Abstract
An integral maximum principle is developed for a class of nonlinear systems containing time delays in state and control variables. Its proof is based on the theory of quasiconvex families of functions, originally developed by Gamkrelidze and extended by Banks. This result is used to obtain a pointwise principle of the Pontryagin type.
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Communicated by P. Varaiya
The authors wish to acknowledge Professor J. M. Blatt for suggesting this problem. Further, they also wish to acknowledge the referee of the paper for bringing to their attention the problems discussed in Section 6.
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Teo, K.L., Moore, E.J. Necessary conditions for optimality for control problems with time delays appearing in both state and control variables. J Optim Theory Appl 23, 413–428 (1977). https://doi.org/10.1007/BF00933450
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DOI: https://doi.org/10.1007/BF00933450