Neural-network-based adaptive optimal tracking control scheme for discrete-time nonlinear systems with approximation errors

Neurocomputing

Volumn 149, Issue Part A, 2015, Pages 106-115

  Wei, Qinglai ^a   Liu, Derong ^a  

^a INSTITUTE OF AUTOMATION   (China)

Author keywords

Adaptive critic designs; Adaptive dynamic programming; Approximate dynamic programming; Approximation errors; Optimal tracking control; Value iteration

Indexed keywords

ADAPTIVE CONTROL SYSTEMS; APPROXIMATION ALGORITHMS; CONTROL THEORY; DISCRETE TIME CONTROL SYSTEMS; ERRORS; ITERATIVE METHODS; NAVIGATION; NONLINEAR SYSTEMS;

ADAPTIVE CRITIC DESIGNS; ADAPTIVE DYNAMIC PROGRAMMING; APPROXIMATE DYNAMIC PROGRAMMING; APPROXIMATION ERRORS; OPTIMAL TRACKING CONTROL; VALUE ITERATION;

DYNAMIC PROGRAMMING;

ACCURACY; ADAPTIVE DYNAMIC PROGRAMMING ALGORITHM; ALGORITHM; ANALYTICAL ERROR; ARTICLE; CONTROL SYSTEM; LAW; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; NERVE CELL NETWORK; NONLINEAR SYSTEM; POLICY; SIMULATION; STATISTICAL PARAMETERS;

EID: 84961289199     PISSN: 09252312     EISSN: 18728286     Source Type: Journal    
DOI: 10.1016/j.neucom.2013.09.069     Document Type: Article

References (47)

1. Ha I.J., Gilbert E.G. Robust tracking in nonlinear systems. IEEE Trans. Autom. Control 1987, 32:763-771.
2. Cui L., Zhang H., Chen B., Zhang Q. Asymptotic tracking control scheme for mechanical systems with external disturbances and friction. Neurocomputing 2010, 73:1293-1302.
3. Miao B., Li T., Luo W. A DSC and MLP based robust adaptive NN tracking control for underwater vehicle. Neurocomputing 2013, 111:184-189.
4. ∞ tracking control of uncertain nonlinear systems. Neurocomputing 2013, 99:15-24.
5. Zhang X., Zhang H., Sun Q., Luo Y. Adaptive dynamic programming-based optimal control of unknown nonaffine nonlinear discrete-time systems with proof of convergence. Neurocomputing 2012, 91:48-55.
6. Werbos P.J. Advanced forecasting methods for global crisis warning and models of intelligence. Gen. Syst. Yearb. 1977, 22:25-38.
7. Werbos P.J. A menu of designs for reinforcement learning over time. Neural Networks for Control 1991, 67-95. MIT Press, Cambridge. W.T. Miller, R.S. Sutton, P.J. Werbos (Eds.).
8. Si J., Wang Y.T. On-line learning control by association and reinforcement. IEEE Trans. Neural Netw. 2001, 12:264-276.
9. Wei Q., Zhang H., Dai J. Model-free multiobjective approximate dynamic programming for discrete-time nonlinear systems with general performance index functions. Neurocomputing 2009, 72:1839-1848.
10. Xu X., Hou Z., Lian C., He H. Online learning control using adaptive critic designs with sparse kernel machines. IEEE Trans. Neural Netw. Learn. Syst. 2013, 24:762-775.
11. Wei Q., Liu D. Numerical adaptive learning control scheme for discrete-time nonlinear systems. IET Control Theory Appl. 2013, 7:1472-1486.
12. Wang D., Liu D. Neuro-optimal control for a class of unknown nonlinear dynamic systems using SN-DHP technique. Neurocomputing 2013, 121:218-225.
13. Liu D., Huang Y., Wang D., Wei Q. Neural network observer-based optimal control for unknown nonlinear systems using adaptive dynamic programming. Int. J. Control 2013, 86:1554-1566.
14. Liu D., Zhang Y., Zhang H. A self-learning call admission control scheme for CDMA cellular networks. IEEE Trans. Neural Netw. 2005, 16:1219-1228.
15. Prokhorov D.V., Wunsch D.C. Adaptive critic designs. IEEE Trans. Neural Netw. 1997, 8:997-1007.
16. Murray J.J., Cox C.J., Lendaris G.G., Saeks R. Adaptive dynamic programming. IEEE Trans. Syst. Man Cybern.-Part C: Appl. Rev. 2002, 32:140-153.
17. Wang F., Zhang H., Liu D. Adaptive dynamic programming. an introduction. IEEE Comput. Intell. Mag. 2009, 4:39-47.
18. Al-Tamimi A., Lewis F.L., Abu-Khalaf M. Discrete-time nonlinear HJB solution using approximate dynamic programming. convergence proof. IEEE Trans. Syst. Man Cybern.-Part B: Cybern. 2008, 38:943-949.
19. P.J. Werbos, Approximate dynamic programming for real-time control and neural modeling, in: D.A. White, D.A. Sofge (Eds.), Handbook of Intelligent Control: Neural Fuzzy and Adaptive Approaches, New York, 1992 (Chapter 13).
20. Enns R., Si J. Helicopter trimming and tracking control using direct neural dynamic programming. IEEE Trans. Neural Netw. 2003, 14:929-939.
21. Bertsekas D.P., Tsitsiklis J.N. Neuro-Dynamic Programming 1996, Athena Scientific, MA.
22. Lewis F.L., Kyriakos V.G. Reinforcement learning for partially observable dynamic processes: adaptive dynamic programming using measured output data. IEEE Trans. Syst. Man Cybern.-Part B: Cybern. 2011, 41:14-25.
23. C. Watkins, Learning from Delayed Rewards (Ph.D. Thesis), Cambridge University, Cambridge, England, 1989.
24. Song R., Xiao W., Zhang H. Multi-objective optimal control for a class of unknown nonlinear systems based on finite-approximation-error ADP algorithm. Neurocomputing 2013, 119:212-221.
25. Wang F., Jin N., Liu D., Wei Q. Adaptive dynamic programming for finite-horizon optimal control of discrete-time nonlinear systems with ε-error bound. IEEE Trans. Neural Netw. 2011, 22:24-36.
26. Wei Q., Liu D. An iterative ε-optimal control scheme for a class of discrete-time nonlinear systems with unfixed initial state. Neural Netw. 2012, 32:236-244.
27. Zhang H., Song R., Wei Q., Zhang T. Optimal tracking control for a class of nonlinear discrete-time systems with time delays based on heuristic dynamic programming. IEEE Trans. Neural Netw. 2011, 22:1851-1862.
28. Zhang H., Wei Q., Liu D. An iterative adaptive dynamic programming method for solving a class of nonlinear zero-sum differential games. Automatica 2011, 47:207-214.
29. Li H., Liu D. Optimal control for discrete-time affine nonlinear systems using general value iteration. IET Control Theory Appl. 2012, 6:2725-2736.
30. Wang D., Liu D., Wei Q., Zhao D., Jin N. Optimal control of unknown nonlinear discrete-time systems based on adaptive dynamic programming approach. Automatica 2012, 48:1825-1832.
31. Wei Q., Zhang H., Liu D., Zhao Y. An optimal control scheme for a class of discrete-time nonlinear systems with time delays using adaptive dynamic programming. Acta Autom. Sin. 2010, 36:121-129.
32. Song R., Zhang H., Luo Y., Wei Q. Optimal control laws for time-delay systems with saturating actuators based on heuristic dynamic programming. Neurocomputing 2010, 73:16-18.
33. Lewis F.L., Vrabie D. Reinforcement learning and adaptive dynamic programming for feedback control. IEEE Circuits Syst. Mag. 2009, 9:32-50.
34. Abu-Khalaf M., Lewis F.L. Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach. Automatica 2005, 41:779-791.
35. R. Beard, Improving the Closed-Loop Performance of Nonlinear Systems (Ph.D. Thesis) Rensselaer Polytechnic Institute, Troy, NY, 1995.
36. Zhang H., Wei Q., Luo Y. 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. 2008, 38:937-942.
37. Liu D., Wang D., Zhao D., Wei Q., Jin N. Neural-network-based optimal control for a class of unknown discrete-time nonlinear systems using globalized dual heuristic programming. IEEE Trans. Autom. Sci. Eng. 2012, 9:628-634.
38. Heydari A., Balakrishnan S.N. Finite-horizon control-constrained nonlinear optimal control using single network adaptive critics. IEEE Trans. Neural Netw. Learn. Syst. 2013, 24:145-157.
39. Huang T., Liu D. A self-learning scheme for residential energy system control and management. Neural Comput. Appl. 2013, 22:259-269.
40. Liu D., Li H., Wang D. Neural-network-based zero-sum game for discrete-time nonlinear systems via iterative adaptive dynamic programming algorithm. Neurocomputing 2013, 110:92-100.
41. Liu D., Wei Q. Finite-approximation-error-based optimal control approach for discrete-time nonlinear systems. IEEE Trans. Cybern. 2013, 43:779-789.
42. Ni Z., He H., Wen J. Adaptive learning in tracking control based on the dual critic network design. IEEE Trans. Neural Netw. Learn. Syst. 2013, 24:913-928.
43. Liu D., Wang D., Yang X. An iterative adaptive dynamic programming algorithm for optimal control of unknown discrete-time nonlinear systems with constrained inputs. Inf. Sci. 2013, 220:331-342.
44. Wang D., Liu D., Wei Q. Finite-horizon neuro-optimal tracking control for a class of discrete-time nonlinear systems using adaptive dynamic programming approach. Neurocomputing 2012, 78:14-22.
45. Liu D., Li H., Wang D. Neural-network-based zero-sum game for discrete-time nonlinear systems via iterative adaptive dynamic programming algorithm. Neurocomputing 2013, 110:92-100.
46. Liu D., Wei Q. Finite-approximation-error-based optimal control approach for discrete-time nonlinear systems. IEEE Trans. Cybern. 2013, 43:779-789.
47. Wang D., Liu D., Zhao D., Huang Y., Zhang D. A neural-network-based iterative GDHP approach for solving a class of nonlinear optimal control problems with control constraints. Neural Comput. Appl. 2013, 22:219-227.