A Hamilton-Jacobi Setup for Constrained Neural Network Control

IEEE International Symposium on Intelligent Control - Proceedings

Volumn , Issue , 2003, Pages 1-15

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

^a UNIVERSITY OF TEXAS AT ARLINGTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; ASYMPTOTIC STABILITY; CONSTRAINT THEORY; CONVERGENCE OF NUMERICAL METHODS; FEEDBACK CONTROL; INVARIANCE; ITERATIVE METHODS; LEAST SQUARES APPROXIMATIONS; NONLINEAR SYSTEMS; OPTIMAL CONTROL SYSTEMS; OPTIMIZATION; ROBUSTNESS (CONTROL SYSTEMS); STATE FEEDBACK;

DISTURBANCE ATTENUATION; HAMILTON-JACOBI EQUATIONS; NONQUADRATIC FUNCTIONALS;

NEURAL NETWORKS;

EID: 0344666492     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/isic.2003.1253906     Document Type: Conference Paper

References (44)

1. Abu-Khalaf, M., F. L. Lewis (2002). Nearly Optimal HJB Solution for Constrained Input Systems Using a Neural Networks Least-Squares Approach. Proc. IEEE Conference on Decision and Control, pp. 943-948.
2. Beard, R. (1995). Improving the Closed-Loop Performance of Nonlinear Systems. PhD thesis, Rensselaer Polytechnic Institute, Troy, NY 12180.
3. Beard, R., G. Saridis, J. Wen (1997). Galerkin Approximations of the Generalized Hamilton-Jacobi-Bellman Equation. Automatica 33:12, December, pp. 2159-2177.
4. Beard, R., G. Saridis, J. Wen (1998). Approximate Solutions to the Time-Invariant Hamilton-Jacobi-Bellman Equation. Journal of Optimization Theory and Application, vol 96, no. 3, pp. 589-626.
5. Beard, R., T. McLain, (1998). Successive Galerkin approximation algorithms for nonlinear optimal and robust control. International Journal of Control, vol 71. no. 5, pp 717-743.
6. Bernstein, D. S. (1995). Optimal nonlinear, but continuous, feedback control of systems with saturating actuators. International Journal of Control, vol 62, no. 5, pp. 1209-1216.
7. Bertsekas, D. P., J. N. Tsitsiklis (1996). Neuro-Dynamic Programming. Athena Scientific, Belmont, MA.
8. Bitsoris, G., E. Gravalou. (1999). Design Techniques for the Control of Discrete-Time Systems Subject to State and Control Constraints. IEEE Trans. Automat. Control, vol. 44, no. 5, pp. 1057-1061.
9. Burk, F. (1998). Lebesgue Measure and Integration. John Wiley & Sons, New York, NY.
10. Chen F. C., C.-C. Liu (1994). Adaptively controlling nonlinear continuous-time systems using multilayer neural networks. IEEE Trans. Automat. Control, vol. 39, no. 6, pp. 1306-1310.
11. Finlayson, B. A. (1972). The Method of Weighted Residuals and Variational Principles. Academic Press, New York, NY.
12. Genesio, R., M. Tartaglia (1985). On the Estimation of Asymptotic Stability Regions: State of the Art and New Proposals. IEEE Trans. Automat. Control, vol. 30, no. 8, pp. 747-755.
13. Gilbert, E., K. T. Tan (1991). Linear Systems with State and Control Constraints: The Theory and Application of Maximal Output Admissible Sets. IEEE Trans. Automat. Control, vol. 36, no. 9, pp. 1008-1020.
14. Han D., S. N. Balakrishnan (2000). State-Constrained Agile Missile Control, with Adaptive-Critic Based Neural Networks. Proc. American Control Conference, pp.1929 - 1933.
15. Henrion, D., S. Tarbouriech, V. Kucera (2001). Control of Linear Systems Subject to Input Constraints: A polynomial Approach. Automatica, vol.37, no.4, pp.597-604.
16. Hu, T., Z. Lin, B. M. Chen (2002), "An analysis and design method for linear systems subject to actuator saturation and disturbance," Automatica, vol. 38, no. 2. pp. 351-359.
17. Hu, T., Z. Lin, (2003), "Composite Quadratic Lyapunov Functions for Constrained Control Systems." IEEE Trans. Automat. Control, vol. 48 no. 3. pp. 440-450.
18. ∞ Control Laws. Journal of Guidance, Control, and Dynamics, vol. 18, no. 5, pp. 989-994.
19. rd Edition, Prentice Hall, Upper Saddle River, NJ.
20. Kim, Y. H., F. L. Lewis, D. Dawson (2000). Intelligent optimal control of robotic manipulators using neural networks. Automatic 36, 2000, pp. 1355 - 1364.
21. Kirk, D. (1970). Optimal Control Theory: An Introduction. Prentice Hall, New Jersey.
22. Kleinman, D. (1968). On an iterative Technique for Riccati Equation Computations. IEEE Trans. Automatic Control, pp. 114-115.
23. Lewis, F. L., V. L. Syrmos (1995). Optimal Control. John Wiley & Sons, Inc. New York, NY.
24. Lewis, F. L., S. Jagannathan, A. Yesildirek (1999). Neural Network Control of Robot Manipulators and Nonlinear Systems. Taylor & Francis.
25. Lewis, F. L., M. Abu-Khalaf, (2003). Nearly Optimal State Feedback Control of Constrained Nonlinear Systems Using A Neural Network HJB Approach. IFAC International Conference on Intelligent Control Systems and Signal Processing, (Plenary paper).
26. Liu, X., S. N. Balakrishnan (2000). Convergence Analysis of Adaptive Critic Based Optimal Control. Proc. American Control Conference, pp.1929 - 1933.
27. Lyshevski, S. E., A. U. Meyer (1995). "Control System Analysis and Design Upon the Lyapunov Method," Proc. American Control Conference, pp. 3219-3223.
28. Lyshevski, S. E. (1996). Constrained Optimization and Control of Nonlinear Systems: New Results in Optimal Control. Proc. IEEE Conference on Decision and Control, pp. 541 - 546.
29. Lyshevski, S. E. (1998). Optimal Control of Nonlinear Continuous-Time Systems: Design of Bounded Controllers Via Generalized Nonquadratic Functional. Proc. American Control Conference, pp.205-209.
30. Lyshevski, S. E. (2001a). Role of Performance Functional in Control Laws Design. Proc. American Control Conference, pp. 2400 - 2405.
31. Lyshevski, S. E. (2001b) Control Systems Theory with Engineering Applications. Birkhauser, Boston, MA.
32. Miller, W. T., R. Sutton, P. Werbos (1990). Neural Networks for Control. The MIT Press, Cambridge, Massachusetts.
33. Munos, R. L. C. Baird, A. Moore (1999). Gradient Descent Approaches to Neural-Net-Based Solutions of the Hamilton-Jacobi-Bellman Equation. International Joint Conference on Neural Networks IJCNN, vol 3, pp. 2152 - 2157.
34. Murray, J. C. Cox, R. Saeks, G. Lendaris (2001). Globally Convergent Approximate Dynamic Programming Applied to an Autolander, Proc. American Control Conference, pp.2901 - 2906.
35. Narendra, K. S., F. L. Lewis ed. (2001). Special issue on neural network feedback control. Automatica vol 37, no. 8, pp. 1147-1148.
36. Parisini, T., R. Zoppoli (1998). Neural Approximations for Infinite-Horizon Optimal Control of Nonlinear Stochastic Systems. IEEE Trans Neural Net. vol. 9, no. 6, pp. 1388-1408.
37. Polycarpou, M.M. (1996). Stable adaptive neural control scheme for nonlinear systems. IEEE Trans. Automat. Control, vol 41, no. 3, pp. 447-451.
38. Rovithakis, G.A., M.A. Christodoulou (1994). Adaptive control of unknown plants using dynamical neural networks. IEEE Trans. Systems, Man, and Cybernetics, vol 24, no. 3, pp. 400-412.
39. Saberi, A., Z. Lin, A. Teel (1996). Control of Linear Systems with Saturating Actuators. IEEE Transactions on Automatic Control, Vol 41, no. 3, March 1996, pp. 368-378.
40. Sadegh, N. (1993). A perceptron network for functional identification and control of nonlinear systems. IEEE Trans. Neural Networks, vol. 4, no. 6, pp. 982-988.
41. Sanner, R.M., J.-J.E. Slotine (1991). Stable adaptive control and recursive identification using radial gaussian networks. Proc. IEEE Conf. Decision and Control, pp. 2116-2123.
42. Saridis, G. C. S. Lee (1979). An Approximation Theory of optimal Control for Trainable Manipulators. IEEE Trans. Systems, Man, Cybernetics, vol 9, no. 3, pp. 152-159.
43. Sussmann, H., E. D. Sontag, Y. Yang (1994). A General Result on the Stabilization of Linear Systems Using Bounded Controls. IEEE Trans. Automatic Control, vol 39, no. 12, pp. 2411-2425.
44. ∞ Control", IEEE Trans. Automat. Control, vol. 37 no. 6, pp. 770-784.