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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Barbu, V.,Boundary Control Problems with Convex Cost Criterion, SIAM Journal on Control and Optimization, Vol. 18, pp. 227–243, 1980.
Fattorini, H. O.,The Time-Optimal Control Problem in Banach Spaces, Applied Mathematics and Optimization, Vol. 1, pp. 163–188, 1974.
Ahmed, N. U., andTeo, K. L.,Optimal Control of Distributed-Parameter Systems, North-Holland, New York, New York, 1981.
Butzer, P. L., andBerens, H.,Semigroups of Operators and Approximation, Springer-Verlag, Berlin, Germany, 1967.
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.
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).
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
- Maximum principle
- distributed-boundary controls
- time-optimal control
- bang-bang principle