Abstract
We develop a technique to utilize the Cole–Hopf transformation to solve an optimal control problem for Burgers' equation. While the Burgers' equation is transformed into a simpler linear equation, the performance index is transformed to a complicated rational expression. We show that a simpler performance index, that retains the behavior of the original performance index near optimal values of the functional, can be used.
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Vedantham, R. Optimal Control of the Viscous Burgers Equation Using an Equivalent Index Method. Journal of Global Optimization 18, 255–263 (2000). https://doi.org/10.1023/A:1008362822027
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DOI: https://doi.org/10.1023/A:1008362822027