Adaptive dynamic programming for a class of complex-valued nonlinear systems

IEEE Transactions on Neural Networks and Learning Systems

Volumn 25, Issue 9, 2014, Pages 1733-1739

  Song, Ruizhuo ^a   Xiao, Wendong ^a   Zhang, Huaguang ^b   Sun, Changyin ^a  

^a UNIVERSITY OF SCIENCE AND TECHNOLOGY BEIJING   (China)

^b NORTHEASTERN UNIVERSITY   (China)

Author keywords

Adaptive critic designs; adaptive dynamic programming (ADP); approximate complex valued systems; dynamic programming; neural networks.; optimal control

Indexed keywords

COMPLEX NETWORKS; MATHEMATICAL TRANSFORMATIONS; NEURAL NETWORKS; NONLINEAR SYSTEMS; OPTIMAL CONTROL SYSTEMS; STABILITY;

ADAPTIVE CRITIC DESIGNS; ADAPTIVE DYNAMIC PROGRAMMING; COMPENSATION CONTROLLER; COMPLEX-VALUED; CONVERGENCE PROPERTIES; OPTIMAL CONTROL PROBLEM; OPTIMAL CONTROL SCHEME; OPTIMAL CONTROLS;

DYNAMIC PROGRAMMING;

EID: 84906781179     PISSN: 2162237X     EISSN: 21622388     Source Type: Journal    
DOI: 10.1109/TNNLS.2014.2306201     Document Type: Article

References (44)

1. T. Adali, P. Schreier, and L. Scharf, "Complex-valued signal processing: The proper way to deal with impropriety," IEEE Trans. Signal Process., vol. 59, no. 11, pp. 5101-5125, Nov. 2011.
2. T. Fang and J. Sun, "Stability analysis of complex-valued impulsive system," IET Control Theory Appl., vol. 7, no. 8, pp. 1152-1159, Aug. 2013.
3. C. Yang, "Stability and quantization of complex-valued nonlinear quantum systems," Chaos, Solitons Fractals, vol. 42, no. 2, pp. 711-723, Oct. 2009.
4. J. Hu and J. Wang, "Global stability of complex-valued recurrent neural networks with time-delays," IEEE Trans. Neural Netw. Learn. Syst., vol. 23, no. 6, pp. 853-865, Jun. 2012.
5. S. Huang, C. Li, and Y. Liu, "Complex-valued filtering based on the minimization of complex-error entropy," IEEE Trans. Neural Netw. Learn. Syst., vol. 24, no. 5, pp. 695-708, May 2013.
6. X. Hong and S. Chen, "Modeling of complex-valued Wiener systems using B-spline neural network," IEEE Trans. Neural Netw., vol. 22, no. 5, pp. 818-825, May 2011.
7. S. Goh and D. Mandic, "Nonlinear adaptive prediction of complexvalued signals by complex-valued PRNN," IEEE Trans. Signal Process., vol. 53, no. 5, pp. 1827-1836, May 2005. (Pubitemid 40679154)
8. S. Bolognani, A. Smyshlyaev, and M. Krstic, "Adaptive output feedback control for complex-valued reaction-advection-diffusion systems," in Proc. Amer. Control Conf., Seattle, Washington, USA, Jun. 2008, pp. 961-966.
9. T. Hamagami, T. Shibuya, and S. Shimada, "Complex-valued reinforcement learning," in Proc. IEEE Int. Conf. Syst., Man, Cybern., Taipei, Taiwan, Oct. 2006, pp. 4175-4179. (Pubitemid 47297734)
10. A. Paulraj, R. Nabar, and D. Gore, Introduction to Space-Time Wireless Communications. Cambridge, U.K.: Cambridge Univ. Press, 2003.
11. P. J. Werbos, "Advanced forecasting methods for global crisis warning and models of intelligence," General Syst. Yearbook, vol. 22, pp. 25-38, 1977.
12. 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, Eds. Cambridge, MA, USA: MIT Press, 1991, pp. 67-95.
13. 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.
14. D. Liu, H. Javaherian, O. Kovalenko, and T. Huang, "Adaptive critic learning techniques for engine torque and air-fuel ratio control," IEEE Trans. Syst., Man, Cybern., B, Cybern., vol. 38, no. 4, pp. 988-993, Aug. 2008.
15. D. Liu, D. Wang, and X. Yang, "An iterative adaptive dynamic programming algorithm for optimal control of unknown discrete-time nonlinear systems with constrained inputs," Inf. Sci., vol. 220, pp. 331-342, Jan. 2013.
16. 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.
17. 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)
18. Z. Wang and D. Liu, "A data-based state feedback control method for a class of nonlinear systems," IEEE Trans. Ind. Inf., vol. 9, no. 4, pp. 2284-2292, Nov. 2013.
19. 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, no. 6, pp. 236-244, Aug. 2012.
20. Q. Wei and D. Liu, "A novel iterative ?-adaptive dynamic programming for discrete-time nonlinear systems," IEEE Trans. Autom. Sci. Eng., 2014, doi: 10.1109/TASE.2013.2280974.
21. 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.
22. D. V. Prokhorov and D. C. Wunsch, "Adaptive critic designs," IEEE Trans. Neural Netw., vol. 8, no. 5, pp. 997-1007, Sep. 1997. (Pubitemid 127763331)
23. J. Liang, D. D. Molina, G. K. Venayagamoorthy, and R. G. Harley, "Two-level dynamic stochastic optimal power flow control for power systems with intermittent renewable generation," IEEE Trans. Power Syst., vol. 28, no. 3, pp. 2670-2678, Aug. 2013.
24. Z. Ni, H. He, J. Wen, and X. Xu, "Goal representation heuristic dynamic programming on maze navigation," IEEE Trans. Neural Netw. Learn. Syst., vol. 24, no. 12, pp. 2038-2050, Dec. 2013.
25. 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.
26. Q. Wei and D. Liu, "Adaptive dynamic programming for optimal tracking control of unknown nonlinear systems with application to coal gasification," IEEE Trans. Autom. Sci. Eng., 2014, doi: 10.1109/TIE.2014.2301770.
27. M. Fairbank, E. Alonso, and D. Prokhorov, "An equivalence between adaptive dynamic programming with a critic and backpropagation through time," IEEE Trans. Neural Netw. Learn. Syst., vol. 24, no. 12, pp. 2088-2100, Dec. 2013.
28. X. Xu, C. Lian, L. Zuo, and H. He, "Kernel-based approximate dynamic programming for real-time online learning control: An experimental study," IEEE Trans. Control Syst. Technol., vol. 22, no. 1, pp. 146-156, Jan. 2014.
29. D. Molina, G. K. Venayagamoorthy, J. Liang, and R. G. Harley, "Intelligent local area signals based damping of power system oscillations using virtual generators and approximate dynamic programming," IEEE Trans. Smart Grid, vol. 4, no. 1, pp. 498-508, Jan. 2013.
30. D. P. Bertsekas and J. N. Tsitsiklis, Neuro-Dynamic Programming. Belmont, MA, USA: Athena Scientific, 1996.
31. 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.
32. 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.
33. B. Xu, C. Yang, and Z. Shi, "Reinforcement learning output feedback NN control using deterministic learning technique," IEEE Trans. Neural Netw. Learn. Syst., vol. 25, no. 3, pp. 635-641, Feb. 2014.
34. 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.
35. K. G. Vamvoudakis and F. L. Lewis, "Multi-player non-zero-sum games: Online adaptive learning solution of coupled Hamilton-Jacobi equations," Automatica, vol. 47, no. 8, pp. 1556-1569, Aug. 2011.
36. 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., B, Cybern., vol. 38, no. 4, pp. 937-942, Aug. 2008.
37. Y. Huang and D. Liu, "Neural-network-based optimal tracking control scheme for a class of unknown discrete-time nonlinear systems using iterative ADP algorithm," Neurocomputing, vol. 125, pp. 46-56, Feb. 2014.
38. K. Hengster-Movric, K. You, F. L. Lewis, and L. Xie, " Synchronization of discrete-time multi-agent systems on graphs using Riccati design," Automatica, vol. 49, no. 2, pp. 414-423, Feb. 2013.
39. D. P. Mandic and V. S. L. Goh, Complex Valued Nonlinear Adaptive Filters: Noncircularity, Widely Linear and Neural Models. New York, NY, USA: Wiley, 2009.
40. K. G. Vamvoudakis and F. L. Lewis, "Online actor-critic algorithm to solve the continuous-time infinite horizon optimal control problem," Automatica, vol. 46, no. 5, pp. 878-888, May 2010.
41. 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. Neural Netw. Learn. Syst., vol. 23, no. 7, pp. 1118-1129, Apr. 2012.
42. H. K. Khalil, Nonlinear System. Upper Saddle River, NJ, USA: Prentice-Hall, 2002.
43. G. M. Mahmoud, S. A. Aly, and A. A. Farghaly, "On chaos synchronization of a complex two coupled dynamos system," Chaos, Solitons Fractals, vol. 33, pp. 178-187, Jul. 2007. (Pubitemid 46209788)
44. F. L. Lewis, S. Jagannathan, and A. Yesildirek, Neural Network Control of Robot Manipulators and Nonlinear Systems. New York, NY, USA: Taylor & Francis, 1999.