An introduction to bounded rate systems

  • C. Bruni
  • G. Koch
  • A. Germani
Optimal Control Deterministic
Part of the Lecture Notes in Computer Science book series (LNCS, volume 41)


In this work a new class of nonlinear systems is introduced, for which the denomination "bounded rate systems" is proposed. This class appears to be quite relevant for its capability of modeling important physical phenomena in different field such as biology, ecology, engineering.

Bounded rate systems situate between bilinear and linear-in-control systems, so that a bounded rate system theory may be usefully investigated and developed exploiting already available results.


Bilinear System Quadratic System Free Response Coolant Flow Rate Variable Structure System 
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.


  1. [1]
    C. BRUNI, G. DI PILLO, G. KOCH: Bilinear systems: an appealing class of "nearly linear" systems in theory and applications. IEEE Trans. on Automatic Control, vol. AC-19, n. 4 August 1974.Google Scholar
  2. [2]
    R.R. MOHLER: Bilinear control processes with application to engineering, ecology and medicine. Academic Press 1974.Google Scholar
  3. [3]
    C. LOBRY: Controllabilité des systèmes non lineares. SIAM J. on Control, v. 3, n. 4, November 1970.Google Scholar
  4. [4]
    G. HAYNES, H. HERMES: Nonlinear controllability via Lie theory. SIAM J. on Control, v. 8, n. 4, November 1970.Google Scholar
  5. [5]
    R.W. BROCKETT: System theory on group manifolds and coset space. SIAM J. on Control, v. 10, n. 2, May 1972.Google Scholar
  6. [6]
    V. JURDJEVIC: Certain controllability properties of analytic control systems. SIAM J. on Control, v. 10, n. 2, May 1972.Google Scholar
  7. [7]
    G.E. LADAS, V. LAKSHMIKANTHAM: Differential equations in abstract spaces. Academic Press 1972.Google Scholar
  8. [8]
    C. BRUNI, M.A. GIOVENCO, G. KOCH, R. STROM: A dynamical model of humoral immune response. To appear in mathematical biosciences. Rapp. Ist. Autom. Univ. di Roma, R. 74-22, Luglio 1974.Google Scholar
  9. [9]
    C. BRUNI, M.A. GIOVENCO, G. KOCH, R. STROM: The immune response as a variable structure system. Variable structure systems in Biology and Socieconomics, Springer Verlag 1975.Google Scholar
  10. [10]
    R.A. ALBERTY: The enzymes. Academic Press, 1959.Google Scholar
  11. [11]
    I. MALEK: Present state and perspectives of biochemical engineering. Advances in Biochemical Engineering, vol. 3, Ed. T.K. Ghose, A. Fiechter, N. Blakebrough. Springer Verlag, 1974.Google Scholar
  12. [12]
    G. D'ANS, D. GOTTLIEB, P. KOKOTOVIC: Optimal control of bacterial growth. Automatica, vol. 8, Pergamon Press, 1972.Google Scholar
  13. [13]
    R. ROSEN: Dynamical system theory in biology. Vol. 1, Wiley Interscience, 1970.Google Scholar
  14. [14]
    GOEL, MAITRA, MONTROLL: Models of interacting populations. Reviews of modern physics. April 1971, Part. 1.Google Scholar
  15. [15]
    O. BILANS, N.R. AMUNDSON: Chemical reactor stability and sensitivity. A.I.Ch.E.J., vol. 1, n. 4, 1955.Google Scholar
  16. [16]
    E.P. GYFTOPULOS: General reactor dynamics in the technology of nuclear reactor safety. Vol. 1, Ed. T.J. Thompson, J.G. BECKERLEY, M.I.T. Press, 1964.Google Scholar
  17. [17]
    D.L. HETRICK: Dynamics of nuclear reactors. The University of Chicago Press, 1971.Google Scholar
  18. [18]
    W. LEONTIEFF: The dynamics inverse. Contribution to Input Output. Analysis. Ed. Carter-Brody, North Holland, 1970.Google Scholar
  19. [19]
    A.D. SMIRNOV: Problems of constructing n optimal interbranch model of socialist reproduction. Contribution to Input Out-put Analysis. Ed. Carter-Brody, North Holland, 1970.Google Scholar
  20. [20]
    G.S. SAUER, J.L. MELSA: Stochastic insect-pest control with variable observation policy. IV San Diego Symposium in Nonlinear Estimation and Its Application. 10–12 Sept. 1973.Google Scholar
  21. [21]
    V. JURDJEVIC, H.J. SUSSMANN: Control systems on Lie groups. Division of engineering and applied physics. Harvard University. Technical Report N. 628. Cambridge Massachusetts. November 1971.Google Scholar
  22. [22]
    H. HERMES, G. HAYNES: On the nonlinear control problem with control appearing linearly. SIAM J. on Control, vol. 1, n. 2, 1963.Google Scholar
  23. [23]
    H. HERMES: Controllability and the singular problem. SIAM J. on Control, vol. 2, n. 2, 1964.Google Scholar
  24. [24]
    E.J. DAVISON, E.G. KUNZE: Some sufficient conditions for the global and local controllability of nonlinear time-varying systems. SIAM J. on Control, vol. 8, n. 4, 1970.Google Scholar
  25. [25]
    H. TOKUMARU, N. ADACHI: On the controllability of nonlinear systems. Automatica, vol. 6, 1970.Google Scholar
  26. [26]
    S.B. GERSHWIN, D.H. JACOBSON: A controllability theory for nonlinear systems. IEEE Trans. on A.C. Vol. AC-16, n.1, 1971.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1976

Authors and Affiliations

  • C. Bruni
    • 1
  • G. Koch
    • 1
  • A. Germani
    • 2
  1. 1.Istituto di AutomaticaUniversità di RomaRoma
  2. 2.CSSCCA — CNRItaly

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