Abstract
An optimal control problem for a deterministic model of chemical birth and growth processes is studied. The cost functional takes into account the two main industrial competitive interests: to avoid low temperatures and to shorten the cooling time. Explicit expressions of the optimal controls are obtained by using an analytical approximation of the relation between the instantaneous amount of crystallized polymer and the total amount of cold injected into the sample until this instant of time. Numerical simulations are shown to illustrate the good agreement with the analytical expressions. It is surprising and remarkable that the explicit expressions of the optimal controls can be derived by minimizing an elementary function in one real variable.
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Escobedo, R., Fernández, L.A. Optimal control of chemical birth and growth processes in a deterministic model. J Math Chem 48, 118–127 (2010). https://doi.org/10.1007/s10910-009-9638-x
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DOI: https://doi.org/10.1007/s10910-009-9638-x