Advertisement

Optimal sensors and actuators placement for large-scale switched systems

  • Masoud Seyed Sakha
  • Hamid Reza ShakerEmail author
  • Maryamsadat Tahavori
Article
  • 39 Downloads

Abstract

The problem of sensor and actuator placement is computationally expensive in particular in dealing with large-scale systems. This problem is even more computationally intensive in the case of switched systems. In this paper, we propose a new numerical approach for sensor and actuator placement for large-scale switched systems. We first introduce restricted genetic algorithm (RGA). RGA is an evolutionary algorithm which is developed specifically for sensors and actuator placement. We then use RGA to reduce the computational burden of the sensor and actuator placement for switched system. The proposed method uses the generalized gramians for switched systems which are called nice gramians. The nice gramians quantify the level of observability and reachability of switched systems. To the best of our knowledge, this paper presents the first results on sensor and actuator placement of switched systems. We show the effectiveness of the approach with the help of numerical examples.

Keywords

Switched systems Sensor placement Actuator placement Restricted genetic algorithm 

Notes

Acknowledgements

The authors declare that they have no conflict of interest.

References

  1. 1.
    Cardim R, Teixeira MC, Assuncao E, Covacic MR (2009) Variable-structure control design of switched systems with an application to a dc–dc power converter. IEEE Trans Ind Electron 56(9):3505–3513CrossRefGoogle Scholar
  2. 2.
    Hernandez-Vargas E, Colaneri P, Middleton R, Blanchini F (2011) Discrete-time control for switched positive systems with application to mitigating viral escape. Int Jo Robust Nonlinear Control 21(10):1093–1111MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Rinehart M, Dahleh M, Reed D, Kolmanovsky I (2008) Suboptimal control of switched systems with an application to the disc engine. IEEE Trans Control Syst Technol 16(2):189–201CrossRefGoogle Scholar
  4. 4.
    Lee T, Jiang ZP (2008) Uniform asymptotic stability of nonlinear switched systems with an application to mobile robots. IEEE Trans Autom Control 53(5):1235–1252MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Borrelli F, Bemporad A, Morari M (2017) Predictive control for linear and hybrid systems. Cambridge University Press, CambridgeCrossRefzbMATHGoogle Scholar
  6. 6.
    Böhme TJ, Frank B (2017) Hybrid systems and hybrid optimal control. In: Grimble MJ, Johnson MA (eds) Hybrid systems, optimal control and hybrid vehicles. Springer, Berlin, pp 79–115CrossRefGoogle Scholar
  7. 7.
    Zhu F, Antsaklis PJ (2015) Optimal control of hybrid switched systems: a brief survey. Discrete Event Dyn Syst 25(3):345–364MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Georges D (1995) The use of observability and controllability gramians or functions for optimal sensor and actuator location in finite-dimensional systems. In: Proceedings of the 34th IEEE conference on decision and control, 1995, vol 4, pp 3319–3324Google Scholar
  9. 9.
    Van De Wal M, De Jager B (2001) A review of methods for input/output selection. Automatica 37(4):487–510MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Marx B, Koenig D, Georges D (2002) Optimal sensor/actuator location for descriptor systems using lyapunov-like equations. In: Proceedings of the 41st IEEE conference on decision and control, 2002, vol 4, pp 4541–4542Google Scholar
  11. 11.
    Sakha MS, Shaker HR (2017) A new computationally efficient algorithm for optimal sensors and actuators placement for large-scale systems. In: International conference on control, decision and information technologiesGoogle Scholar
  12. 12.
    Marx B, Koenig D, Georges D (2004) Optimal sensor and actuator location for descriptor systems using generalized gramians and balanced realizations. In: Proceedings of the 2004 American control conference, IEEE, vol 3, pp 2729–2734Google Scholar
  13. 13.
    Singh AK, Hahn J (2005) Determining optimal sensor locations for state and parameter estimation for stable nonlinear systems. Ind Eng Chem Res 44(15):5645–5659CrossRefGoogle Scholar
  14. 14.
    Shaker HR, Tahavori M (2013) Optimal sensor and actuator location for unstable systems. J Vib Control 19(12):1915–1920MathSciNetCrossRefGoogle Scholar
  15. 15.
    Singh AK, Hahn J (2006) Sensor location for stable nonlinear dynamic systems: multiple sensor case. Ind Eng Chem Res 45(10):3615–3623CrossRefGoogle Scholar
  16. 16.
    Kasinathan D, Morris K (2013) H-optimal actuator location. IEEE Trans Autom Control 58(10):2522–2535MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Shaker HR, Shaker F (2014) Control configuration selection for linear stochastic systems. J Process Control 24(1):146–151MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Morris K, Yang S (2015) Comparison of actuator placement criteria for control of structures. J Sound Vib 353:1–18CrossRefGoogle Scholar
  19. 19.
    Kalman R (1959) On the general theory of control systems. IRE Trans Autom Control 4(3):110–110CrossRefGoogle Scholar
  20. 20.
    Kalman RE (1962) Controllability of linear dynamical systems. Contrib Differ Equ 1(2):189–213MathSciNetGoogle Scholar
  21. 21.
    Kalman RE et al (1960) Contributions to the theory of optimal control. Bol Soc Mat Mexicana 5(2):102–119MathSciNetGoogle Scholar
  22. 22.
    Kalman RE (1963) Mathematical description of linear dynamical systems. J Soc Ind Appl Math Ser A: Control 1(2):152–192MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Petreczky M, Wisniewski R, Leth J (2013) Balanced truncation for linear switched systems. Nonlinear Anal: Hybrid Syst 10:4–20MathSciNetzbMATHGoogle Scholar
  24. 24.
    Kammer D, Yao L (1994) Enhancement of on-orbit modal identification of large space structures through sensor placement. J Sound Vib 171(1):119–139CrossRefzbMATHGoogle Scholar
  25. 25.
    Cherng AP (2003) Optimal sensor placement for modal parameter identification using signal subspace correlation techniques. Mech Syst Signal Process 17(2):361–378CrossRefGoogle Scholar
  26. 26.
    Antoy S, Middeldorp A (1996) A sequential reduction strategy. Theor Comput Sci 165(1):75–95MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Yi TH, Li HN, Gu M (2011) Optimal sensor placement for health monitoring of high-rise structure based on genetic algorithm. Math Prob Eng 2011:1–12Google Scholar
  28. 28.
    Guo H, Zhang L, Zhang L, Zhou J (2004) Optimal placement of sensors for structural health monitoring using improved genetic algorithms. Smart Mater Struct 13(3):528CrossRefGoogle Scholar
  29. 29.
    Huang M, Li J, Zhu H (2009) Optimal sensor layout for bridge health monitoring based on dual-structure coding genetic algorithm. In: IEEE international conference on computational intelligence and software engineering, CiSE 2009, pp 1–4Google Scholar
  30. 30.
    Liu W, Gao Wc, Sun Y, Xu Mj (2008) Optimal sensor placement for spatial lattice structure based on genetic algorithms. J Sound Vib 317(1):175–189CrossRefGoogle Scholar
  31. 31.
    Maojun L, Tiaosheng T (1999) A partheno-genetic algorithm and analysis on its global convergence. Acta Autom Sinica 25(1):68–72MathSciNetGoogle Scholar
  32. 32.
    Bai JC, Chang H, Yi Y (2005) A partheno-genetic algorithm for multidimensional knapsack problem. In: Proceedings of 2005 IEEE international conference on machine learning and cybernetics, 2005. vol 5, pp 2962–2965Google Scholar
  33. 33.
    Kang F, Li Jj, Xu Q (2008) Virus coevolution partheno-genetic algorithms for optimal sensor placement. Adv Eng Inf 22(3):362–370CrossRefGoogle Scholar
  34. 34.
    Shaker HR, Tahavori M (2014) Time-interval model reduction of bilinear systems. Int J Control 87(8):1487–1495MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Shaker HR, Lazarova-Molnar S (2017) A new data-driven controllability measure with application in intelligent buildings. Energy Build 138:526–529CrossRefGoogle Scholar
  36. 36.
    Shaker HR, Tahavori M (2015) Control configuration selection for bilinear systems via generalised hankel interaction index array. Int J Control 88(1):30–37MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Marx B (2003) Contribution à la commande et au diagnostic des systèmes algébro-différentiels linéaires. Ph.D. thesis, Institut National Polytechnique de Grenoble-INPGGoogle Scholar
  38. 38.
    Dochain D, Tali-Maamar N, Babary J (1997) On modelling, monitoring and control of fixed bed bioreactors. Comput Chem Eng 21(11):1255–1266CrossRefGoogle Scholar
  39. 39.
    Müller P, Weber H (1972) Analysis and optimization of certain qualities of controllability and observability for linear dynamical systems. Automatica 8(3):237–246MathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    Waldraff W, Dochain D, Bourrel S, Magnus A (1998) On the use of observability measures for sensor location in tubular reactor. J Process Control 8(5):497–505CrossRefGoogle Scholar
  41. 41.
    Bäck T (1994) Selective pressure in evolutionary algorithms: a characterization of selection mechanisms. In: Proceedings of the first IEEE conference on evolutionary computation, IEEE world congress on computational intelligence, pp 57–62Google Scholar
  42. 42.
    Goldberg DE, Deb K (1991) A comparative analysis of selection schemes used in genetic algorithms. Found Genet Algorithms 1:69–93MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Control Engineering, Faculty of Electrical and Computer EngineeringUniversity of TabrizTabrizIran
  2. 2.Center for Energy InformaticsUniversity of Southern DenmarkOdenseDenmark

Personalised recommendations