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A novel ADP based model-free predictive control

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Abstract

Dynamic programming is a very useful tool in solving optimization and optimal control problems. Here, the Approximate Dynamic Programming (ADP) and the notion of neural networks based predictive control are combined with a model-free control method based on SPSA (Simultaneous perturbation stochastic approximation), and a novel ADP based model-free predictive control strategy for nonlinear systems is proposed. Dynamic programming is used to adjust the control parameters in the novel model-free control method and the notion of predictive control is introduced to modify the whole control structure. Finally, the proposed ADP based model-free predictive control strategy is applied to solve nonlinear tracking problems and the effectiveness of this novel control method is fully illustrated though simulation tests on two typical nonlinear systems.

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References

  1. Cheng, S.X.: Model-free adaptive (MFA) control. IEE Comput. Control Eng. 15(3), 28–33 (2004)

    Article  Google Scholar 

  2. Han, Z.G., Wang, D.: Controller without model. J. Nat. Sci. Heilongjiang Univ. 11(4), 29–35 (1994)

    MathSciNet  Google Scholar 

  3. Shen, Y.L., Wang, D.: The design and realization of controller without model. J. Nat. Sci. Heilongjiang Univ. 15(2), 24–27 (1998)

    Google Scholar 

  4. Hou, Z.S.: The parameter identification, adaptive control and model free learning adaptive control for nonlinear systems. Ph.D. thesis, North-eastern University, Shenyang, China (1994)

  5. Han, Z.G.: Designing problem of model free controller. Control Eng. China 9(3), 19–22 (2002)

    Google Scholar 

  6. Hou, Z.S.: Non-parametric model and its adaptive control theory. Science Press, Beijing (1999)

    Google Scholar 

  7. Cheng, S.X.: Model-free adaptive process control. United States Patent, 6055524, April 25 (2000)

    Google Scholar 

  8. Spall, J.C., Cristion, J.A.: Model-free control of general discrete-time systems. In: Proceedings of the 32nd IEEE Conference on Decision and Control, San Antonio, TX, December 15–17 (1993)

    Google Scholar 

  9. Murray, J.J., Cox, C.J., Lendaris, G.G., Seaks, R.: Adaptive dynamic programming. IEEE Trans. Syst. Man Cybern., Part C Appl. Rev. 32(2), 140–153 (2002)

    Article  Google Scholar 

  10. Prokhorov, D.V., Wunsch, D.C.: Adaptive critic designs. IEEE Trans. Neural Netw. 8(5), 997–1007 (1997)

    Article  Google Scholar 

  11. Si, J., Wang, Y.T.: On-line learning control by association and reinforcement. IEEE Trans. Neural Netw. 12(2), 264–276 (2001)

    Article  MathSciNet  Google Scholar 

  12. Werbos, P.J.: Building and understanding adaptive systems: a statistical/numerical approach to factory automation and brain research. IEEE Trans. Syst. Man Cybern. SMC-17, 7–20 (1987)

    Article  Google Scholar 

  13. Hendzel, Z.: An adaptive critic neural network for motion control of a wheeled mobile robot. Nonlinear Dyn. 50(4), 849–855 (2007)

    Article  MATH  Google Scholar 

  14. Jin, N., Liu, D.: Discrete-time e-adaptive dynamic programming algorithm using neural networks. In: IEEE International Symposium on Intelligent Control Part of 2008 IEEE Multi-conference on Systems and Control, San Antonio, TX, September 3–5 (2008)

    Google Scholar 

  15. Liu, D., Jin, N.: Finite horizon discrete-time approximate dynamic programming. In: Proceedings of the 2006 IEEE International Symposium on Intelligent Control, Munich, Germany, October 4–6 (2006)

    Google Scholar 

  16. Werbos, P.J.: Beyond regression: New Tools for Prediction and Analysis in the Behavioral Sciences. Ph.D. thesis, Harvard Univ., Cambridge (1974)

  17. Werbos, P.J.: Advanced forecasting methods for global crisis warning and models of intelligence. Gen. Syst. Yearbook 22, 25–38 (1977)

    Google Scholar 

  18. Li, X., Chen, Z.Q., Yuan, Z.Z.: Simple recurrent neural network-based adaptive predictive control for nonlinear systems. Asian J. Control 4(2), 231–239 (2002)

    Article  Google Scholar 

  19. Spall, J.C.: Multivariate stochastic approximation using a simultaneous perturbation gradient approximation. IEEE Trans. Autom. Control 37(3), 332–341 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  20. Prokhorov, D.V., Wunsch, D.C.: Adaptive critic designs. IEEE Trans. Neural Netw. 8(5), 997–1007 (1997)

    Article  Google Scholar 

  21. Tan, Y., Cauwenberghe, A.: Nonlinear one-step-ahead control using neural networks: control strategy and stability design. Automatica 32(12), 1701–1706 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  22. Noriega, J.R., Wang, H.: A direct adaptive neural-network control for unknown nonlinear systems and its application. IEEE Trans. Neural Netw. 9(1), 27–34 (1998)

    Article  Google Scholar 

  23. Yildirim, S.: A proposed hybrid neural network for position control of a walking robot. Nonlinear Dyn. 52(3), 207–215 (2008)

    Article  MATH  Google Scholar 

  24. Rumelhart, D., McClelland, J.: Parallel Disttibnctl Processing: Explorations in the Micro-Structure of Cognition, vol. 1. MIT Press, Cambridge (1986)

    Google Scholar 

  25. Spall, J.C., Cristion, J.A.: Model-free control of nonlinear stochastic systems with discrete-time measurements. IEEE Trans. Autom. Control 43(9), 1198–1210 (1998)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Automation, School of Electrical Engineering and Automation, Tianjin University, 92 Weijin Road, Tianjin, 300071, China

    Na Dong

  2. Department of Automation, Nankai University, 94 Weijin Road, Tianjin, 300071, China

    Zengqiang Chen

Authors
  1. Na Dong
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  2. Zengqiang Chen
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Correspondence to Na Dong.

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Dong, N., Chen, Z. A novel ADP based model-free predictive control. Nonlinear Dyn 69, 89–97 (2012). https://doi.org/10.1007/s11071-011-0248-3

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  • DOI: https://doi.org/10.1007/s11071-011-0248-3

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