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State-based supervisory control with restrictions on the supervisor realization

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Abstract

In this paper, we formalize and solve a state-based Supervisory Control problem with restrictions on the supervisor realization that have not been tackled by the Supervisory Control Theory (SCT) community so far. This problem was derived from the application of SCT to intervene in the dynamics of gene regulatory networks, a relevant problem in the fields of Systems and Synthetic Biology. In our framework, a plant, whose states x are represented by Boolean strings, must be driven from an initial state to a target one, by means of m state-feedback control laws ui = hi(x). The Boolean functions hi, though, cannot be freely chosen, but must rather belong to a (possibly strict) subset R of all the Boolean functions on x.

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References

  • Akutsu T, Hayashida M, Ching WK, Ng MK (2007) Control of boolean networks: Hardness results and algorithms for tree structured networks. J Theor Biol 244(4):670. https://doi.org/10.1016/j.jtbi.2006.09.023

    Article  MathSciNet  Google Scholar 

  • Albert R (2004) Boolean modeling of genetic regulatory networks. In: Complex networks. Springer, Berlin, pp 459–481

  • Alberts B, Bray D, Hopkin K, Johnson A, Lewis J, Raff M, Roberts K, Walter P (2013) Essential cell biology. Garland Science, New York

    Book  Google Scholar 

  • Baldissera FL, Cury JE, Raisch J (2016) A supervisory control theory approach to control gene regulatory networks. IEEE Trans Autom Control 61(1):18

    Article  MathSciNet  MATH  Google Scholar 

  • Benenson Y (2012) Biomolecular computing systems: principles, progress and potential. Nat Rev Genet 13(7):455

    Article  Google Scholar 

  • Blazeck J, Carg R, Reed B, Alper HS (2012) Controlling promoter strength and regulation in Saccharomyces cerevisiae using synthetic hybrid promoters. Biotech Bioeng 109:1

    Article  Google Scholar 

  • Brave Y, Heymann M (1989). In: proceedings of the 28th IEEE Conference on Decision and Control, vol 3, pp 2737–2742

  • Buchler NE, Gerland U, Hwa T (2003) On schemes of combinatorial transcription logic. P Natl Acad Sci 100(9):5136

    Article  Google Scholar 

  • Cheng D, Qi H, Li Z, Liu JB (2011) Stability and stabilization of boolean networks. Int J Robust Nonlin Control 21(2):134

    Article  MathSciNet  MATH  Google Scholar 

  • Cox RS III, Surette MG, Elowitz MB (2007) Programming gene expression with combinatorial promoters. Mol Syst Biol 3(1):1

    Google Scholar 

  • Cury JER, Baldissera FL (2013) Systems biology, synthetic biology and control theory: A promising golden braid. Annu Rev Control 37(1):57

    Article  Google Scholar 

  • Datta A, Pal R, Choudhary A, Dougherty ER (2007) Control approaches for probabilistic gene regulatory networks - what approaches have been developed for addressinig the issue of intervention?. IEEE Signal Proc Mag 24(1):54. https://doi.org/10.1109/MSP.2007.273057

    Article  Google Scholar 

  • El-Samad H (2010) Control Strategies in Times of Adversity: How Organisms Survive Stressful Conditions. In: Control Theory and Systems Biology (MIT Press), chap. 5

  • Gingold H, Pilpel Y (2011) Determinants of translation efficiency and accuracy. Mol Syst Biol 7:1

    Article  Google Scholar 

  • Golaszewski CH, Ramadge PJ (1987) Control of discrete event processes with forced events. In: 26th IEEE Conference on Decision and Control, vol 26, pp 247–251

  • Hawkes EW, Kutkosky MR (2018) Designs of materials and mechanisms for responsive robots. Annual Review of Control Robotics and Autonomous Systems 1 (6228):359

    Article  Google Scholar 

  • Hawkes E, Benbernou NM, Tanaka H, Kim S, Demaine ED, Rus D, Wood RJ (2010) Programmable matter by folding. Proc Natl Acad Sci 107(28):12441

    Article  Google Scholar 

  • Hsiao V, Swaminathan A, Murray RM (2018) Control theory for synthetic biology. IEEE Control Systems Magazine 38(3):32

    Article  Google Scholar 

  • Karlebach G, Shamir R (2008) Modeling and analysis of gene regulatory networks. Nat Rev Mol Cell Biol 9(10):770

    Article  Google Scholar 

  • Karlsson M, Weber W (2012) Therapeutic synthetic gene networks. Curr Opin Biotech 23(5):703

    Article  Google Scholar 

  • Langmead SKJCJ (2009) Symbolic approaches for finding control strategies in boolean networks. J Bioinforma Comput Biol 7(2):323

    Article  Google Scholar 

  • Li H, Wang Y (2017) Further results on feedback stabilization control design of boolean control networks. Automatica 83:303. https://doi.org/10.1016/j.automatica.2017.06.043

    Article  MathSciNet  MATH  Google Scholar 

  • McEvoy MA, Correll N (2015) Materials that couple sensing, actuation, computation and communication. Science 347(6228):1261689

    Article  Google Scholar 

  • Purnick PE, Weiss R (2009) The second wave of synthetic biology: from modules to systems. Nat Rev Mol Cell Biol 10(6):410

    Article  Google Scholar 

  • Ramadge P, Wonham W (1987a) Modular feedback logic for discrete event systems. IFAC Proceedings 20(9):93. 4th IFAC/IFORS Symposium on Large Scale Systems: Theory and Applications 1986, Zurich Switzerland, pp. 26–29, August 1986

    Article  MATH  Google Scholar 

  • Ramadge P, Wonham W (1987b) Supervisory control of a class of discrete event processes. SIAM J Control Optim 25(1):206

    Article  MathSciNet  MATH  Google Scholar 

  • Saadtapour A, Albert I, Albert R (2010) Attractor analysis of asynchronous boolean models of signal transduction networks. J Theor Biol 266(4):641

    Article  MathSciNet  MATH  Google Scholar 

  • Samal A, Jain S (2008) The regulatory network of e. coli metabolism as a boolean dynamical system exhibits both homeostasis and flexibility of response. BMC Syst Biol 2(1):21

    Article  Google Scholar 

  • Schmidt KW, Breindl C (2014) A framework for state attraction of discrete event systems under partial observation. Inf Sci 281:265

    Article  MathSciNet  MATH  Google Scholar 

  • Vecchio DD, Dy AJ, Qian Y (2016) Control theory meets synthetic biology. J R Soc Interface 13(120):1

    Google Scholar 

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Authors and Affiliations

  1. Universidade Federal de Santa Catarina, Florianópolis, SC 88040-970, Brazil

    Pedro A. C. F. Leite, Fabio L. Baldissera & José E. R. Cury

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  1. Pedro A. C. F. Leite
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  2. Fabio L. Baldissera
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  3. José E. R. Cury
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Correspondence to Fabio L. Baldissera.

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Leite, P.A.C.F., Baldissera, F.L. & Cury, J.E.R. State-based supervisory control with restrictions on the supervisor realization. Discrete Event Dyn Syst 30, 671–693 (2020). https://doi.org/10.1007/s10626-020-00319-9

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  • DOI: https://doi.org/10.1007/s10626-020-00319-9

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