On existence problems for the optimal control of certain nonlinear integral equations of Urysohn type
In the papers of \textit{T. Zolezzi} [Ann. Mat. pura appl. IV. Ser. 91, 97- 118 (1972; Zbl 0238.49003)], \textit{T. S. Angell} [J. Optimization Theory Appl. 19, 29-45 (1976; Zbl 0305.49021)] and \textit{M. L. Bennati} [Ann. Mat. Pura Appl., IV. Ser. 121, 187-197 (1979; Zbl 0422.49013)] existence results have been obtained for optimal control problems whose state equations are described by certain nonlinear integral equations of Urysohn type. We generalize and synthesize these results by formulating a general lower closure result from which the results in the above mentioned papers are shown to follow. In the course of this, we also present a novel and rather abstract treatment of existence problems for variable-time optimal control, quite in the spirit of a previous paper of the author [SIAM J. Control Optimization 20, 198-210 (1982; Zbl 0499.49006)].
nonlinear integral equations of Urysohn type
scientific article; zbMATH DE number 3848092
scientific article