Nearly optimal state feedback control of constrained nonlinear systems using a neural networks HJB approach

Annual Reviews in Control

Volumn 28, Issue 2, 2004, Pages 239-251

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

^a UNIVERSITY OF TEXAS AT ARLINGTON   (United States)

Author keywords

Actuator saturation; Minimum time control; Neural network; Optimal control; State constraints

Indexed keywords

ACTUATORS; APPROXIMATION THEORY; DIFFERENTIAL EQUATIONS; FEEDBACK CONTROL; HAMILTONIANS; LEAST SQUARES APPROXIMATIONS; NEURAL NETWORKS; OPTIMIZATION;

ACTUATOR SATURATION; MINIMUM-TIME CONTROL; OPTIMAL CONTROL; STATE CONSTRAINTS;

NONLINEAR CONTROL SYSTEMS;

EID: 8344241850     PISSN: 13675788     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.arcontrol.2004.07.002     Document Type: Article

References (37)

1. Beard, R. (1995). Improving the closed-loop performance of nonlinear systems. Ph.D. thesis, Rensselaer Polytechnic Institute, Troy, NY 12180.
2. Beard, R., Saridis, G., & Wen, J. (1997). Galerkin approximations of the generalized Hamilton-Jacobi-Bellman equation. Automatica, 33(12, December), 2159-2177.
3. Beard, R., Saridis, G., & Wen, J. (1998). Approximate solutions to the time-invariant Hamilton-Jacobi-Bellman equation. Journal of Optimization Theory and Application, 95(3), 589-626.
4. Bernstein, D. S. (1995). Optimal nonlinear, but continuous, feedback control of systems with saturating actuators. International Journal of Control, 62(5), 1209-1216.
5. Bertsekas, D. P., & Tsitsiklis, J. N. (1996). Neuro-dynamic programming. Belmont, MA: Athena Scientific.
6. Bitsoris, G., & Gravalou, E. (1999). Design techniques for the control of discrete-time systems subject to state and control constraints. IEEE Transactions on Automatic Control, 44(5), 1057-1061.
7. Burk, F. (1998). Lebesgue measure and integration. New York, NY: John Wiley & Sons.
8. Chen, F. C., & Liu, C.-C. (1994). Adaptively controlling nonlinear continuous-time systems using multilayer neural networks. IEEE Transactions on Automatic Control, 39(6), 1306-1310.
9. Finlayson, B. A. (1972). The method of weighted residuals and variational principles. New York, NY: Academic Press.
10. Gilbert, E., & Tan, K. T. (1991). Linear systems with state and control constraints: The theory and application of maximal output admissible sets. IEEE Transactions on Automatic Control, 36(9), 1008-1020.
11. Han, D., & Balakrishnan, S. N. (2000). State-constrained agile missile control with adaptive-critic based neural networks. Proceedings of American Control Conference, 1929-1933.
12. Henrion, D., Tarbouriech, S., & Kucera, V. (2001). Control of linear systems subject to input constraints: A polynomial approach. Automatica, 37(4), 597-604.
13. Hu, T., Lin, Z., & Chen, B. M. (2002). An analysis and design method for linear systems subject to actuator saturation and disturbance. Automatica, 38(2), 351-359.
14. Huang, J., & Lin, C. F. (1995). Numerical approach to computing nonlinear H∞ control laws. Journal of Guidance, Control, and Dynamics, 18(5), 989-994.
15. Kim, Y. H., Lewis, F. L., & Dawson, D. (2000). Intelligent optimal control of robotic manipulators using neural networks. Automatic, 36, 1355-1364.
16. Kirk, D. (1970). Optimal control theory: An introduction. New Jersey: Prentice-Hall.
17. Kleinman, D. (1968). On an iterative technique for Riccati equation computations. IEEE Transactions on Automatic Control, 114-115.
18. Lewis, F. L., Jagannathan, S., & Yesildirek, A. (1999). Neural network control of robot manipulators and nonlinear systems, Taylor & Francis.
19. Lewis, F. L., & Syrmos, V. L. (1995). Optimal control. New York, NY: John Wiley & Sons Inc.
20. Liu, X., & Balakrishnan, S. N. (2000). Convergence analysis of adaptive critic based optimal control. Proceedings of American Control Conference, 1929-1933.
21. Lyshevski, S. E. (1996). Constrained optimization and control of nonlinear systems: New results in optimal control. Proceedings of IEEE Conference on Decision and Control, 541-546.
22. Lyshevski, S. E. (1998). Optimal control of nonlinear continuous-time systems: Design of bounded controllers via generalized nonquadratic functional. Proceedings of American Control Conference, 205-209.
23. Lyshevski, S. E. (2001). Role of performance functional in control laws design. Proceedings of American Control Conference, 2400-2405.
24. Lyshevski, S. E. (2001). Control systems theory with engineering applications. Boston, MA: Birkhauser.
25. Lyshevski, S. E., & Meyer, A. U. (1995). Control system analysis and design upon the Lyapunov method. Proceedings of American Control Conference, 3219-3223.
26. Miller, W. T., Sutton, R., & Werbos, P. (1990). Neural networks for control. Cambridge, MA: MIT Press.
27. Munos, R. L., Baird, C., & Moore, A. (1999). Gradient descent approaches to neural-net-based solutions of the Hamilton-Jacobi-Bellman equation. International Joint Conference on Neural Networks IJCNN, 3, 2152-2157.
28. Murray, J., Cox, C., Saeks, R., & Lendaris, G. (2001). Globally convergent approximate dynamic programming applied to an autolander. Proceedings of American Control Conference, 2901-2906.
29. Narendra, K. S., & Lewis, F. L. (2001). Special issue on neural network feedback control. Automatica, 37(8), 1147-1148.
30. Parisini, T., & Zoppoli, R. (1998). Neural approximations for infinite-horizon optimal control of nonlinear stochastic systems. IEEE Transactions on Neural Network, 9(6), 1388-1408.
31. Polycarpou, M. M. (1996). Stable adaptive neural control scheme for nonlinear systems. IEEE Transactions on Automatic Control, 41(3), 447-451.
32. Rovithakis, G. A., & Christodoulou, M. A. (1994). Adaptive control of unknown plants using dynamical neural networks. IEEE Transactions on Systems, Man, and Cybernetics, 24(3), 400-412.
33. Saberi, A., Lin, Z., & Teel, A. (1996). Control of linear systems with saturating actuators. IEEE Transactions on Automatic Control, 41(3), 368-378.
34. Sadegh, N. (1993). A perceptron network for functional identification and control of nonlinear systems. IEEE Transactions on Neural Networks, 4(6), 982-988.
35. Sanner, R. M., & Slotine, J.-J.E. (1991). Stable adaptive control and recursive identification using radial Gaussian networks. Proceedings of IEEE Conference on Decision and Control, 2116-2123.
36. Saridis, G. C. S. & Lee, (1979). An approximation theory of optimal control for trainable manipulators. IEEE Transactions on Systems, Man, Cybernetics, 9(3), 152-159.
37. Sussmann, H., Sontag, E. D., & Yang, Y. (1994). A general result on the stabilization of linear systems using bounded controls. IEEE Transactions on Automatic Control, 39(12), 2411-2425.