A neural network solution for fixed-final time optimal control of nonlinear systems

Automatica

Volumn 43, Issue 3, 2007, Pages 482-490

  Cheng, Tao ^a   Lewis, Frank L ^a   Abu Khalaf, Murad ^a  

^a UNIVERSITY OF TEXAS AT ARLINGTON   (United States)

Author keywords

Finite horizon optimal control; Hamilton Jacobi Bellman; Neural networks

Indexed keywords

APPROXIMATION THEORY; MATRIX ALGEBRA; NONLINEAR SYSTEMS; OPTIMAL CONTROL SYSTEMS;

FINITE-HORIZON OPTIMAL CONTROL; HAMILTON-JACOBI-BELLMAN; KRONECKER MATRIX; OFFLINE TUNING;

NEURAL NETWORKS;

EID: 33846781133     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2006.09.021     Document Type: Article

References (25)

1. Abu-Khalaf M., and Lewis F.L. Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach. Automatica 41 5 (2005) 779-791
2. Adams R., and Fournier J. Sobolev spaces. (2nd ed.) (2003), Academic Press, New York
3. ∞-control of nonsmooth time-varying systems with application to friction mechanical manipulators. Automatica 39 (2003) 1531-1542
4. Arnold V.I. Ordinary differential equations (1973), MIT Press, Cambridge, MA
5. Bartle R.G. The elements of real analysis. 2nd ed. (1976), Wiley, New York
6. Beard, R. (1995). Improving the closed-loop performance of nonlinear systems. Ph.D. thesis, Rensselaer Polytechnic Institute, Troy, NY 12180.
7. Bertsekas D.P., and Tsitsiklis J.N. Neuro-dynamic programming: An overview. Proceedings of the IEEE conference on decision and control (1995) 560-564
8. Brockett R.W. Asymptotic stability and feedback stabilization. In: Brockett R.W., Millman R.S., and Sussmann H.J. (Eds). Differential geometric control theory (1983), Birkhauser, Boston, MA
9. Chen F.C., and Liu C.C. Adaptively controlling nonlinear continuous-time systems using multiplayer neural networks. IEEE Transactions on Automatic Control 39 6 (1994) 1306-1310
10. Finlayson B.A. The method of weighted residuals and variational principles (1972), Academic Press, New York
11. Hornik K., Stinchcombe M., and White H. Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks. Neural Networks 3 (1990) 551-560
12. Huang C.S., Wang S., and Teo K.L. Solving Hamilton-Jacobi-Bellman equations by a modified method of characteristics. Nonlinear Analysis 40 (2000) 279-293
13. ∞ control laws. Journal of Guidance, Control, and Dynamics 18 5 (1995) 989-994
14. ∞-control via measurement feedback in nonlinear systems. IEEE Transactions on Automatic Control 37 9 (1992) 1283-1293
15. Khalil H.K. Nonlinear systems (2002), Prentice-Hall, Upper Saddle River
16. Kim Y.H., Lewis F.L., and Dawson D. Intelligent optimal control of robotic manipulators using neural networks. Automatica 36 (2000) 1355-1364
17. Kolmanovsky I., and McClamroch N.H. Developments in nonholonomic control problems. IEEE Control Systems (1995) 20-36
18. Lewis F.L., and Syrmos V.L. Optimal control (1995), Wiley, New York, NY
19. Lio F.D. On the Bellman equation for infinite horizon problems with unbounded cost functional. Applied Mathematics and Optimization 41 (2000) 171-197
20. Miller W.T., Sutton R., and Werbos P. Neural networks for control (1990), The MIT Press, Cambridge, Massachusetts
21. Murray, R.M., Sastry, S.S. (1991). Steering nonholonomic systems in chained form. Proceedings of the 30th Conference on Decision & Control, Brighton, England, December 1991.
22. Parisini T., and Zoppoli R. Neural approximations for infinite-horizon optimal control of nonlinear stochastic systems. IEEE Transactions on Neural Networks 9 6 (1998) 1388-1408
23. Sandberg E.W. Notes on uniform approximation of time-varying systems on finite time intervals. IEEE Transactions on Circuits and Systems-1: Fundamental Theory and Applications 45 8 (1998)
24. Saridis G., and Lee C.S. An approximation theory of optimal control for trainable manipulators. IEEE Transactions on Systems, Man, Cybernetics 9 3 (1979) 152-159
25. ∞ control. IEEE Transactions on Automatic Control 37 6 (1992) 770-784