Optimal Control of the Viscous Burgers Equation Using an Equivalent Index Method

This paper studies the problem of optimal control of the viscous KdV-Burgers’ equation. We develop a technique to utilize the Cole-Hopf transformation to solve an optimal control problem for the viscous KdV-Burgers’ equation. While the viscous KdV-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.