Abstract
In this paper, we give a variational characterization of the uniqueness of the optimal state in a proper linear control process for the time-optimal problem; we extend to control processes with time-variable coefficients a characterization of normality given by Hajek in Ref. 1.
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References
Hajek, O.,Geometric Theory of Time-Optimal Control, SIAM Journal on Control, Vol. 9, pp. 339–350, 1971.
Hermes, H., andLasalle, J. P.,Functional Analysis and Time-Optimal Control, Academic Press, New York, New York, 1969.
Pieri, G., Sulla Stabilità Variazionale del Problema del Minimo Tempo, Bollettino della Unione Matematica Italiana, Vol. 15B, pp. 108–118, 1978.
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Pieri, G.,Variational Perturbations of the Linear-Quadratic Problem, Journal of Optimization Theory and Applications, Vol. 22, pp. 63–77, 1977.
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Communicated by R. Conti
This work was supported by CNR-GNAFA, Rome, Italy.
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Pieri, G. Variational characterization of the uniqueness of the optimal state for the minimal-time problem. J Optim Theory Appl 30, 635–642 (1980). https://doi.org/10.1007/BF01686726
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DOI: https://doi.org/10.1007/BF01686726