Abstract
The paper presents a closure theorem for the attainable trajectories of a class of control systems governed by a large class of nonlinear evolution equations in reflexive Banach spaces. Several existence theorems for optimal controls are proven that include a terminal control problem, a time-optimal control problem, and a special Bolza problem. Some results of independent interest are also presented.
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Communicated by L. Cesari
This work was supported in part by the National Research Council of Canada under Grant No. 7109.
The authors would like to thank Professor L. Cesari for pointing out that joint continuity off is required for the setsG andR to satisfy the upper semicontinuity property (Theorems 5.1 and 5.2).
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Ahmed, N.U., Teo, K.L. Optimal control of systems governed by a class of nonlinear evolution equations in a reflexive Banach space. J Optim Theory Appl 25, 57–81 (1978). https://doi.org/10.1007/BF00933255
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DOI: https://doi.org/10.1007/BF00933255