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Neuro-based Canonical Transformation of Port Controlled Hamiltonian Systems

  • Control Theory and Applications
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Abstract

In the literature of control theory, tracking control of port controlled Hamiltonian systems is generally achieved using canonical transformation. Closed form evaluation of state-feedback for the canonical transformation requires the solution of certain partial differential equations which becomes very difficult for nonlinear systems. This paper presents the application of neural networks for the canonical transformation of port controlled Hamiltonian systems. Instead of solving the partial differential equations, neural networks are used to approximate the closed-form state-feedback required for canonical transformation. Ultimate boundedness of the tracking and neural network weight errors is guaranteed. The proposed approach is structure preserving. The application of neural networks is direct and off-line processing of neural networks is not needed. Efficacy of the proposed approach is demonstrated with the examples of a mass-spring system, a two-link robot arm and an Autonomous Underwater Vehicle (AUV).

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References

  1. S. P. Nageshrao, G. A. D. Lopes, D. Jeltsema, and R. Babuška, “Port-Hamiltonian systems in adaptive and learning control: a survey,” IEEE Transactions on Automatic Control, vol. 61, no. 5, pp. 1223–1238, 2016.

    Article  MathSciNet  Google Scholar 

  2. Q. Zhang and L. Guangjun, “Precise control of elastic joint robot using an interconnection and damping assignment passivity-based approach,” IEEE/ASME Transactions on Mechatronics, vol. 21, no. 6, pp. 2728–2736, 2016.

    Article  Google Scholar 

  3. J. P. García-Sandoval, N. Hudon, D. Dochain, and V. González-Álvarez, “Stability analysis and passivity properties of a class of thermodynamic processes: An internal entropy production approach,” Chemical Engineering Science, vol. 139, pp. 261–272, 2016.

    Article  Google Scholar 

  4. H. Li, and A. Wei, “Stabilization and H∞ control of nonlinear switched Hamiltonian systems subject to actuator saturation,” Asian Journal of Control, vol. 19, no. 3, pp. 951–960, 2017.

    Article  MathSciNet  Google Scholar 

  5. K. Fujimoto and T. Sugie, “Canonical transformation and stabilization of generalized Hamiltonian systems,” Systems and Control Letters, vol. 42, no. 3, pp. 217–227, 2001.

    Article  MathSciNet  Google Scholar 

  6. K. Fujimoto, K. Sakurama, and T. Sugie, “Trajectory tracking control of port-controlled Hamiltonian systems via generalized canonical transformations,” Automatica, vol. 39, no. 12, pp. 2059–2069, 2003.

    Article  MathSciNet  Google Scholar 

  7. M. Ryalat and D. S. Laila, “A simplified IDA-PBC design for underactuated mechanical systems with applications,” European Journal of Control, vol. 27, pp. 1–16, 2016.

    Article  MathSciNet  Google Scholar 

  8. A. Yesilderek and F. L. Lewis, “Feedback linearizion using neural networks,” Automatica, vol. 31, no. 11, pp. 2059–2069, 1995.

    Google Scholar 

  9. J. T. Spooner and K. M. Passino, “Stable adaptive control using fuzzy systems and neural networks,” IEEE Transection on Fuzzy Systems, vol. 4, no. 3, pp. 339–359, 1996.

    Article  Google Scholar 

  10. H. A. Abdel, F. A. F. Sakr, and A. Bahgat, “Nonlinear system control via feedback linearization using neural networks,” Proceedings of IEEE International Conference on Neural Networks, vol. 4, pp. 2238–2243, 1996.

    Google Scholar 

  11. S. He, K. Reif, and R. Unbehauen, “A neural approach for control of nonlinear systems with feedback linearization,” IEEE Transactions on Neural Networks, vol. 9, no. 6, pp. 1409–1512, 1998.

    Article  Google Scholar 

  12. A. Qureshi, S. Elferik, and F. L. Lewis, “L2 neuro-adaptive tracking control of uncertain port controlled Hamiltonian systems,” IET Control Theory and Applications, vol. 9, no. 12, pp. 1781–1790, 2015.

    Article  MathSciNet  Google Scholar 

  13. D. A. Dirksz and J. M. A. Sherpen, “Structure preserving adaptive control of port-Hamiltonian system,” IEEE Trans. Automatic Control, vol. 57, no. 11, pp. 2880–2884, 2012.

    Article  MathSciNet  Google Scholar 

  14. S. Elferik, A. Qureshi, and F. L. Lewis, “Robust neuroadaptive cooperative control of multi-agent port controlled Hamiltonian systems,” Int. J. Robust & Nonlinear Control, vol. 30, no. 3, pp. 488–510, 2016.

    Article  Google Scholar 

  15. S. S. Ge, C. C. Hang, T. H. Lee, and T. Zhang, Stable Adaptive Neural Network Control, Springer New York, 2002.

    Book  Google Scholar 

  16. K. S. Nerendra and A. M. Annaswami, “A new adaptive law for robust adaptation without persistent excitation,” IEEE Trans. Automatic Control, vol. AC-32, no. 2, pp. 134–145, 1987.

    Article  MathSciNet  Google Scholar 

  17. K. S. Narendra and K. Parthasarathy, “Identification and control of dynamical systems using neural networks,” IEEE Trans. Neural Networks, vol. 1, pp. 4–27, 1990.

    Article  Google Scholar 

  18. B. Igelink and Y. H. Pao, “Stochastic choice of basis function in adaptive function approximation and functional-link net,” IEEE Transection on Neural Networks, vol. 6, no. 6, pp. 1320–1329, 1995.

    Article  Google Scholar 

  19. G. Cybenko, “Approximation by superpositions of a sigmoidal function,” Mathematics of Control, Signals and Systems, vol. 2, no. 4, pp. 303–314, 1989.

    Article  MathSciNet  Google Scholar 

  20. A. Macchelli, C. Melchiorri, C. Secchiy, and C. Fantuzziy, “A variable structure approach to energy shaping,” Proc. European Control Conference, Cambridge, UK, 2003.

  21. Y. Wang, G. Feng, and D. Cheng, “Simultaneous stabilization of a set of nonlinear port-controlled Hamiltonian systems,” Automatica, vol. 43, no. 3, pp. 403–415, 2007.

    Article  MathSciNet  Google Scholar 

  22. T. Shen, R. Ortega, Q. Lu, S. Mei, and K. Tamura, “Adaptive L2 disturbance attenuation of Hamiltonian systems with parametric purturbation and application to power systems,” Asian Journal of Control, vol. 5, no. 1, pp. 143–152, 2003.

    Article  Google Scholar 

  23. D. A. Dirksz and J. M. A. Sherpen, “Power-based control: canonical coordinate transformations, integral and adaptive control,” Automatica, vol. 48, pp. 1045–1056, 2012.

    Article  MathSciNet  Google Scholar 

  24. J. J. E. Slotine and W. Li, Applied, Nonlinear Control, Printice-Hall, Englewood Cliffs, NJ, 1991.

    MATH  Google Scholar 

  25. F. L. Lewis, S. Jagannathan, and A. Yesilderek, Neural Network Control of Robot Manipulator and Nonlinear Systems, Taylor and Francis, London, 1998.

    Google Scholar 

  26. P. A. Ioannu and J. Sun, Robust Adaptive Control, Dover Publications Inc., Mineola, New York, 2012.

    Google Scholar 

  27. M. Krstic, I. Kanellakopoulos, and P. Kokotovic, Nonlinear and Adaptive Control Design, Wiley, New York, 1995.

    MATH  Google Scholar 

  28. P. Ioannou and B. Fidan, Adaptive Control Tutorial, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 2006.

    Book  Google Scholar 

  29. Y. Boutalis, D. Theodoridis, T. Kottas, and M. A. Christodoulou, System Identification and Adaptive Control: Theory and Applications of the Neurofuzzy and Fuzzy Cognitive Network Models, Springer International Publishing, Switzerland, 2014.

    Book  Google Scholar 

  30. B. Ferreira, A. Matos, N. Cruz, and M. Pinto, “Modeling and control of the MARES autonomous underwater vehicle,” Marine Technology Society Journal, vol. 44, no. 2, pp. 19–36, 2010.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Systems Engineering, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Aminuddin Qureshi & Sami El Ferik

  2. Research Institute, The University of Texas at Arlington, Arlington, Texas, 76118, USA

    Frank L. Lewis

Authors
  1. Aminuddin Qureshi
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  2. Sami El Ferik
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  3. Frank L. Lewis
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Corresponding author

Correspondence to Sami El Ferik.

Additional information

Recommended by Editor Kyoung Kwan Ahn.

The authors would like to acknowledge the support provided by King Fahd University of Petroleum and Minerals (KFUPM) for funding this work through project, no.IN141048.

Aminuddin Qureshi obtained his degrees of B.Sc. in Electrical Engineering from UET Peshawar-Pakistan, an M.Sc. in Systems Engineering from PIEAS-Pakistan and Ph.D. in Systems Engineering from KFUPM-Saudi Arabia, in 2001, 2003, and 2014, respectively. He has worked on several R&D projects in the areas of signal processing and control. Currently, he is involved in the diagnostics and prognostics of industrial structures, systems and components. His areas of interest are signal processing, artificial intelligence applied to control systems and diagnostics and prognostics.

Sami El Ferik is an Associate Professor in Control and Instrumentation, Department of Systems Engineering, at KFUPM. He obtained his B.Sc degree in Electrical Engineering from Laval University, Quebec, Canada, and both of his M.S. and Ph.D. in Electrical and Computer Engineering from Ecole Polytechnique, University of Montreal, Montreal, Canada. He worked with Pratt and Whitney Canada as a Staff Control Analyst at the Research and Development Center of Systems, Controls, and Accessories. His research interests are in sensing, monitoring, and control with strong multidisciplinary research and applications. His research contributions are in control of drug administration, process control and control loop performance monitoring, control of systems with delays, modeling and control of stochastic systems, analysis of network stability, condition monitoring and condition-based maintenance.

Frank L. Lewis, National Academy of Inventors, Fellow IEEE, Fellow IFAC, PE Texas, U.K. Chartered Engineer, is a UTA Distinguished Scholar Professor, UTA Distinguished Teaching Professor, and Moncrief-O’Donnell Chair at the University of Texas at Arlington Research Institute. He obtained his Bachelor’s Degree in Physics/EE and the MSEE at Rice University, an M.S. degree in Aeronautical Engineering from the University of West Florida, and a Ph.D. degree at Ga. Tech. He is the author of seven U.S. patents, numerous journal papers, and 14 books.

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Qureshi, A., El Ferik, S. & Lewis, F.L. Neuro-based Canonical Transformation of Port Controlled Hamiltonian Systems. Int. J. Control Autom. Syst. 18, 3101–3111 (2020). https://doi.org/10.1007/s12555-019-0029-1

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  • DOI: https://doi.org/10.1007/s12555-019-0029-1

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