • 84885176157 scopus 로고    scopus 로고
    • Adaptive optimal control of unknown constrained-input systems using policy iteration and neural networks
    • Aug. to be published
    • H. Modares, F. L. Lewis, and M. B. Naghibi-Sistani, "Adaptive optimal control of unknown constrained-input systems using policy iteration and neural networks," IEEE Trans. Neural Netw. Learn. Syst., Aug. 2013, to be published.
    • (2013) IEEE Trans. Neural Netw. Learn. Syst.
    • Modares, H.1    Lewis, F.L.2    Naghibi-Sistani, M.B.3
  • 32
    • 78651311269 scopus 로고    scopus 로고
    • Adaptive dynamic programming for finite-horizon optimal control of discrete-time nonlinear systems with error bound
    • Jan.
    • F. Wang, N. Jin, D. Liu, and Q. Wei, "Adaptive dynamic programming for finite-horizon optimal control of discrete-time nonlinear systems with error bound," J. Control Theory Appl., vol. 22, no. 1, pp. 24-36, Jan. 2011.
    • (2011) J. Control Theory Appl. , vol.22 , Issue.1 , pp. 24-36
    • Wang, F.1    Jin, N.2    Liu, D.3    Wei, Q.4
  • 33
    • 82755160758 scopus 로고    scopus 로고
    • Finite-horizon neuro-optimal tracking control for a class of discrete-time nonlinear systems using adaptive dynamic programming approach
    • Feb.
    • D. Wang, D. Liu, and Q. Wei, "Finite-horizon neuro-optimal tracking control for a class of discrete-time nonlinear systems using adaptive dynamic programming approach," Neurocomputing, vol. 78, no. 1, pp. 14-22, Feb. 2012.
    • (2012) Neurocomputing , vol.78 , Issue.1 , pp. 14-22
    • Wang, D.1    Liu, D.2    Wei, Q.3
  • 34
    • 61849184281 scopus 로고    scopus 로고
    • Model-free multiobjective approximate dynamic programming for discrete-time nonlinear systems with general performance index functions
    • Q. Wei, H. Zhang, and J. Dai, "Model-free multiobjective approximate dynamic programming for discrete-time nonlinear systems with general performance index functions," Neurocomputing, vol. 72, nos. 7-9, pp. 1839-1848, 2009.
    • (2009) Neurocomputing , vol.72 , Issue.7-9 , pp. 1839-1848
    • Wei, Q.1    Zhang, H.2    Dai, J.3
  • 35
    • 83855165164 scopus 로고    scopus 로고
    • Optimal tracking control for a class of nonlinear discrete-time systems with time delays based on heuristic dynamic programming
    • Dec.
    • H. Zhang, R. Song, Q. Wei, and T. Zhang, "Optimal tracking control for a class of nonlinear discrete-time systems with time delays based on heuristic dynamic programming," IEEE Trans. Neural Netw., vol. 22, no. 12, pp. 1851-1862, Dec. 2011.
    • (2011) IEEE Trans. Neural Netw. , vol.22 , Issue.12 , pp. 1851-1862
    • Zhang, H.1    Song, R.2    Wei, Q.3    Zhang, T.4
  • 36
    • 70349116541 scopus 로고    scopus 로고
    • Reinforcement learning and adaptive dynamic programming for feedback control
    • Jul.
    • F. L. Lewis and D. Vrabie, "Reinforcement learning and adaptive dynamic programming for feedback control," IEEE Circuits Syst. Mag., vol. 9, no. 3, pp. 32-50, Jul. 2009.
    • (2009) IEEE Circuits Syst. Mag. , vol.9 , Issue.3 , pp. 32-50
    • Lewis, F.L.1    Vrabie, D.2
  • 37
    • 84883537695 scopus 로고    scopus 로고
    • Reinforcement learning and feedback control: Using natural decision methods to design optimal adaptive controllers
    • Dec.
    • F. L. Lewis, D. Vrabie, and K. G. Vamvoudakis, "Reinforcement learning and feedback control: Using natural decision methods to design optimal adaptive controllers," IEEE Control Syst., vol. 32, no. 6, pp. 76-105, Dec. 2012.
    • (2012) IEEE Control Syst. , vol.32 , Issue.6 , pp. 76-105
    • Lewis, F.L.1    Vrabie, D.2    Vamvoudakis, K.G.3
  • 39
    • 49049089962 scopus 로고    scopus 로고
    • Discrete-time nonlinear HJB solution using approximate dynamic programming: Convergence proof
    • Aug.
    • A. Al-Tamimi, F. L. Lewis, and M. Abu-Khalaf, "Discrete-time nonlinear HJB solution using approximate dynamic programming: Convergence proof," IEEE Trans. Syst., Man, Cybern., Part B, Cybern., vol. 38, no. 4, pp. 943-949, Aug. 2008.
    • (2008) IEEE Trans. Syst., Man, Cybern., Part B, Cybern. , vol.38 , Issue.4 , pp. 943-949
    • Al-Tamimi, A.1    Lewis, F.L.2    Abu-Khalaf, M.3
  • 40
    • 49049119493 scopus 로고    scopus 로고
    • A novel infinite-time optimal tracking control scheme for a class of discrete-time nonlinear systems via the greedy HDP iteration algorithm
    • Jul.
    • H. Zhang, Q. Wei, and Y. Luo, "A novel infinite-time optimal tracking control scheme for a class of discrete-time nonlinear systems via the greedy HDP iteration algorithm," IEEE Trans. Syst., Man, Cybern., Part B, Cybern., vol. 38, no. 4, pp. 937-942, Jul. 2008.
    • (2008) IEEE Trans. Syst., Man, Cybern., Part B, Cybern. , vol.38 , Issue.4 , pp. 937-942
    • Zhang, H.1    Wei, Q.2    Luo, Y.3
  • 41
    • 84876066909 scopus 로고    scopus 로고
    • Neural-network-based zero-sum game for discrete-time nonlinear systems via iterative adaptive dynamic programming algorithm
    • Jun.
    • D. Liu, H. Li, and D. Wang, "Neural-network-based zero-sum game for discrete-time nonlinear systems via iterative adaptive dynamic programming algorithm," Neurocomputing, vol. 110, pp. 92-100, Jun. 2013.
    • (2013) Neurocomputing , vol.110 , pp. 92-100
    • Liu, D.1    Li, H.2    Wang, D.3
  • 42
    • 84868467610 scopus 로고    scopus 로고
    • An iterative adaptive dynamic programming algorithm for optimal control of unknown discretetime nonlinear systems with constrained inputs
    • Jan.
    • D. Liu, D. Wang, and X. Yang, "An iterative adaptive dynamic programming algorithm for optimal control of unknown discretetime nonlinear systems with constrained inputs," Inf. Sci., vol. 220, pp. 331-342, Jan. 2013.
    • (2013) Inf. Sci. , vol.220 , pp. 331-342
    • Liu, D.1    Wang, D.2    Yang, X.3
  • 43
    • 14844340822 scopus 로고    scopus 로고
    • Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach
    • DOI 10.1016/j.automatica.2004.11.034, PII S0005109805000105
    • M. Abu-Khalaf and F. L. Lewis, "Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach," Automatica, vol. 41, no. 5, pp. 779-791, May 2005. (Pubitemid 40352391)
    • (2005) Automatica , vol.41 , Issue.5 , pp. 779-791
    • Abu-Khalaf, M.1    Lewis, F.L.2
  • 44
    • 78650805234 scopus 로고    scopus 로고
    • An iterative adaptive dynamic programming method for solving a class of nonlinear zero-sum differential games
    • Jan.
    • H. Zhang, Q. Wei, and D. Liu, "An iterative adaptive dynamic programming method for solving a class of nonlinear zero-sum differential games," Automatica, vol. 47, no. 1, pp. 207-214, Jan. 2011.
    • (2011) Automatica , vol.47 , Issue.1 , pp. 207-214
    • Zhang, H.1    Wei, Q.2    Liu, D.3
  • 45
    • 84864491417 scopus 로고    scopus 로고
    • Multi-agent differential graphical games: Online adaptive learning solution for synchronization with optimality
    • K. G. Vamvoudakis, F. L. Lewis, and G. R. Hudas, "Multi-agent differential graphical games: Online adaptive learning solution for synchronization with optimality," Automatica, vol. 48, no. 8, pp. 1598-1611, 2012.
    • (2012) Automatica , vol.48 , Issue.8 , pp. 1598-1611
    • Vamvoudakis, K.G.1    Lewis, F.L.2    Hudas, G.R.3
  • 46
    • 84871319455 scopus 로고    scopus 로고
    • A novel actor-critic-identifier architecture for approximate optimal control of uncertain nonlinear systems
    • Jan.
    • S. Bhasin, R. Kamalapurkar, M. Johnson, K. G. Vamvoudakis, F. L. Lewis, and W. E. Dixon, "A novel actor-critic-identifier architecture for approximate optimal control of uncertain nonlinear systems," Automatica, vol. 49, no. 1, pp. 82-92, Jan. 2013.
    • (2013) Automatica , vol.49 , Issue.1 , pp. 82-92
    • Bhasin, S.1    Kamalapurkar, R.2    Johnson, M.3    Vamvoudakis, K.G.4    Lewis, F.L.5    Dixon, W.E.6
  • 47
    • 83655163786 scopus 로고    scopus 로고
    • Data-driven robust approximate optimal tracking control for unknown general nonlinear systems using adaptive dynamic programming method
    • Dec.
    • H. Zhang, L. Cui, X. Zhang, and Y. Luo, "Data-driven robust approximate optimal tracking control for unknown general nonlinear systems using adaptive dynamic programming method," IEEE Trans. Neural Netw., vol. 22, no. 12, pp. 2226-2236, Dec. 2011.
    • (2011) IEEE Trans. Neural Netw. , vol.22 , Issue.12 , pp. 2226-2236
    • Zhang, H.1    Cui, L.2    Zhang, X.3    Luo, Y.4
  • 49
    • 84880065287 scopus 로고    scopus 로고
    • Finite-horizon control-constrained nonlinear optimal control using single network adaptive critics
    • Jan.
    • A. Heydari and S. N. Balakrishnan, "Finite-horizon control-constrained nonlinear optimal control using single network adaptive critics," IEEE Trans. Neural Netw. Learn. Syst., vol. 24, no. 1, pp. 145-157, Jan. 2013.
    • (2013) IEEE Trans. Neural Netw. Learn. Syst. , vol.24 , Issue.1 , pp. 145-157
    • Heydari, A.1    Balakrishnan, S.N.2


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