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On the maximum principle for time-optimal controls for a class of distributed-boundary control problems

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Abstract

In this note, we present the necessary conditions of optimality for time-optimal controls for a class of distributed-boundary control problems in general Banach spaces using the semigroup theory. Theorem 3.1 is based on a recent general maximum principle due to Barbu (Ref. 1), which was proved for strictly convex reflexive Banach spaces. Theorem 3.2 generalizes this result (for time-optimal control problems) by lifting the assumption.

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References

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    Barbu, V.,Boundary Control Problems with Convex Cost Criterion, SIAM Journal on Control and Optimization, Vol. 18, pp. 227–243, 1980.

  2. 2.

    Fattorini, H. O.,The Time-Optimal Control Problem in Banach Spaces, Applied Mathematics and Optimization, Vol. 1, pp. 163–188, 1974.

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    Ahmed, N. U., andTeo, K. L.,Optimal Control of Distributed-Parameter Systems, North-Holland, New York, New York, 1981.

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    Butzer, P. L., andBerens, H.,Semigroups of Operators and Approximation, Springer-Verlag, Berlin, Germany, 1967.

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    Georg Schmidt, E. J. P.,The Bang-Bang Principle for the Time-Optimal Problem in Boundary Control of the Heat Equation, SIAM Journal on Control and Optimization, Vol. 18, pp. 101–107, 1980.

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    Ahmed, N. U.,Finite-Time Null Controllability for a Class of Linear Evolution Equations on a Banach Space with Control Constraints, Journal of Optimization Theory and Applications (to appear).

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Additional information

This work was supported by the National Science and Engineering Council of Canada under Grant No. 7109.

Communicated by L. Cesari

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Ahmed, N.U. On the maximum principle for time-optimal controls for a class of distributed-boundary control problems. J Optim Theory Appl 45, 147–157 (1985). https://doi.org/10.1007/BF00940819

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Key Words

  • Maximum principle
  • distributed-boundary controls
  • time-optimal control
  • bang-bang principle