Approximate optimal control for a class of nonlinear discrete-time systems with saturating actuators

Progress in Natural Science

Volumn 18, Issue 8, 2008, Pages 1023-1029

  Luo, Yanhong ^a   Zhang, Huaguang ^a  

^a NORTHEASTERN UNIVERSITY   (China)

Author keywords

Convergence analysis; GI HDP algorithm; Neural networks; Nonquadratic functional; Saturating

Indexed keywords

DIGITAL CONTROL SYSTEMS; DISCRETE TIME CONTROL SYSTEMS; DYNAMIC PROGRAMMING; HEURISTIC PROGRAMMING; ITERATIVE METHODS; OPTIMAL CONTROL SYSTEMS;

CONVERGENCE ANALYSIS; DYNAMIC PROGRAMMING ALGORITHM; GREEDY ITERATIVE HEURISTIC DYNAMIC PROGRAMMING ALGORITHM; HEURISTIC DYNAMIC PROGRAMMING; ITERATIVE HEURISTICS; NEURAL-NETWORKS; NONLINEAR DISCRETE-TIME SYSTEMS; NONQUADRATIC FUNCTIONAL; SATURATING; SATURATING ACTUATOR;

ACTUATORS;

EID: 50049091526     PISSN: 10020071     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.pnsc.2008.03.006     Document Type: Article

References (20)

1. H. Sussmann E.D. Sontag Y. Yang A general result on the stabilization of linear systems using bounded controls IEEE Trans Automatic Control 39 12 1994 2411 2425
2. D.S. Bernstein Optimal nonlinear, but continuous, feedback control of systems with saturating actuators Int J Control 62 5 1995 1209 1216
3. A. Saberi Z. Lin A. Teel Control of linear systems with saturating actuators IEEE Trans Automatic Control 41 3 1996 368 378
4. B. Widrow N. Gupta S. Maitra Punish/reward: learning with a critic in adaptive threshold systems IEEE Trans Syst Man Cybern 3 5 1973 455 465
5. Watkins C. Learning from delayed rewards. Ph.D. thesis, Cambridge University, Cambridge, England; 1989.
6. D.P. Bertsekas J.N. Tsitsiklis Neuro-dynamic programming 1996 Athena Scientific Massachusetts
7. Liu X, Balakrishnan SN. Convergence analysis of adaptive critic based optimal control. In: Proceedings of American control conference, Chicago, IL, USA; 2000. p. 1929–33.
8. J. Si Y.T. Wang On-line learning control by association and reinforcement IEEE Trans Neural Netw 12 2 2001 264 276
9. Liu D, Xiong X, Zhang Y. Action-dependent adaptive critic designs. In: Proceedings of the INNS-IEEE international joint conference on neural networks, Washington, DC; 2001. p. 990–5.
10. D. Liu H.G. Zhang A neural dynamic programming approach for learning control of failure avoidance problems Int J Intell Control Syst 10 1 2005 21 32
11. J.J. Murray C.J. Cox G.G. Lendaris Adaptive dynamic programming IEEE Trans Syst Man Cybern C Appl Rev 32 2 2002 140 153
12. M. Abu-Khalaf F.L. Lewis Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach Automatica 41 5 2005 779 791
13. D. Liu Approximate dynamic programming for self-learning control Acta Automatica Sin 31 1 2005 13 18
14. Al-Tamimi A, Lewis FL. Discrete-time nonlinear HJB solution using approximate dynamic programming: convergence proof. In: Proceedings of the IEEE symposium on approximate dynamic programming and reinforcement learning, Honolulu, HI, USA; 2007. p. 38–43.
15. Zhang HG, Wei QL, Liu D. On-line learning control for discrete nonlinear systems via an improved ADDHP method. In: Proceedings of the 4th International Symposium on Neural Networks. Nanjing, China; 2007, p. 387–96.
16. D.V. Prokhorov D.C. Wunsch Adaptive critic designs IEEE Trans Neural Netw 8 5 1997 997 1007
17. Lyshevski SE. Optimal control of nonlinear continuous-time systems: design of bounded controllers via generalized nonquadratic functionals. In: Proceedings of the American control conference, Philadelphia, USA; 1998. p. 205–9.
18. Lyshevski SE. Nonlinear discrete-time systems: constrained optimization and application of nonquadratic costs. In: Proceedings of the American control conference, Philadelphia, USA; 1998. p. 3699–703.
19. Beard R. Improving the closed-loop performance of nonlinear systems. Ph.D. thesis, Rensselaer Polytechnic Institute, Troy, New York, USA; 1995.
20. Z. Chen S. Jagannathan Generalized Hamilton–Jacobi–Bellman formulation-based neural network control of affine nonlinear discrete-time systems IEEE Trans Neural Netw 19 1 2008 90 106