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Control Paradigms and Self-Organization in Living Systems

  • Edwin B. Stear
Part of the Life Science Monographs book series (LSMO)

Abstract

This chapter describes control of systems characterized by numerically valued variables. It opens with a qualitative description of the fundamental concepts behind open-loop and feedback control methods. The chief aim of feedback control is to cause a system’s output to maintain some desired relation to an input, in spite of disturbances or deviations in plant dynamics.

Classical linear control theory is quantitatively described, using the standard, frequency-domain (jω) notation and Fourier transform method. The open-loop and closed-loop (feedback) equations are each shown for a continuous, linear system with time-invariant parameters and structure and single input with single output. In some cases it is necessary to achieve independent control of each of multiple disturbances or to control more than a single plant output. Or there may be more than a single control input available with which to control the plant’s outputs. One may then employ multiloop control or more complex control arrangements for multivariable control.

Classical linear control concepts have been extended in modern optimal control theory. The new approach is far more general, and it emphasizes the state-space description of dynamic systems. It is general enough to encompass time-varying and nonlinear conditions. Using the general formulation of the deterministic, optimal control problem, open-loop control is reexamined from the point of view of the Pontryagin Maximum Principle. Some similarities between the optimal control problem and Hamiltonian mechanics are pointed out. It is concluded that optimal control theory in this form represents a significant conceptual generalization of the variational theory of classical mechanics to a much wider class of problems. In this sense, optimal control theory overlaps and transcends ordinary physical theory and cannot properly be considered to be a simple consequence of the known physical laws of mechanics.

The optimal control approach is next generalized to include stochastic processes appearing as unpredictable perturbations. The mathematical difficulty increases, but such difficulties do not detract from the underlying rich structure of optimal control theory and its substantial connections with and differences from the variational theory of mechanics.

The equations of stochastic optimal control do not arise in statistical mechanics because standard statistical mechanics does not deal with concepts that involve estimating the state of dynamic systems for purposes of control. Neither does physical theory appear to deal with any problems analogous to or embedded in the stochastic optimal control problem. Again, one is forced to the conclusion that control theory cannot, in general, be considered to be a part of, or a simple extension of, known physical theory.

Finally, this chapter addresses control in living systems, and asks whether or not the principles of technological control, as outlined in the first part, apply. Living systems are dominated by regulatory processes. The history of our discovery of some of these processes is summarized. Enzyme-catalyzed reactions and feedback control of enzyme levels by genetic repression-derepression constitute interesting sample cases for control theory analysis. The analysis shows that control theory provides a basis for showing what experiments and data are necessary to validate the claims of the biochemists that the closed, inhibitory pathways they discover (usually in vitro) actually have physiological relevance. This validation has yet to be made. It is concluded that some of the concepts of classical control theory do illuminate some biochemical control processes, but that the richness of modern, optimal control theory cannot be brought to bear on the richness of modern genetic control of protein biosynthesis. —The Editor

Keywords

Feedback Control Control Theory Optimal Control Problem Optimal Control Theory Sensor Noise 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Abraham, R., and J. Marsden (1978) Foundations of Mechanics, 2nd ed. Menlo Park, Calif.Google Scholar
  2. Black, H. S. (1934) Stabilized feedback amplifiers. Bell Syst Tech. J. 12:1–19.Google Scholar
  3. Bryson, A. E. Jr.,, and Y. C. Ho (1969) Applied Optimal Control. Ginn (Blaisdell), Boston.Google Scholar
  4. Cannon, W. B. (1929) Organization for physiological homeostasis. Physiol. Rev. 9:399–431.Google Scholar
  5. Cannon, W. B. (1939) The Wisdom of the Body. Norton, New York.Google Scholar
  6. Chance, B. (1961) Control characteristics of enzyme systems. Cold Spring Harbor Symp. Quant. Biol. 26:289–299.Google Scholar
  7. Changeux, J. P. (1961) The feedback control mechanism of biosynthetic L-threonine deaminase by L-isoleucine. Cold Spring Harbor Symp. Quant. Biol. 26:313–318.PubMedGoogle Scholar
  8. D’Azzo, J. J., and C. H. Houpis (1960) Control System Analysis and Synthesis. McGraw-Hill, New York.Google Scholar
  9. DeRobertis, E. D. P., and E. M. F. DeRobertis (1980) Cell and Molecular Biology, 7th ed. Saunders, Philadelphia.Google Scholar
  10. Gerhart, J. C., and A. B. Pardee (1962) The enzymology of control by feedback inhibition. J. Biol. Chem. 237:891–896.PubMedGoogle Scholar
  11. Gordon, M. S. (1968) Animal Function: Principles and Adaptions. Macmillan Co., New York.Google Scholar
  12. Guyton, A. C. (1971) Textbook of Medical Physiology. Saunders, Philadelphia.Google Scholar
  13. Haken, H. (1977) Synergetics—An Introduction. Springer-Verlag, Berlin.Google Scholar
  14. Horowitz, I. M. (1963) Synthesis of Feedback Systems. Academic Press, New York.Google Scholar
  15. Jacob, F., and J. Monod (1961a) On the regulation of gene activity. Cold Spring Harbor Symp. Quant. Biol. 26:193–211.Google Scholar
  16. Jacob, F., and J. Monod (1961b) Genetic regulatory mechanisms in the synthesis of proteins. J. Mol. Biol. 3:318–356.PubMedCrossRefGoogle Scholar
  17. Jazwinski, A. (1970) Stochastic Processes and Filtering. Academic Press, New York.Google Scholar
  18. Judson, H. F. (1979) The Eighth Day of Creation. Simon & Schuster, New York.Google Scholar
  19. Lehninger, A. L. (1975) Biochemistry, 2nd ed. Worth, New York.Google Scholar
  20. McShane, E. J. (1939) On multipliers for Lagrange problems. Am. J. Math. 61:809–819.CrossRefGoogle Scholar
  21. Minorsky, N. (1922) Directional stability of automatically steered bodies. J. Am. Soc. Nav. Eng. 34(2).Google Scholar
  22. Mohler, R. R. (1973) Bilinear Control Processes. Academic Press, New York.Google Scholar
  23. Mohler, R. R., C. Bruni, and A. Gandolfi (1980) A systems approach to immunology. Proc. IEEE 68:964–990.CrossRefGoogle Scholar
  24. Monod, J., and F. Jacob (1961) Teleonomic mechanisms in cellular metabolism, growth, and differentiation. Cold Spring Harbor Symp. Quant. Biol. 26:389–401.PubMedGoogle Scholar
  25. Novick, A., and L. Szilard (1954) Experiments with the chemostat on the rates of amino acid synthesis in bacteria. In: Dynamics of Growth Processes. Princeton University Press, Princeton, N.J., pp. 21–32.Google Scholar
  26. Nyquist, H. (1932) Regeneration theory. Bell Syst. Tech. J. 11:126–147.Google Scholar
  27. Platt, T. (1980) Regulation of gene expression in the tryptophan Operon of Escherichia coli. In: The Operon, 2nd ed., J. H. Miller and W. S. Reznikoff (eds.). Cold Spring Harbor Laboratory, Cold Spring Harbor, N.Y., pp. 263–302.Google Scholar
  28. Pontryagin, L. S., V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko (1962) Mathematical Theory of Optimal Processes. Wiley-Interscience, New York.Google Scholar
  29. Reznikoff, W. S., and J. N. Abelson (1980) The Lacpromotor. In: The Operon, 2nd ed., J. H. Miller and W. S. Reznikoff (eds.). Cold Spring Harbor Laboratory, Cold Spring Harbor, N.Y., pp. 221–243.Google Scholar
  30. Savegeau, M. (1976) Biochemical Systems Analysis. Addison-Wesley, Reading, Mass.Google Scholar
  31. Soodak, H., and A. Iberall (1978) Homeokinetics: A physical science for complex systems. Science 201:579.PubMedCrossRefGoogle Scholar
  32. Sophianopoulos, A. (1973) Differential conductivity. Methods Enzymol. 17:557–590.CrossRefGoogle Scholar
  33. Stear, E. B. (1975) Application of control theory to endocrine regulation and control. Ann. Biomed. Eng. 3:439–455.PubMedCrossRefGoogle Scholar
  34. Truxal, J. G. (1955) Automatic Feedback Control Synthesis. McGraw-Hill, New York.Google Scholar
  35. Umbarger, H. E. (1955) Evidence for a negative-feedback mechanism in the biosynthesis of isoleucine. Science 123:848.CrossRefGoogle Scholar
  36. Umbarger, H. E. (1961) Endproduct inhibition of the initial enzyme in a biosynthetic sequence as a mechanism of feedback control. In: Control Mechanisms in Cellular Processes, D. M. Bonner (ed.). Ronald Press, New York, pp. 67–85.Google Scholar
  37. Umbarger, H. E. (1978) Amino acid biosynthesis and its regulation. Annu. Rev. Biochem. 47:533–606.CrossRefGoogle Scholar
  38. Wiener, N. (1948) Cybernetics, 2nd ed. Wiley, New York.Google Scholar
  39. Yates, R. A., and A. B. Pardee (1956) Control of pyrimidine biosynthesis in Escherichia coliby a feedback mechanism. J. Biol. Chem. 221:757–770.PubMedGoogle Scholar

Copyright information

© Plenum Press, New York 1987

Authors and Affiliations

  • Edwin B. Stear
    • 1
  1. 1.Washington Technology CenterUniversity of WashingtonSeattleUSA

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