DOI QR코드

DOI QR Code

Policy Iteration Algorithm Based Fault Tolerant Tracking Control: An Implementation on Reconfigurable Manipulators

  • Li, Yuanchun (Department of Control Science and Engineering, Changchun University of Technology) ;
  • Xia, Hongbing (Department of Control Science and Engineering, Changchun University of Technology) ;
  • Zhao, Bo (The State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences)
  • Received : 2016.11.01
  • Accepted : 2018.04.20
  • Published : 2018.07.01

Abstract

This paper proposes a novel fault tolerant tracking control (FTTC) scheme for a class of nonlinear systems with actuator failures based on the policy iteration (PI) algorithm and the adaptive fault observer. The estimated actuator failure from an adaptive fault observer is utilized to construct an improved performance index function that reflects the failure, regulation and control simultaneously. With the help of the proper performance index function, the FTTC problem can be transformed into an optimal control problem. The fault tolerant tracking controller is composed of the desired controller and the approximated optimal feedback one. The desired controller is developed to maintain the desired tracking performance at the steady-state, and the approximated optimal feedback controller is designed to stabilize the tracking error dynamics in an optimal manner. By establishing a critic neural network, the PI algorithm is utilized to solve the Hamilton-Jacobi-Bellman equation, and then the approximated optimal feedback controller can be derived. Based on Lyapunov technique, the uniform ultimate boundedness of the closed-loop system is proven. The proposed FTTC scheme is applied to reconfigurable manipulators with two degree of freedoms in order to test the effectiveness via numerical simulation.

Keywords

Acknowledgement

Supported by : National Natural Science Foundation of China, State Key Laboratory of Management and Control for Complex Systems

References

  1. S. Tong, B. Huo and Y. Li, "Observer-based adaptive decentralized fuzzy fault-tolerant control of nonlinear large-scale systems with actuator failures," IEEE Transactions on Fuzzy Systems, vol. 22, no. 1, pp. 1- 15, Feb 2014. https://doi.org/10.1109/TFUZZ.2013.2241770
  2. B. Zhao, Y. Li, and D. Liu, "Self-tuned local feedback gain based decentralized fault tolerant control for a class of large-scale nonlinear Systems," Neurocomputing, vol. 235, pp. 147-156, Feb 2017. https://doi.org/10.1016/j.neucom.2016.12.063
  3. R. J. Patton, "Fault tolerant control: The 1997 situation," Proceedings of the 3rd IFAC Symposium on Fault Detection Supervision and Safety for Technical Processes, Hull, United Kingdom pp. 759- 762, 1997.
  4. Y. Zhang and J. Jiang, "Bibliographical review on reconfigurable fault-tolerant control systems," Annual Reviews in Control, vol. 32, no. 2, pp. 229-252, Dec 2008. https://doi.org/10.1016/j.arcontrol.2008.03.008
  5. M. Blanke, M. Kinnaert, J. Lunze and M. Staroswiecki, "Diagnosis and fault-tolerant control," Springer-Verlag, vol. 49, no. 6, pp. 873-893, 2006.
  6. M. Benosman and K. Y. Lum, "Passive actuators' fault-tolerant control for affine nonlinear systems," IEEE Transactions on Control Systems Technology, vol. 18, no. 1, pp. 152-163, Jan 2010. https://doi.org/10.1109/TCST.2008.2009641
  7. W. Wang and C. Wen, "Adaptive compensation for infinite number of actuator failures or faults," Automatica, vol. 47, no. 10, pp. 2197-2210, Oct 2011. https://doi.org/10.1016/j.automatica.2011.08.022
  8. S. Chatterjee, S. Sadhu and T. K. Ghoshal, "Fault detection and identification of non-linear hybrid system using self-switched sigma point filter bank." IET Control Theory and Applications, vol. 9, no. 7, pp. 1093-1102, May 2015. https://doi.org/10.1049/iet-cta.2014.0716
  9. W. H. Lee, K. H. Kim, G. P. Chan and J. G. Lee, "Two-faults detection and isolation using extended parity space approach," Journal of Electrical Engineering and Technology, vol. 7, no. 3, pp. 411- 419, May 2012. https://doi.org/10.5370/JEET.2012.7.3.411
  10. K. Zhang, B. Jiang and V. Cocquempot, "Adaptive observer-based fast fault estimation," International Journal of Control Automation and Systems, vol. 6, no. 3, pp. 320-326, June 2008.
  11. Y. Xu, S. Tong and Y. Li, "Observer-based fuzzy adaptive control of nonlinear systems with actuator faults and unmodeled dynamics" Neural Computing and Applications, vol. 23, no. s1, pp. 391-405, Oct 2013.
  12. Q. Jia, W. Chen, Y. Zhang and H. Li, "Fault reconstruction and fault-tolerant control via learning observers in Takagi-Sugeno fuzzy descriptor systems with time delays" IEEE Transactions on Industrial Electronics, vol. 62, no. 6, pp. 3885-3895, June 2015. https://doi.org/10.1109/TIE.2015.2404784
  13. D. Q. Khanh and Y. S. Suh, "Mobile robot destination generation by tracking a remote controller using a vision-aided inertial navigation algorithm," Journal of Electrical Engineering and Technology, vol. 8, no. 3, pp. 616-620, May 2013.
  14. I. A. Raptis, K. P. Valavanis and G. J. Vachtsevanos, "Linear tracking control for Small-Scale unmanned helicopters," IEEE Transactions on Control Systems Technology, vol. 20, no. 4, pp. 995-1010, July 2012. https://doi.org/10.1109/TCST.2011.2158213
  15. F. Liao, J. Wang and G. Yang "Reliable robust flight tracking control: an LMI approach," IEEE Transactions on Control Systems Technology, vol. 10, no. 1, pp. 76-89, Jan 2002. https://doi.org/10.1109/87.974340
  16. B. Yao, F. Wang and Q. Zhang, "LMI-based design of reliable tracking controller," Acta Automatica Sinica, vol. 30, no. 6, pp. 863-871, June 2004.
  17. B. Jiang, Z. Gao, P. Shi and Y. Xu, "Adaptive faulttolerant tracking control of near-space vehicle using Takagi-Sugeno fuzzy models," IEEE Transactions on Fuzzy Systems, vol. 18, no. 5, pp. 1000-1007, Oct 2010. https://doi.org/10.1109/TFUZZ.2010.2058808
  18. P. J. Werbos, "Approximate dynamic programming for real-time control and neural modeling," Handbook of Intelligent Control Neural Fuzzy and Adaptive Approaches, ch 13, 1992.
  19. D. Vrabie and F. L. Lewis, "Adaptive dynamic programming for online solution of a zero-sum differential game," Journal of Control Theory and Applications, vol. 9, no. 3, pp. 353-360, 2011. https://doi.org/10.1007/s11768-011-0166-4
  20. D. Liu, D. Wang, F. Wang and X. Yang, "Neuralnetwork-based online HJB solution for optimal robust guaranteed cost control of continuous-time uncertain nonlinear systems," IEEE Transactions on Cybernetics, vol. 44, no. 12, pp. 2834-2847, Dec 2014. https://doi.org/10.1109/TCYB.2014.2357896
  21. Q. Wei and D. Liu, "Stable iterative adaptive dynamic programming algorithm with approximation errors for discrete-time nonlinear systems," Neural Computing and Applications, vol. 24, no. 6, pp. 1355-1367, May 2014. https://doi.org/10.1007/s00521-013-1361-7
  22. L. Yang, J. Si, K. S. Tsakalis, and A.A. Rodriguez, "Direct heuristic dynamic programming for nonlinear tracking conrol with filtered tracking error," IEEE Transactions on Systems, Man, and Cybernetics, Part B, vol. 39, no. 6, pp. 617-1622, Dec 2009.
  23. B. Zhao, D. Wang, G. Shi, D. Liu and Y. Li, "Decentralized control for large-scale nonlinear systems with unknown mismatched interconnections via policy iteration," IEEE Transactions on Systems, Man, and Cybernetics: Systems, DOI: 10.1109/ TSMC.2017.2690665, Apr 2017.
  24. D. Liu and Q. Wei, "Policy iteration adaptive dynamic programming algorithm for discrete-time nonlinear systems," IEEE Transactions on Neural Networks and Learning Systems, vol. 25, no. 3, pp. 621-634, March 2014. https://doi.org/10.1109/TNNLS.2013.2281663
  25. D. Liu, D. Wang and H. Li, "Decentralized stabilization for a class of continuous-time nonlinear interconnected systems using online learning optimal control approach," IEEE Transactions on Neural Networks and Learning Systems, vol. 25, no. 2, pp. 411-428, Feb 2014.
  26. J. Wang, X. Xu, D. Liu, Z. Sun and Q. Chen, "Self-learning cruise control using kernel-based least squares policy iteration," IEEE Transactions on Control Systems Technology, vol. 22, no. 3, pp. 1078- 1087, May 2014. https://doi.org/10.1109/TCST.2013.2271276
  27. D. Wang, D. Liu and H. Li, "Policy iteration algorithm for online design of robust control for a class of continuous-time nonlinear systems," IEEE Transactions on Automation Science and Engineering, vol. 11, no. 2, pp. 627-632, Apr 2014. https://doi.org/10.1109/TASE.2013.2296206
  28. R. Song, F. L. Lewis, Q. Wei and H. Zhang, "Offpolicy actor-critic structure for optimal control of unknown systems with disturbances," IEEE Transactions on Cybernetics, vol. 46, no. 5, pp. 1041- 1050, May 2016. https://doi.org/10.1109/TCYB.2015.2421338
  29. H. Zhang , L. Cui, X. Zhang and Y. Luo, "Datadriven robust approximate optimal tracking control for unknown general nonlinear systems using adaptive dynamic programming method," IEEE Transactions on Neural Networks, vol. 22, no. 12, pp. 2226-2236, Dec 2011. https://doi.org/10.1109/TNN.2011.2168538
  30. S. Chang, J. Y. Lee, J. B. Park and Y. H. Choi, "An online fault tolerant actor-critic neuro-control for a class of nonlinear systems using neural network HJB approach," International Journal of Control Automation and Systems, vol. 13, no. 2, pp. 311-318, April 2015. https://doi.org/10.1007/s12555-014-0034-3
  31. Q. Fan and G. Yang, "Adaptive fault-tolerant control for affine non-linear systems based on approximate dynamic programming," IET Control Theory and Applications, vol. 10, no. 6, pp. 655-663, March 2016. https://doi.org/10.1049/iet-cta.2015.1081
  32. Z. Wang, L. Liu, H. Zhang and G. Xiao, "Faulttolerant controller design for a class of nonlinear mimo discrete-time systems via online reinforcement learning algorithm," IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 46, no. 5, pp. 611-622, May 2016. https://doi.org/10.1109/TSMC.2015.2478885
  33. P. A. Ioannou and J. Sun, "Robust adaptive control," Adaptive and Learning Systems, 1996.
  34. L. Tang, Y. Liu and S. Tong, "Adaptive neural control using reinforcement learning for a class of robot manipulator," Neural Computing and Applications, vol. 25, pp. 135-141, July 2014. https://doi.org/10.1007/s00521-013-1455-2
  35. H. J. Uang and B. Chen, "Robust adaptive optimal tracking design for uncertain missile systems: a fuzzy approach," Fuzzy Sets and Systems, vol. 126, no. 1, pp. 63-87, Feb 2002. https://doi.org/10.1016/S0165-0114(00)00139-1
  36. M. Krstic, P. V. Kokotovic and I. Kanellakopoulos, "Nonlinear and adaptive control design," New York: Wiley, 1995.
  37. M. Yim, W. M. Shen, B. Salemi, D. Rus and M. Moll , "Modular self-reconfigurable robot systems," IEEE Robotics and Automation Magazine, vol. 14, no. 1, pp. 43-52, March 2007.
  38. B. Zhao, C. Li, T. Ma and Y. Li, "Multiple faults detection and isolation via decentralized sliding mode observer for reconfigurable manipulator," Journal of Electrical Engineering and Technology, vol. 10, no. 6, pp. 2393-2405, Nov 2015. https://doi.org/10.5370/JEET.2015.10.6.2393
  39. S. Ahmad, H. Zhang and G. Liu, "Distributed fault detection for modular and reconigurable robots with joint torque sensing: a prediction error based approach," Mechatronics, vol. 23, no. 6, pp. 607-616, 2013. https://doi.org/10.1016/j.mechatronics.2013.05.008
  40. B. Zhao, and Y. Li, "Local joint information based active fault tolerant control for reconfigurable manipulator," Nonlinear Dynamics, vol. 77, no. 3, pp. 859-876, Aug 2014. https://doi.org/10.1007/s11071-014-1347-8
  41. M. Abu-Khalaf and F. L. Lewis, "Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach," Automatica, vol. 41, no. 5, pp. 779-791, May 2005. https://doi.org/10.1016/j.automatica.2004.11.034
  42. K. G. Vamvoudakis and F. L. Lewis, "Online actorcritic algorithm to solve the continuous-time infinite horizon optimal control problem," Automatica, vol. 46, no. 5, pp. 878-888, May 2010. https://doi.org/10.1016/j.automatica.2010.02.018
  43. B. Zhao, D. Liu, and Y. Li, "Online fault compensation control based on policy iteration algorithm for a class of affine nonlinear systems with actuator failures," IET Control Theory & Applications, vol. 10, no. 15, pp. 1816-1823, October 2016. https://doi.org/10.1049/iet-cta.2015.1105
  44. B. Zhao, D. Liu, and Y. Li, "Observer based adaptive dynamic programming for fault tolerant control of a class of nonlinear systems," Information Sciences, vol. 384, pp. 21-33, 2017. https://doi.org/10.1016/j.ins.2016.12.016
  45. E. Khalastchi, M. Kalech and L. Rokach, "A hybrid approach for improving unsupervised fault detection for robotic systems," Expert Systems with Applications, vol. 81, pp. 372-383, Sep 2017. https://doi.org/10.1016/j.eswa.2017.03.058
  46. D. Kim, D. Lee and K. C. Veluvolu, "Accommodation of actuator fault using local diagnosis and IMCPID," International Journal of Control Automation and Systems, Vol. 12, no. 6, pp. 1139-1149, Dec 2017. https://doi.org/10.1007/s12555-013-0164-z