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State estimation in MIMO nonlinear systems subject to unknown deadzones using recurrent neural networks

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Abstract

This paper deals with the problem of state observation by means of a continuous-time recurrent neural network for a broad class of MIMO unknown nonlinear systems subject to unknown but bounded disturbances and with an unknown deadzone at each input. With respect to previous works, the main contribution of this study is twofold. On the one hand, the need of a matrix Riccati equation is conveniently avoided; in this way, the design process is considerably simplified. On the other hand, a faster convergence is carried out. Specifically, the exponential convergence of Euclidean norm of the observation error to a bounded zone is guaranteed. Likewise, the weights are shown to be bounded. The main tool to prove these results is Lyapunov-like analysis. A numerical example confirms the feasibility of our proposal.

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References

  1. Thau FE (1973) Observing the state of nonlinear dynamical systems. Int J Control 17:471–479

    Article  MATH  Google Scholar 

  2. Raghavan S, Hedrick JK (1994) Observer design for a class of nonlinear systems. Int J Control 59:515–528

    Article  MATH  MathSciNet  Google Scholar 

  3. Rajamani R (1998) Observers for Lipschitz nonlinear systems. IEEE Trans Autom Control 43:397–401

    Article  MATH  MathSciNet  Google Scholar 

  4. Rajamani R, Cho YM (1998) Existence and design of observers for nonlinear systems: relation to distance of unobservability. Int J Control 69:717–731

    Article  MATH  MathSciNet  Google Scholar 

  5. Pertew A, Marquez HJ, and Zhao Q (2005) Dynamic observer for nonlinear Lipschitz systems. In: The proceedings of the 16th IFAC World Congress

  6. Marino R, Santosuosso GL, Tomei P (2001) Robust adaptive observers for nonlinear systems with bounded disturbances. IEEE Trans Autom Control 46:967–972

    Article  MATH  MathSciNet  Google Scholar 

  7. Choi YU, Shim H, Son YI, Seo JH (2003) Design of an adaptive observer for a class of nonlinear systems. Int J Control Autom Syst 1:28–34

    Google Scholar 

  8. Kim YH, Lewis F, Abdallah CT (1997) A dynamic recurrent neural network based adaptive observer for a class of nonlinear systems. Automatica 33:1539–1543

    Article  MATH  MathSciNet  Google Scholar 

  9. Poznyak Alexander S, Wen Yu (2000) Robust asymptotic neuro observer with time delay. Int J Robust Nonlinear Control 10:535–560

    Article  MATH  Google Scholar 

  10. Norgaard M, Ravn O, Poulsen NK, Hansen LK (2000) Neural networks for modelling and control of dynamic systems. Springer, Berlin

    Book  Google Scholar 

  11. Haykin S (2009) Neural networks and learning machines, 3rd edn. Prentice Hall, Upper Saddle River

    Google Scholar 

  12. Poznyak AS, Sanchez EN, Yu W (2001) Dynamic neural networks for nonlinear control: identification, state estimation and trajectory tracking. World Scientific, Singapore

    Google Scholar 

  13. Chairez I, García-Peña I, Cabrera A (2009) Dynamic numerical reconstruction of a fungal biofiltration system using differential neural network. J Process Control 19:1103–1110

    Article  Google Scholar 

  14. Chairez I, Poznyak A, Poznyak T, (2004) Model free sliding mode neural observer for ozonation reaction. In: Proceedings of the 8th international workshop on variable structure systems, Villanova i la Geltru′, Spain

  15. Chairez I, Poznyak A, Poznyak T (2006) New sliding mode learning law for dynamic neural network observer. Trans IEEE Circ Syst II 53:1338–1342

    Article  Google Scholar 

  16. Chairez I, Poznyak A, Poznyak T (2009) Stable weights dynamics for a class of differential neural network observer. IET Control Theory Appl 3:1437–1447

    Article  MathSciNet  Google Scholar 

  17. Magyar B, Hős C, Stépán G (2010) Influence of control valve delay and dead zone on the stability of a simple hydraulic positioning system. Math Probl Eng 2010:15, Article ID 349489

  18. Yuan X, Yang Y, Wang H, Wang Y (2013) Genetic algorithm-based adaptive fuzzy sliding mode controller for electronic throttle valve. Neural Comput Appl. doi:10.1007/s00521-012-1327-1

    Google Scholar 

  19. Bessa WM, Dutra MS, Kreuzer E (2010) Sliding mode control with adaptive fuzzy dead-zone compensation of an electro-hydraulic servo-system. J Intell Rob Syst 58:3–16

    Article  MATH  Google Scholar 

  20. Valdiero AC, Ritter CS, Rios CF, Rafikov M (2011) Nonlinear mathematical modeling in pneumatic servo position applications. Math Probl Eng 2011:16, Article ID 472903

  21. Liu L, Liu Y-J, Chen CLP (2013) Adaptive neural network control for a DC motor system with dead-zone. Nonlinear Dyn 72:141–147

    Article  Google Scholar 

  22. Tao G, Kokotovic PV (1996) Adaptive control of systems with actuator and sensor nonlinearities. Wiley, New York

    MATH  Google Scholar 

  23. Liu L, Liu Y-J, Li D-J (2012) Intelligence computation based on adaptive tracking design for a class of non-linear discrete-time systems. Neural Comput Appl. doi:10.1007/s00521-012-1080-5

    Google Scholar 

  24. Li D-J, Tang L (2013) Adaptive control for a class of chemical reactor systems in discrete-time form. Neural Comput Appl. doi:10.1007/s00521-013-1420-0

    Google Scholar 

  25. Chang C-Y, Chiang T-C (2009) Overhead cranes fuzzy control design with deadzone compensation. Neural Comput Appl 18:749–757

    Article  Google Scholar 

  26. Lewis FL, Campos J, Selmic R (2002) Neuro-fuzzy control of industrial systems with actuator nonlinearities, Siam, Philadelphia

  27. Wang XS, Su CY, Hong H (2004) Robust adaptive control of a class of nonlinear systems with unknown dead zone. Automatica 40:407–413

    Article  MATH  MathSciNet  Google Scholar 

  28. Zhou J, Shen XZ (2007) Robust adaptive control of nonlinear uncertain plants with unknown dead-zone. IET Control Theory Appl 1:25–32

    Article  MathSciNet  Google Scholar 

  29. Wang ZH, Zhang Y, Fang H (2008) Neural adaptive control for a class of nonlinear systems with unknown dead zone. Neural Comput Appl 17:339–345

    Article  Google Scholar 

  30. Liu YJ, Zhou N (2010) Observer-based adaptive fuzzy-neural control for a class of uncertain nonlinear systems with unknown dead-zone input. ISA Trans 49:462–469

    Article  Google Scholar 

  31. Poznyak T, Chairez I, Poznyak A (2005) Application of a neural observer to phenols ozonation in water: simulation and kinetic parameters identification. Water Res 39:2611–2620

    Article  Google Scholar 

  32. Chairez I, Poznyak A, Poznyak T (2007) Reconstruction of dynamics of aqueous phenols and their products formation in ozonation using differential neural network observer. Ind Eng Chem Res 46:5855–5866

    Article  Google Scholar 

  33. Poznyak T, García A, Chairez I, Gómez M, Poznyak A (2007) Application of the differential neural network observer to the kinetic parameters identification of the anthracene degradation in contaminated model soil. J Hazard Mater 146:661–667

    Article  Google Scholar 

  34. Chairez I, Fuentes R, Poznyak T, Franco M, Poznyak A (2010) Numerical modeling of the benzene reaction with ozone in gas phase using differential neural networks. Catal Today 151:159–165

    Article  Google Scholar 

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Acknowledgments

First author would like to thank the financial support through a postdoctoral fellowship from Mexican National Council for Science and Technology (CONACYT) under Grant 194775-IPN.

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Authors and Affiliations

  1. Sección de Estudios de Posgrado e Investigación, ESIME UA-IPN, Av. de las Granjas no. 682, Col. Santa Catarina, C.P. 02250, Mexico, D.F., Mexico

    J. Humberto Pérez-Cruz, José de Jesús Rubio, Jaime Pacheco & Ezequiel Soriano

  2. DEPI, Instituto Tecnológico de Oaxaca, Av. Ing. Victor Bravo Ahuja No. 125, C.P. 68030, Oaxaca, Mexico

    J. Humberto Pérez-Cruz

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  1. J. Humberto Pérez-Cruz
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  2. José de Jesús Rubio
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  3. Jaime Pacheco
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  4. Ezequiel Soriano
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Correspondence to J. Humberto Pérez-Cruz.

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Pérez-Cruz, J.H., Rubio, J.J., Pacheco, J. et al. State estimation in MIMO nonlinear systems subject to unknown deadzones using recurrent neural networks. Neural Comput & Applic 25, 693–701 (2014). https://doi.org/10.1007/s00521-013-1533-5

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  • DOI: https://doi.org/10.1007/s00521-013-1533-5

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