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.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
Cheng, S.X.: Model-free adaptive (MFA) control. IEE Comput. Control Eng. 15(3), 28–33 (2004)
Han, Z.G., Wang, D.: Controller without model. J. Nat. Sci. Heilongjiang Univ. 11(4), 29–35 (1994)
Shen, Y.L., Wang, D.: The design and realization of controller without model. J. Nat. Sci. Heilongjiang Univ. 15(2), 24–27 (1998)
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)
Han, Z.G.: Designing problem of model free controller. Control Eng. China 9(3), 19–22 (2002)
Hou, Z.S.: Non-parametric model and its adaptive control theory. Science Press, Beijing (1999)
Cheng, S.X.: Model-free adaptive process control. United States Patent, 6055524, April 25 (2000)
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)
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)
Prokhorov, D.V., Wunsch, D.C.: Adaptive critic designs. IEEE Trans. Neural Netw. 8(5), 997–1007 (1997)
Si, J., Wang, Y.T.: On-line learning control by association and reinforcement. IEEE Trans. Neural Netw. 12(2), 264–276 (2001)
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)
Hendzel, Z.: An adaptive critic neural network for motion control of a wheeled mobile robot. Nonlinear Dyn. 50(4), 849–855 (2007)
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)
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)
Werbos, P.J.: Beyond regression: New Tools for Prediction and Analysis in the Behavioral Sciences. Ph.D. thesis, Harvard Univ., Cambridge (1974)
Werbos, P.J.: Advanced forecasting methods for global crisis warning and models of intelligence. Gen. Syst. Yearbook 22, 25–38 (1977)
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)
Spall, J.C.: Multivariate stochastic approximation using a simultaneous perturbation gradient approximation. IEEE Trans. Autom. Control 37(3), 332–341 (1992)
Prokhorov, D.V., Wunsch, D.C.: Adaptive critic designs. IEEE Trans. Neural Netw. 8(5), 997–1007 (1997)
Tan, Y., Cauwenberghe, A.: Nonlinear one-step-ahead control using neural networks: control strategy and stability design. Automatica 32(12), 1701–1706 (1996)
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)
Yildirim, S.: A proposed hybrid neural network for position control of a walking robot. Nonlinear Dyn. 52(3), 207–215 (2008)
Rumelhart, D., McClelland, J.: Parallel Disttibnctl Processing: Explorations in the Micro-Structure of Cognition, vol. 1. MIT Press, Cambridge (1986)
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)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-011-0248-3