Gao, Anna; Shen, Chunyu; Fan, Xinghua Optimal control of the viscous KdV-Burgers equation using an equivalent index method. (English) Zbl 1176.35155 Int. J. Nonlinear Sci. 7, No. 3, 312-318 (2009). 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. MSC: 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 Keywords:viscous KdV-Burgers’ equation; optimal control; Cole-Hopf transformation; Euler-Langrange; equivalent indices PDF BibTeX XML Cite \textit{A. Gao} et al., Int. J. Nonlinear Sci. 7, No. 3, 312--318 (2009; Zbl 1176.35155)