Optimal Controller Switching for Resource-constrained Dynamical Systems

  • Kooktae Lee
  • Raktim Bhattacharya
Regular Papers Robot and Applications


In this paper, we present the resource-optimal controller switching synthesis for dynamical systems subject to resource constraints. Particularly, for systems having limited computational power (CPU) and onboard energy (battery), it is crucial to keep resource usage as low as possible. Although restrictions on resource utilization may save a CPU time and battery life, it degrades system performance. This paper provides three distinct algorithms that synthesize a controller switching policy for the purpose of resource savings, while not debasing system performance significantly. To measure system performance, we adopted the Waserstein distance that quantifies uncertainty in a probability density function level. The cost function to minimize is then defined based on this Wasserstein metric with a resource utilization penalty. As an example, quadrotor dynamics with two controllers, high performing / high resource consuming and moderate performing / resource saving controllers, is presented. The efficiency and usefulness of the proposed methods are validated in this example.


Optimal controller switching resource-constrained system switched system Wasserstein distance 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    F. Vahid and T. Givargis, Embedded System Design: A Unified Hardware/software Introduction, vol. 4. John Wiley & Sons, New York, NY, 2002.Google Scholar
  2. [2]
    S. Chakraborty, S. Künzli, and L. Thiele, “A general framework for analysing system properties in platform-based embedded system designs.,” DATE, vol. 3, p. 10190, Citeseer, 2003.Google Scholar
  3. [3]
    J. Henkel, W. Wolf, and S. Chakradhar, “On-chip networks: a scalable, communication-centric embedded system design paradigm,” Proceedings of 17th International Conference on VLSI Design, pp. 845–851, IEEE, 2004. [click]CrossRefGoogle Scholar
  4. [4]
    T. Liu, C. M. Sadler, P. Zhang, and M. Martonosi, “Timplementing software on resource-constrained mobile sensors: experiences with impala and zebrane,” Proceedings of the 2nd International Conference on Mobile Systems, Applications, and Services, pp. 256–269, ACM, 2004.Google Scholar
  5. [5]
    A. Messer, I. Greenberg, P. Bernadat, D. Milojicic, D. Chen, T. J. Giuli, and X. Gu, “Towards a distributed platform for resource-constrained devices,” in Proceedings of 22nd International Conference on Distributed Computing Systems, pp. 43–51, IEEE, 2002. [click]CrossRefGoogle Scholar
  6. [6]
    H. Kim and B. K. Kim, “Minimum-energy cornering trajectory planning with self-rotation for three-wheeled omnidirectional mobile robots,” International Journal of Control, Automation and Systems, vol. 15, no. 4, pp. 1857–1866, 2017. [click]CrossRefGoogle Scholar
  7. [7]
    E. Skafidas, R. J. Evans, and I. Mareels, “Optimal controller switching for stochastic systems,” Proceedings of the 36th IEEE Conference on Decision and Control, vol. 4, pp. 3950–3955, IEEE, 1997.CrossRefGoogle Scholar
  8. [8]
    H. Wang, X. Liu, and K. Liu, “Adaptive fuzzy tracking control for a class of pure-feedback stochastic nonlinear systems with non-lower triangular structure,” Fuzzy Sets and Systems, vol. 302, pp. 101–120, 2016. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    H. Wang, P. X. Liu, and P. Shi, “Observer-based fuzzy adaptive output-feedback control of stochastic nonlinear multiple time-delay systems,” IEEE Transactions on Cybernetics, 2017.Google Scholar
  10. [10]
    E. Skafidas, R. J. Evans, A. V. Savkin, and I. R. Petersen, “Stability results for switched controller systems,” Automatica, vol. 35, no. 4, pp. 553–564, 1999. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    K. Kogiso and K. Hirata, “Controller switching strategies for constrained mechanical systems with applications to the remote control over networks,” Proceedings of IEEE International Conference on Control Applications, vol. 1, pp. 480–484, IEEE, 2004. [click]Google Scholar
  12. [12]
    H. Jin and M. Safonov, “Unfalsified adaptive control: controller switching algorithms for nonmonotone cost functions,” International Journal of Adaptive Control and Signal Processing, vol. 26, no. 8, pp. 692–704, 2012. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    J. P. Hespanha and A. S. Morse, “Switching between stabilizing controllers,” Automatica, vol. 38, no. 11, pp. 1905–1917, 2002. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    K. Lee and R. Bhattacharya, “Optimal switching synthesis for jump linear systems with gaussian initial state uncertainty,” ASME 2014 Dynamic Systems and Control Conference, pp. V002T24A003–V002T24A003, American Society of Mechanical Engineers, 2014.Google Scholar
  15. [15]
    C. Villani, Topics in Optimal Transportation, No. 58, American Mathematical Soc., 2003.CrossRefzbMATHGoogle Scholar
  16. [16]
    S. Zhang, J. Li, and L. Wu, “A novel multiple maneuvering targets tracking algorithm with data association and track management,” International Journal of Control, Automation and Systems, vol. 11, no. 5, pp. 947–956, 2013. [click]CrossRefGoogle Scholar
  17. [17]
    B. Li, “Multiple-model rao-blackwellized particle probability hypothesis density filter for multitarget tracking,” International Journal of Control, Automation, and Systems, vol. 13, no. 2, p. 426, 2015.CrossRefGoogle Scholar
  18. [18]
    S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, 1994.CrossRefzbMATHGoogle Scholar
  19. [19]
    D. Liberzon, Switching in Systems and Control, Springer Science & Business Media, 2012.zbMATHGoogle Scholar
  20. [20]
    X. Zhao, Y. Yin, B. Niu, and X. Zheng, “Stabilization for a class of switched nonlinear systems with novel average dwell time switching by T-S fuzzy modeling,” IEEE Transactions on Cybernetics, vol. 46, no. 8, pp. 1952–1957, 2016. [click]CrossRefGoogle Scholar
  21. [21]
    D. Zhang, Z. Xu, H. R. Karimi, and Q.-G. Wang, “Distributed filtering for switched linear systems with sensor networks in presence of packet dropouts and quantization,” IEEE Transactions on Circuits and Systems I: Regular Papers, 2017.Google Scholar
  22. [22]
    B. Niu, H. R. Karimi, H. Wang, and Y. Liu, “Adaptive output-feedback controller design for switched nonlinear stochastic systems with a modified average dwell-time method,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2017.Google Scholar
  23. [23]
    M. Rabbat and R. Nowak, “Distributed optimization in sensor networks,” Proceedings of the 3rd International Symposium on Information Processing in Sensor Networks, pp. 20–27, ACM, 2004.Google Scholar
  24. [24]
    A. Krause, A. Singh, and C. Guestrin, “Near-optimal sensor placements in gaussian processes: theory, efficient algorithms and empirical studies,” The Journal of Machine Learning Research, vol. 9, pp. 235–284, 2008.zbMATHGoogle Scholar
  25. [25]
    K. Gilholm and D. Salmond, “Spatial distribution model for tracking extended objects,” IEE Proceedings-Radar, Sonar and Navigation, vol. 152, no. 5, pp. 364–371, 2005. [click]CrossRefGoogle Scholar
  26. [26]
    L. Xiao, S. Boyd, and S. Lall, “A scheme for robust distributed sensor fusion based on average consensus,” The Fourth International Symposium on Information Processing in Sensor Networks, IPSN 2005, pp. 63–70, IEEE, 2005. [click]Google Scholar
  27. [27]
    K. Lee, A. Halder, and R. Bhattacharya, “Performance and robustness analysis of stochastic jump linear systems using wasserstein metric,” Automatica, vol. 51, pp. 341–347, 2015. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    Y. Wei, J. H. Park, J. Qiu, L. Wu, and H. Y. Jung, “Sliding mode control for semi-markovian jump systems via output feedback,” Automatica, vol. 81, pp. 133–141, 2017.MathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    L. Vandenberghe and S. Boyd, “Semidefinite programming,” SIAM Review, vol. 38, no. 1, pp. 49–95, 1996. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    Y. Wei, J. Qiu, H. R. Karimi, and M. Wang, “New results on h dynamic output feedback control for markovian jump systems with time-varying delay and defective mode information,” Optimal Control Applications and Methods, vol. 35, no. 6, pp. 656–675, 2014.MathSciNetCrossRefzbMATHGoogle Scholar
  31. [31]
    Y. Wei, J. Qiu, and S. Fu, “Mode-dependent nonrational output feedback control for continuous-time semi-markovian jump systems with time-varying delay,” Nonlinear Analysis: Hybrid Systems, vol. 16, pp. 52–71, 2015. [click]MathSciNetzbMATHGoogle 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 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringNew Mexico Institute of Mining and TechnologySocorroUSA
  2. 2.Department of Aerospace EngineeringTexas A&M UniversityCollege StationUSA

Personalised recommendations