Optimal control of systems with a single control and several cost functionals†

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Abstract
Necessary conditions are derived for the optimal control of a deterministic system with a single control and several cost scales by using Pontryogin's maximum principle It is shown that the optimization of a system with respect to an objective function which is expressed as some function of several coat scales can be handled by first optimizing the system with respect to another criterion which is a linear combination of the given cost scales. The optimal control for this criterion is obtained in terms of the weighting factors in the linear combination functional. A search procedure is then used to determine the optimum values of these weighting factors for the specified objective function. The technique is applied to two examples.

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