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On normal control processes

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Control processes of the form\(\dot x - A(t) x = B(t) u(t)\), which are normal with respect to the unit ballB p′, r′ of the control spaceL p′([τ, T]),l m r ′ are characterized in terms ofH(t)=X(T)X −1(t),B(t),X(t) any fundamental matrix solution of\(\dot x - A(t)x = 0\), and directly in terms ofA, B, when bothA andB are independent oft.

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  1. 1.

    Hermes, H., andLasalle, J. P.,Functional Analysis and Time Optimal Control, Academic Press, New York, New York, 1969.

  2. 2.

    Pontryagin, L. S.,et al.,The Mathematical Theory of Optimal Processes, John Wiley and Sons (Interscience Publishers), New York, New York, 1962.

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Dedicated to Professor M. R. Hestenes

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Conti, R. On normal control processes. J Optim Theory Appl 14, 497–503 (1974). https://doi.org/10.1007/BF00932844

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Key Words

  • Control theory
  • controllability
  • differential equations