A direct method for feedback optimal control of fluid flow and heat transfer systems is investigated. The method consists of discretizing the spatial component of the governing partial differential equations using standard finite-volume methods (FVM) while leaving the transient term in its differential form. This partial discretization method is commonly known as the Numerical Method of Lines (NUMOL). The control is then applied to the partially discretized system of linear ordinary time differential equations. Of particular interest is the effectiveness of linearizing about the current state rather than the origin. The effectiveness of this method is investigated through numerical implementation on a simple one-dimensional heat transfer system.

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