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Optimal control of the viscous KdV-Burgers equation using an equivalent index method. (English) Zbl 1176.35155
Summary: 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.
35Q53 KdV equations (Korteweg-de Vries equations)
49J20 Existence theories for optimal control problems involving partial differential equations
76D55 Flow control and optimization for incompressible viscous fluids
93C20 Control/observation systems governed by partial differential equations