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Nearly Optimal Control for Nonlinear Systems with Dead-Zone Control Input Based on the Iterative ADP Approach

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Neural Information Processing (ICONIP 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7663))

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Abstract

This paper focuses on a class of unknown discrete-time nonlinear systems with dead-zone control constraints based on adaptive dynamic programming (ADP). The discrete-time Hamilton-Jacobi-Bellman (DTHJB) equation corresponding to the dead-zone control input is formulated. Based on ADP technique, a new cost function is proposed that solves the optimal control with dead zone constraints effectively. It shows that this algorithm allows the implementation of the optimal control without knowing nonlinear affine system model and dead-zone dynamics. Finally, a simulation example is provided to verify the effectiveness of the proposed iterative algorithm.

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References

  1. Tao, G., Kokotovic, P.V.: Adaptive control of systems with unknown output backlash. IEEE Transactions on Automatic Control 40, 326–330 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  2. Tao, G., Kokotovic, P.V.: Continuous-time adaptive control of systems with unknown backlash. IEEE Transactions on Automatic Control 40, 1083–1087 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  3. Tao, G., Kokotovic, P.V.: Adaptiv control of systems with actuator and sensor nonlinearities. John Wiley, New York (1996)

    Google Scholar 

  4. Zhang, H., Luo, Y., Liu, D.: Neural-network-based near-optimal control for a class of discrete-time affine nonlinear systems with control constraints. IEEE Transactions on Neural Networks 20, 1490–1503 (2009)

    Article  Google Scholar 

  5. Tao, G., Kokotovic, P.V.: Adaptive control of plants with unknown dead-zones. IEEE Transactions on Automatic Control 39, 59–68 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  6. Gao, W., Rastko, R.S.: Neural network control of a class of nonlinear systems with actuator saturation. IEEE Transactions on Neural Networks 17, 147–156 (2006)

    Article  MATH  Google Scholar 

  7. Recker, D., Kokotovic, P., Rhode, D., Winkelman, J.: Adaptive nonlinear control of systems containing a dead-zone. In: Proceedings of the 30th IEEE Conference on Decision and Control, Brighton, England, pp. 2111–2115 (1991)

    Google Scholar 

  8. Selmic, R.R., Lewis, F.L.: Deadzone compensation in motion control systems using neural networks. IEEE Transactions on Automatic Control 45, 602–613 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  9. Bernstein, D.S.: Optimal nonlinear, but continuous, feedback control of systems with saturating actuators. International Journal of Control 62, 1209–1216 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  10. Saberi, A., Lin, Z., Teel, A.: Control of linear systems with saturating actuators. IEEE Transactions on Automatic Control 41, 368–378 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  11. Sussmann, H., Sontag, E.D., Yang, Y.: A general result on the stabilization of linear systems using bounded controls. IEEE Transactions on Automatic Control 39, 2411–2425 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  12. Lewis, F.L., Tim, W.K., Wang, L.Z., Li, Z.X.: Deadzone compensation in motion control systems using adaptive fuzzy logic control. IEEE Transactions on Control Systems Technology 7, 731–742 (1999)

    Article  Google Scholar 

  13. Abu-Khalaf, M., Lewis, F.L.: Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach. Automatica 41, 779–791 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  14. Lyshevski, S.E.: Optimal control of nonlinear continuous-time systems: design of bounded controllers via generalized nonquadratic functional. In: Proceedings of American Control Conference, Philadelphia, America, pp. 205–209 (1998)

    Google Scholar 

  15. Balakrishnan, S.N., Ding, J., Lewis, F.L.: Issues on stability of ADP feedback controllers for dynamical systems. IEEE Transactions on Systems, Man, and Cybernetics 38, 913–917 (2008)

    Article  Google Scholar 

  16. Werbos, P.J.: Approximate dynamic programming for real-time control and neural Modeling. In: White, D.A., Sofge, D.A. (eds.) Handbook of Intelligent Control: Neural, Fuzzy, and Adaptive Approaches, New York (1992)

    Google Scholar 

  17. Prokhorov, D.V., Wunsch, D.C.: Adaptive critic designs. IEEE Transactions on Neural Networks 8, 997–1007 (1997)

    Article  Google Scholar 

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© 2012 Springer-Verlag Berlin Heidelberg

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Zhang, D., Liu, D., Wei, Q. (2012). Nearly Optimal Control for Nonlinear Systems with Dead-Zone Control Input Based on the Iterative ADP Approach. In: Huang, T., Zeng, Z., Li, C., Leung, C.S. (eds) Neural Information Processing. ICONIP 2012. Lecture Notes in Computer Science, vol 7663. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34475-6_16

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  • DOI: https://doi.org/10.1007/978-3-642-34475-6_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34474-9

  • Online ISBN: 978-3-642-34475-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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