Fault Tolerant Time Optimization of Switched Systems with Application to Multi-agent Flight Control

  • Yuhang Xu
  • Hao Yang
  • Bin JiangEmail author
Regular Papers Control Theory and Applications


This paper considers the problem of determining optimal switching time for the switched system in the presence of switching faults, which may result in the deviation of the prescribed switching time from normal. A passive fault-tolerant scheme, which relies on the min-max strategy containing gradient descent algorithm, is proposed to guarantee that the faulty switched system has the minimal upper bound of the cost function. In the case that the switching faults take place regularly, an active fault-tolerant scheme is further developed which can decrease the minimal upper bound of the cost function, and thus reduce the conservativeness of the passive one. These two new schemes are applied to resolve the route conflict among multi-airplanes in multi-agent flight control to illustrate their efficiency and applicability.


Fault tolerant control multi-agent flight control switched system time optimization 


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  1. [1]
    H. Lin and P. J. Antsaklis, Hybrid Dynamical Systems: An Introduction to Control and Verification, Now Foundations and Trends, 2014.Google Scholar
  2. [2]
    S. M. Tayebi and I. Batarseh, “Analysis and optimization of variable–frequency soft–switching peak current mode control techniques for microinverters,” IEEE Trans. on Power Electronics, vol. 33, no. 2, pp. 1644–1653, February 2018.CrossRefGoogle Scholar
  3. [3]
    D. O. Boillat, F. Krismer, and J. W. Kolar, “Design space analysis and rh Pareto optimization of LC output filters for switch–mode AC power sources,” IEEE Trans. on Power Electronics, vol. 30, no. 12, pp. 6906–6923, December 2015.CrossRefGoogle Scholar
  4. [4]
    A. Mavrommati, J. Schultz, and T. D. Murphey, “Real–time dynamic–mode scheduling using single–integration hybrid optimization,” IEEE Trans. on Automation Science and Engineering, vol. 13, no. 3, pp. 1385–1398, July 2016.CrossRefGoogle Scholar
  5. [5]
    X. Liu, S. Li, and K. Zhang, “Optimal control of switching time in switched stochastic systems with multi–switching times and different costs,” International Journal of Control, vol. 90, no. 8, pp. 1604–1611, July 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    B. Stellato, S. Ober–Blobaum, and P. J. Goulart, “Secondorder switching time optimization for switched dynamical systems,” IEEE Trans. on Automatic Control, vol. 6. no. 10, pp. 5407–5414, October 2017.CrossRefzbMATHGoogle Scholar
  7. [7]
    A. Heydari and S. N. Balakrishnan, “Optimal switching and control of nonlinear switching systems using approximate dynamic programming,” IEEE Trans. on Neural Networks & Learning Systems, vol. 25, no. 6, pp. 1106–1117, June 2014.CrossRefGoogle Scholar
  8. [8]
    L. Wu, P. Shi, and X. Su, Sliding Mode Control of Uncertain Parameter–switching Hybrid Systems, John Wiley & Sons, London, 2014.CrossRefGoogle Scholar
  9. [9]
    J. Wu and Z. Sun, “Observer–driven switching stabilization of switched linear systems,” Automatica, vol. 49, no. 8, pp. 2556–2560, August 2013.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    X. Ding and X. Liu, “Stability analysis for switched positive linear systems under state–dependent switching,” International Journal of Control Automation & Systems, vol. 15, no. 2, pp. 481–488, March 2017.CrossRefGoogle Scholar
  11. [11]
    L. Jiao and J. Zhao, “Incremental passivity and incremental passivity–based output regulation for switched discretetime systems,” IEEE Trans. on Cybernetics, vol. 47. no. 5, pp.1122–1132, May 2017.Google Scholar
  12. [12]
    S. Li, Z. Xiang, and H. R. Karimi, “Mixed l/ l1, fault detection observer design for positive switched systems with time–varying delay via delta operator approach,” International Journal of Control Automation & Systems, vol. 12, no. 4, pp. 709–721, August 2014.CrossRefGoogle Scholar
  13. [13]
    G. Zong, R. Wang, W. X. Zheng, and L. Hou, “Finitetime stabilization for a class of switched time–delay systems under asynchronous switching,” Applied Mathematics & Computation, vol. 219, no. 11, pp. 5757–5771, February 2013.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    X. Q. Zhang, X. Y. Li, and J. Zhao, “Stability analysis and anti–windup design of switched systems with actuator saturation,” International Journal of Automation and Computing, vol. 14, no. 5, pp. 615–625, December 2017.CrossRefGoogle Scholar
  15. [15]
    S. Huang and Z. Xiang, “Finite–time output tracking for a class of switched nonlinear systems,” International Journal of Robust & Nonlinear Control, vol. 27, no. 6, pp. 1017–1038, January 2017.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    X. G. Guo, J. L. Wang, and F. Liao, “Adaptive fuzzy faulttolerant control for multiple high–speed trains with proportional and integral–based sliding mode,” IET Control Theory & Applications, vol. 11, no. 8, pp. 1234–1244, December 2017.MathSciNetCrossRefGoogle Scholar
  17. [17]
    X. G. Guo, J. L. Wang, and F. Liao, “CNN–based distributed adaptive control for vehicle–following platoon with input saturation,” IEEE Trans. on Intelligent Transportation Systems, vol. 19, no. 10, pp. 3121–3132, October 2018.CrossRefGoogle Scholar
  18. [18]
    H. T. Chen, B. Jiang, and N.Y. Lu, “A multi–mode incipient sensor fault detection and diagnosis method for electrical traction systems,” International Journal of Control Automation & Systems, vol. 16, no. 4, pp. 1783–1793, December 2018.CrossRefGoogle Scholar
  19. [19]
    W. J. Ren, H. Yang, and B. Jiang, “Fault recoverability analysis of nonlinear systems: a piecewise affine system approach,” International Journal of Control Automation & Systems, vol. 15, no. 2, pp. 547–556, April 2017.CrossRefGoogle Scholar
  20. [20]
    A. Munir, A. Gordon–Ross, and S. Ranka, Modeling and Analysis of Fault Detection and Fault Tolerance in Embedded Wireless Sensor Networks, John Wiley & Sons, 2016.CrossRefGoogle Scholar
  21. [21]
    H. Yang, H. Li, B. Jiang, and V. Cocquempot, “Fault Tolerant Control of Switched Systems: A Generalized Separation Principle,” IEEE Trans. on Control Systems Technology, 2017. Available Online, DOI: 10.1109/TCST.2017.2785808.Google Scholar
  22. [22]
    H. Yang, B. Jiang, and G. Tao, “Robust stability of switched nonlinear systems with switching uncertainties,” IEEE Trans. on Automatic Control, vol. 61, no. 9, pp. 2531–2537, September 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    S. S. Fang, J. B. Qiu, C. L. Heng, and S. S. Mou, “Adaptive fuzzy observer design for a class of switched nonlinear systems with actuator and sensor faults,” IEEE Trans. on Fuzzy Systems, vol. 26, no. 6, pp. 3730–3742, Dec. 2018.CrossRefGoogle Scholar
  24. [24]
    X. Yu and Y. M. Zhang, “Sense and avoid technologies with applications to unmanned aircraft systems: Review and prospects,” Progress in Aerospace Sciences, vol. 74, no. 1, pp. 152–166, April 2015.MathSciNetCrossRefGoogle Scholar
  25. [25]
    J. Reyes, C. B. Schonlieb, and T. Valkonen, “Bilevel parameter learning for higher–order total variation regularisation models,” Journal of Mathematical Imaging & Vision, vol. 57, no. 1, pp. 1–25, June 2017.MathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    Z. Ping, C. Lee, and H. Shim, “Robust estimation algorithm for both switching signal and state of switched linear systems,” International Journal of Control Automation & Systems, vol. 15, no. 1, pp. 95–103, February 2017.CrossRefGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Automation EngineeringNanjing University of Aeronautics and AstronauticsNanjingP. R. China

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