Neural network solution for finite-horizon H state feedback control of nonlinear systems

International Journal of Systems Science

Volumn 38, Issue 12, 2007, Pages 1029-1041

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

^a UNIVERSITY OF TEXAS AT ARLINGTON   (United States)

Author keywords

Finite horizon zero sum games; H control; Hamilton Jacobi Isaacs; Neural network control

Indexed keywords

FEEDBACK CONTROL; HAMILTONIANS; NEURAL NETWORKS; PROBLEM SOLVING; STATE SPACE METHODS;

FINITE-HORIZON ZERO-SUM GAMES; HAMILTON-JACOBI-ISAACS; NEURAL NETWORK CONTROL;

NONLINEAR SYSTEMS;

EID: 36248941868     PISSN: 00207721     EISSN: 14645319     Source Type: Journal    
DOI: 10.1080/00207720701709044     Document Type: Article

References (39)

1. M. Abu-Khalaf and F.L. Lewis, "Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach," Automatica, 41, pp. 779-791, 2005.
2. ∞ state feedback control with actuator saturation: the nonlinear benchmark problem", Proceedings of the 5th International Conference on Control & Automation, Budapest, Hungary, January 2005.
3. ∞ optimal control using neural networks," in Proceedings of the 12th Mediterranean Conference on Control and Automation, Turkey: Kusadasi. June, 2004.
4. M. Abu-Khalaf, F. L. Lewis and J. Huang, "Hamilton-Jacobi-Isaacs formulation for constrained input nonlinear systems", Proceedings of the 43rd IEEE Conference on Decision & Control, pp. 5034-5040, Bahamas, USA, December 2004.
5. R. Adams and J. Fournier, Sobolev Spaces, 2nd ed., New York: Academic Press, 2003.
6. V.I. Arnold, Ordinary Differential Equations, Cambridge, MA: MIT Press, 1973.
7. M.J. Balas, "Modal control of certain flexible dynamic systems," SIAM J. Control Optim., 16, pp. 450-462, 1978.
8. M. Bardi and I. Capuzzo-Dolcetta, Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, Boston, MA: Birkhauser, 1997.
9. R.G. Bartle, The Elements of Real Analysis, 2nd ed., New York: Wiley, 1976.
10. T. Basar and P. Bernard, H∞ Optimal Control and Related Minimax Design Problems: A dynamic Game Approach, Boston: Birkhauser, 1995.
11. R. Beard, Improving the closed-loop performance of nonlinear systems, PhD thesis, Rensselaer Polytechnic Institute, Troy, NY 12180, 1995.
12. R. Beard and T. McLain, "Successive Galerkin approximation algorithms for nonlinear optimal and robust control," Int. J. Control, 71, pp. 717-743, 1998.
13. R. Beard, G. Saridis and J. Wen, "Approximate solutions to the time-invariant Hamilton-Jacobi-Bellman equation," J. Optim. Theory App., 96, pp. 589-626, March, 1998.
14. J.W. Brewer, "Kronecker Products and Matrix Calculus in System Theory," IEEE Trans. Circuits Syst., 25, pp. 772-781, 1978.
15. R. Bupp, D. Bernstein and V. Coppola, "A benchmark problem for nonlinear control design," Int. J. Robust Nonlin. Cont., 8, pp. 307-310, 1998.
16. F.C. Chen and C.C. Liu, "Adaptively controlling nonlinear continuous-time systems using multiplayer neural networks," IEEE Trans. on Automatic Control, 39, pp. 1306-1310, 1994.
17. T. Cheng, L. L. Frank, M. Abu-Khalaf, "A neural network solution for fixed-final time optimal control of nonlinear systems", Automatica, 43, pp. 482-490, 2007.
18. B.A. Finlayson, The Method of Weighted Residuals and Variational Principles, New York: Academic Press, 1972.
19. S.S. Ge, "Robust adaptive NN feedback linearization control of nonlinear systems," Int. J. Syst. Sci., 27(12), pp. 1327-1338, 1996.
20. D.J. Gorman, Free Vibration Analysis of Beams and Shafts, New York: John Wiley & Sons, 1975.
21. K. Hornik, M. Stinchcombe and H. White, "Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks," Neural Networks, 3, pp. 551-560, 1990.
22. ∞ control laws," J. Guidance, Control Dyn., 18, pp. 989-994, 1995.
23. C.S. Huang, S. Wang and K.L. Teo, "Solving Hamilton-Jacobi-Bellman equations by a modified method of characteristics," Nonlin. Anal., 40, pp. 279-293, 2000.
24. ∞-Control via measurement feedback in nonlinear systems," IEEE Trans. Automat. Control, 37, pp. 1283-1293, 1992.
25. H.K. Khalil, "Nonlinear Systems", Upper Saddle River Prentice-Hall, Inc. 2002.
26. F.L. Lewis and M. Abu-Khalaf, "A Hamilton-Jacobi Setup for constrained neural network control", Proceedings of the 2003 IEEE International Symposium on Intelligent Control, Houston, Texas, October 5-8, pp. 1-15, 2003.
27. F.L. Lewis, M. Abu-Khalaf and J. Huang, "Robust optimal control of constrained input systems using neural networks", Proceedings of 23rd Chinese Control Conference, Plenary Paper, Wuxi, China August 2004.
28. F.L. Lewis, M. Abu-Khalaf and J. Huang, "Hamilton-Jacobi-Isaacs formulation for constrained input systems: Neural network solution", Proceedings of 2nd IFAC Symposium on System, Structure and Control, Plenary Paper, pp. 1-6, Oaxaca, Mexico, December 2004.
29. F.L. Lewis, S. Jagannathan and A. Yesildirek, Neural Network Control of Robot Manipulators and nonlinear Systems, Philadelphia: Taylor & Francis, 1999.
30. F.D. Lio, "On the Bellman equation for infinite horizon problems with unbounded cost functional," Applied Math. Optim., 41, pp. 171-197, 2000.
31. W.T. Miller, R. Sutton and P. Werbos, Neural Networks for Control, Cambridge, Massachusetts: The MIT Press, 1990.
32. C.P. Mracek and J.R. Cloutier, "A preliminary control design for the nonlinear benchmark problem", Proceedings of the 1996 International Conference on Control Applications, Dearborn, Mi, 265-272, 1996.
33. T. Parisini and R. Zoppoli, "Neural, approximations for infinite-horizon optimal control of nonlinear stochastic systems," IEEE Trans. Neural Net., 9, pp. 1388-1408, November, 1998.
34. M.M. Polycarpou, "Stable adaptive neural control scheme for non-linear systems," IEEE Trans. Automat. Control, 41, pp. 447-451, March, 1996.
35. G.A. Rovithakis and M.A. Christodoulou, "Adaptive control of unknown plants using dynamical neural networks," IEEE Trans. Syst. Man Cybern., 24, pp. 400-412, 1994.
36. I.W. Sandberg, "Notes on uniform approximation of time-varying systems on finite time intervals," IEEE Trans. Circuits and Sys.-1: Fundamental Theory App., 45, pp. 863-865, 1998.
37. R.M. Sanner and J.J.E. Slotine, "Stable adaptive control and recursive identification using radial gaussian networks," Proc. IEEE Conf Decision and Control, 2116-2123, Brighton, 1991.
38. P. Tsiotras, M. Corless and M. Rotea, "An L2 disturbance attenuations solution to the nonlinear benchmark problem," Int. J. Robust Nonlin. Control, 8, pp. 311-330, 1998.
39. 2-gain analysis of nonlinear systems and nonlinear state feedback H00 control," IEEE Trans. Automat. Control., 37, pp. 770-784, June, 1992.