Multi-objective optimal control for a class of unknown nonlinear systems based on finite-approximation-error ADP algorithm

Neurocomputing

Volumn 119, Issue , 2013, Pages 212-221

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

^a UNIVERSITY OF SCIENCE AND TECHNOLOGY BEIJING   (China)

^b NORTHEASTERN UNIVERSITY   (China)

Author keywords

Adaptive dynamic programming; Approximate dynamic programming; Finite approximation error; Multi objective; Neural networks; Optimal control

Indexed keywords

ADAPTIVE DYNAMIC PROGRAMMING; APPROXIMATE DYNAMIC PROGRAMMING; FINITE-APPROXIMATION-ERROR; MULTI OBJECTIVE; OPTIMAL CONTROLS;

CONTROL; DYNAMIC PROGRAMMING; ITERATIVE METHODS; NEURAL NETWORKS; NONLINEAR SYSTEMS; OPTIMAL CONTROL SYSTEMS;

APPROXIMATION ALGORITHMS;

ACCURACY; ADAPTIVE DYNAMIC PROGRAMMING; ALGORITHM; ARTICLE; ARTIFICIAL NEURAL NETWORK; HAMILTON JACOBI BELLMAN EQUATION; INFORMATION PROCESSING; MATHEMATICAL COMPUTING; MATHEMATICAL PARAMETERS; NONLINEAR SYSTEM; PRIORITY JOURNAL; PROBLEM SOLVING; PROCESS OPTIMIZATION; THEORETICAL STUDY;

EID: 84881548237     PISSN: 09252312     EISSN: 18728286     Source Type: Journal    
DOI: 10.1016/j.neucom.2013.03.038     Document Type: Article

References (35)

1. Bryson A.E., Ho Y.C. Applied Optimal Control. Optimization, Estimation, and Control 1975, Hemisphere-Wiley, New York, NY.
2. de Ruiter Anton H.J., Liu Hugh H.T. A parameter optimization approach to multiple-objective controller design. IEEE Trans. Control Syst. Technol. 2008, 16(2):330-339.
3. Messac A., Mattson C. Normal constraint method with guarantee of even representation of complete Pareto frontier. AIAA J. 2004, 42:2101-2111.
4. Lai C., Xiang C., Lee T.H. Data-based identification and control of nonlinear systems via piecewise affine approximation. IEEE Trans. Neural Networks 2011, 22(12, Part: 2):2189-2200.
5. Li D., Haimes Y.Y. The envelope approach for multiobjective optimization problems. IEEE Trans. Syst. Man Cybern. B. Cybern. 1987, 17:1026-1038.
6. Liu D., Wei Q. Finite-approximation-error-based optimal control approach for discrete-time nonlinear systems. IEEE Trans. Syst. Man Cybern. B: Cybern 2013, 43:779-789.
7. D. Liu, X. Xiong, Y. Zhang, Action-dependent adaptive critic designs, in: Proceedings of the INNS-IEEE International Joint Conference on Neural Networks, Washington, DC, vol. 2, July 2001, pp. 990-995.
8. Shen D., Hou Z. Iterative learning control with unknown control direction. a novel data-based approach. IEEE Trans. Neural Networks 2011, 22(12):2237-2249.
9. Wang D., Liu D., Wei Q., Zhao D., Jin N. Optimal control of unknown nonaffine nonlinear discrete-time systems based on adaptive dynamic programming. Automatica 2012, 48(August (8)):1825-1832.
10. Navarro-Lopez Eva M. Local feedback passivation of nonlinear discrete-time systems through the speed-gradient algorithm. Automatica 2007, 43(July (7)):1302-1306.
11. ∞-norm bound of non-linear discrete-time uncertain systems with bounded control. Syst. Control Lett. 2003, 50:277-289.
12. Logist F., Sager S., Kirches C., Van Impe J.F. Efficient multiple objective optimal control of dynamic systems with integer controls. J. Process Control 2010, 20:810-822.
13. He H., Ni Z., Fu J. A three-network architecture for on-line learning and optimization based on adaptive dynamic programming. Neurocomputing 2012, 78(1):3-13.
14. Sira-Ramirez H. Non-linear discrete variable structure systems in quasi-sliding mode. Int. J. Control 1991, 54(May (5)):1171-1187.
15. Zhang H., Cui L., Zhang X., Luo Y. Data-driven robust approximate optimal tracking control for unknown general nonlinear systems using adaptive dynamic programming method. IEEE Trans. Neural Networks 2011, 22(12):2226-2236.
16. Zhang H., Liu Z., Huang G., Wang Z. Novel weighting-delay-based stability criteria for recurrent neural networks with time-varying delay. IEEE Trans. Neural Networks 2010, 21(1):91-106.
17. Zhang H., Quan Y. Modeling identification and control of a class of nonlinear system. IEEE Trans. Fuzzy Syst. 2001, 9(2):349-354.
18. 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(January (1)):207-214.
19. 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 Networks 2011, 22(12, Part: 1):1851-1862.
20. 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 Cyber. B. Cybern. 2008, 38(July (4)):937-942.
21. Zhang H., Luo Y., Liu D. Neural-network-based near-optimal control for a class of discrete-time affine nonlinear systems with control constraints. IEEE Trans. Neural Networks 2009, 20:1490-1503.
22. Li J., Chen W., Li J., Fang Y. Adaptive NN output-feedback stabilization for a class of stochastic nonlinear strict-feedback systems. ISA Trans. 2009, 48(October (4)):468-475.
23. Fu J., He H., Zhou X. Adaptive learning and control for MIMO system based on adaptive dynamic programming. IEEE Trans. Neural Networks 2011, 22(7):1133-1148.
24. Liao L.Z., Duan L. Adaptive differential dynamic programming for multiobjective optimal control. Automatica 2002, 38:1003-1015.
25. Q. Wei, D. Liu, Adaptive dynamic programming with stable value iteration algorithm for discrete-time nonlinear systems, in: Proceedings of the International Joint Conference on Neural Networks (IJCNN), Brisbane, Australia, June 2012, pp. 1-6.
26. Wei Q., Liu D. An iterative ε-optimal control scheme for a class of discrete-time nonlinear systems with unfixed initial state. Neural Networks 2012, 32(August):236-244.
27. 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(March (7-9)):1839-1848.
28. Bellman R.E. Dynamic Programming 1957, Princeton University Press, Princeton, NJ.
29. R. Song, H. Zhang, The finite-horizon optimal control for a class of time-delay affine nonlinear system, Neural Computing and Applications, 28 July 2011 (Online First).
30. 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(October (16-18)):3020-3027.
31. Utyuzhnikov S.V., Fantini P., Guenov M.D. A method for generating a well-distributed Pareto set in nonlinear multiobjective optimization. Journal of Computational and Applied Mathematics 2009, 223:820-841.
32. Chen W. Adaptive NN control for discrete-time pure-feedback systems with unknown control direction under amplitude and rate actuator constraints. ISA Trans. 2009, 48(July (3)):304-311.
33. 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).
34. Liu Z., Zhang H., Zhang Q. Novel stability analysis for recurrent neural networks with multiple delays via line integral-type L-K functional. IEEE Trans. Neural Networks 2010, 21(11):1710-1718.
35. Wang Z., Liu D. Data-based controllability and observability analysis of linear discrete-time systems. IEEE Trans. Neural Networks 2011, 22(12, Part: 2):2388-2392.