Advertisement

Robustness vs. Control in Distributed Systems

  • Marta Menci
  • Gabriele Oliva
Chapter
Part of the History, Philosophy and Theory of the Life Sciences book series (HPTL, volume 23)

Abstract

Understanding and controlling the behavior of dynamical distributed systems, especially biological ones, represents a challenging task. Such systems, in fact, are characterized by a complex web of interactions among their composing elements or subsystems. A typical pattern observed in these systems is the emergence of complex behaviors, in spite of the local nature of the interaction among elements in close spatial proximity. Yet, we point out that each element is a proper system, with its inputs, its outputs and its internal behavior. Moreover, such elements tend to implement feedback control or regulation strategies, where the outputs of a subsystem A are fed as inputs to another subsystem B and so on until, eventually, A itself is influenced. Such complex feedback loops are understood only by considering, at the same time, low- and high-level perspectives, i.e., by regarding such systems as a collection of systems and as a whole, emerging entity. In particular, dynamical distributed systems show nontrivial robustness properties, which are, from one side, inherent to the each subsystem and, from another, depend on the complex web of interactions. In this chapter, therefore, we aim at characterizing the robustness of dynamical distributed systems by using two coexisting levels of abstraction: first, we discuss and review the main concepts related to the robustness of systems, and the relation between robustness, model and control; then, we decline these concepts in the case of dynamical distributed systems as a whole, highlighting similarities and differences with standard systems. We conclude the chapter with a case study related to the chemotaxis of a colony of E. Coli bacteria. We point out that the very reason of existence of this chapter is to make accessible to a vast and not necessarily technical audience the main concepts related to control and robustness of dynamical systems, both traditional and distributed ones.

Keywords

Dynamical systems Control Distributed systems Biological systems Robustness 

References

  1. Albert, R., Jeong, H., & Barabási, A. L. (2000). Error and attack tolerance of complex networks. Nature, 406(6794), 378–382.CrossRefGoogle Scholar
  2. Alon, U., Surette, M. G., Barkai, N., & Leibler, S. (1999). Robustness in bacterial chemotaxis. Nature, 397(6715), 168–171.CrossRefGoogle Scholar
  3. Andrews, B. W., Sontag, E. D., & Iglesias, P. A. (2008). An approximate internal model principle: Applications to nonlinear models of biological systems. IFAC Proceedings Volumes, 41(2), 15873–15878.CrossRefGoogle Scholar
  4. Babaoglu, O., Canright, G., Deutsch, A., Caro, G. A. D., Ducatelle, F., Gambardella, L. M., Ganguly, N., Jelasity, M., Montemanni, R., Montresor, A., & Urnes, T. (2006). Design patterns from biology for distributed computing. ACM Transactions on Autonomous and Adaptive Systems (TAAS), 1(1), 26–66.CrossRefGoogle Scholar
  5. Baldoni, R., Bertier, M., Raynal, M., & Tucci-Piergiovanni, S. (2007, September). Looking for a definition of dynamic distributed systems. In International conference on parallel computing technologies (pp. 1–14). Berlin/Heidelberg: Springer.Google Scholar
  6. Barkai, N., & Leibler, S. (1997). Robustness in simple biochemical networks. Nature, 387(6636), 913–917.CrossRefGoogle Scholar
  7. Bazan, N. G. (2005). Lipid signaling in neural plasticity, brain repair, and neuroprotection. Molecular Neurobiology, 32(1), 89–103.CrossRefGoogle Scholar
  8. Bhalla, U. S., & Iyengar, R. (1999). Emergent properties of networks of biological signaling pathways. Science, 283(5400), 381–387.CrossRefGoogle Scholar
  9. Block, S. M., Segall, J. E., & Berg, H. C. (1983). Adaptation kinetics in bacterial chemotaxis. Journal of Bacteriology, 154(1), 312–323.Google Scholar
  10. Bode, H. W. (1945). Network analysis and feedback amplifier design. Huntington: R.E. Krieger Pub. Co.Google Scholar
  11. Box, G. E. (1976). Science and statistics. Journal of the American Statistical Association, 71(356), 791–799.CrossRefGoogle Scholar
  12. Canale, E., Dalmao, F., Mordecki, E., & Souza, M. O. (2015). Robustness of Cucker–Smale flocking model. IET Control Theory & Applications, 9(3), 346–350.CrossRefGoogle Scholar
  13. Cristian, F. (1991). Understanding fault-tolerant distributed systems. Communications of the ACM, 34(2), 56–78.CrossRefGoogle Scholar
  14. Cucker, F., & Smale, S. (2007). Emergent behavior in flocks. IEEE Transactions on Automatic Control, 52(5), 852–862.CrossRefGoogle Scholar
  15. Di Costanzo, E., Menci, M., Messina, E., Natalini, R., & Vecchio, A. (2018). A hybrid mathematical model of collective motion under alignment and chemotaxis. Discrete and continuous dynamical systems, Series B. (Submitted).Google Scholar
  16. Di Paola, L., Platania, C. B. M., Oliva, G., Setola, R., Pascucci, F., & Giuliani, A. (2015). Characterization of protein–protein interfaces through a protein contact network approach. Frontiers in Bioengineering and Biotechnology, 3, 170.CrossRefGoogle Scholar
  17. Egeland, O. (1986). On the robustness of the computed torque technique in manipulator control. In Robotics and automation. Proceedings. 1986 IEEE international conference (Vol. 3, pp. 1203–1208). San Francisco: IEEE.CrossRefGoogle Scholar
  18. Flemming, H. C., Wingender, J., Szewzyk, U., Steinberg, P., Rice, S. A., & Kjelleberg, S. (2016). Biofilms: An emergent form of bacterial life. Nature Reviews Microbiology, 14(9), 563–575.CrossRefGoogle Scholar
  19. Francis, B. A., & Wonham, W. M. (1976). The internal model principle of control theory. Automatica, 12(5), 457–465.CrossRefGoogle Scholar
  20. Holme, P., Kim, B. J., Yoon, C. N., & Han, S. K. (2002). Attack vulnerability of complex networks. Physical Review E, 65(5), 056109.CrossRefGoogle Scholar
  21. Jensen, H. J. (1998). Self-organized criticality: Emergent complex behavior in physical and biological systems (Vol. 10). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  22. Johansson, B. B. (2000). Brain plasticity and stroke rehabilitation. Stroke, 31(1), 223–230.CrossRefGoogle Scholar
  23. Koshland, D. E., Goldbeter, A., & Stock, J. B. (1982). Amplification and adaptation in regulatory and sensory systems. Science, 217(4556), 220–225.CrossRefGoogle Scholar
  24. Liu, Y., & Passino, K. M. (2002). Biomimicry of social foraging bacteria for distributed optimization: Models, principles, and emergent behaviors. Journal of Optimization Theory and Applications, 115(3), 603–628.CrossRefGoogle Scholar
  25. Liu, Y. Y., Slotine, J. J., & Barabási, A. L. (2011). Controllability of complex networks. Nature, 473(7346), 167–173.CrossRefGoogle Scholar
  26. Luenberger, D. (1979). Introduction to dynamic systems: Theory, models, and applications. New York: Wiley.Google Scholar
  27. Miller, M. B., & Bassler, B. L. (2001). Quorum sensing in bacteria. Annual Reviews in Microbiology, 55(1), 165–199 ISO 690.CrossRefGoogle Scholar
  28. Mitrani, I. (1982). Simulation techniques for discrete event systems (No. 14). CUP Archive.Google Scholar
  29. Morari, M., & Zafiriou, E. (1989). Robust process control (Vol. 488). Englewood Cliffs: Prentice hall.Google Scholar
  30. Navlakha, S., & Bar-Joseph, Z. (2015). Distributed information processing in biological and computational systems. Communications of the ACM, 58(1), 94–102.CrossRefGoogle Scholar
  31. Park, J. H., & Kim, K. D. (1998). Biped robot walking using gravity-compensated inverted pendulum mode and computed torque control. In Robotics and automation, 1998. Proceedings. 1998 IEEE international conference on (Vol. 4, pp. 3528–3533). San Francisco: IEEE.Google Scholar
  32. Peak, D., West, J. D., Messinger, S. M., & Mott, K. A. (2004). Evidence for complex, collective dynamics and emergent, distributed computation in plants. Proceedings of the National Academy of Sciences of the United States of America, 101(4), 918–922.CrossRefGoogle Scholar
  33. Silverman, M., & Simon, M. (1977). Chemotaxis in Escherichia coli: Methylation of che gene products. Proceedings of the National Academy of Sciences, 74(8), 3317–3321.CrossRefGoogle Scholar
  34. Singh, S., Rashid, S., Long, Z., Navlakha, S., Salman, H., Oltvai, Z. N., & Bar-Joseph, Z. (2016). Distributed gradient descent in bacterial food search. arXiv preprint arXiv:1604.03052.Google Scholar
  35. Strogatz, S. H. (2001). Exploring complex networks. Nature, 410(6825), 268–276.CrossRefGoogle Scholar
  36. Thar, R., & Kühl, M. (2003). Bacteria are not too small for spatial sensing of chemical gradients: An experimental evidence. Proceedings of the National Academy of Sciences, 100(10), 5748–5753.CrossRefGoogle Scholar
  37. Waters, C. M., & Bassler, B. L. (2005). Quorum sensing: Cell-to-cell communication in bacteria. Annual Review of Cell and Developmental Biology, 21, 319–346.CrossRefGoogle Scholar
  38. Wieland, P., & Allgöwer, F. (2009). An internal model principle for consensus in heterogeneous linear multi-agent systems. IFAC Proceedings Volumes, 42(20), 7–12.CrossRefGoogle Scholar
  39. Wieland, P., Sepulchre, R., & Allgöwer, F. (2011). An internal model principle is necessary and sufficient for linear output synchronization. Automatica, 47(5), 1068–1074.CrossRefGoogle Scholar
  40. Wiggins, P. A., & Stylianidou, S. (2017). Emergent self-similarity in complex biological systems due to strong disorder. Biophysical Journal, 112(3), 240a.CrossRefGoogle Scholar
  41. Winfree, A. T. (2001). The geometry of biological time (Vol. 12). New York: Springer.Google Scholar
  42. Yi, T. M., Huang, Y., Simon, M. I., & Doyle, J. (2000). Robust perfect adaptation in bacterial chemotaxis through integral feedback control. Proceedings of the National Academy of Sciences, 97(9), 4649–4653.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Departmental Faculty of EngineeringUniversity Campus Bio-Medico of RomeRomeItaly

Personalised recommendations