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Dynamic Optimization via Functional Control Vector Parametrization and Simple Gradient-Based Algorithms
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DOI：10.1021/acs.iecr.5c03123.png)
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Abstract
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This work introduces a novel control vector parametrization strategy based on basis function expansions. Considering that the control signals belong to Hilbert space L 2[0, t f], where t f denotes the final reaction time, they are expressed as linear combinations of a selected function basis. The original problem, formulated as a nonlinear dynamic optimization problem, is thereby transformed into a static nonlinear optimization problem, which is subsequently solved using a direct gradient-based method. The proposed approach avoids the use of adjoint variables or complex numerical techniques, demonstrating that even a simple gradient-based algorithm can achieve competitive performance without the need for more sophisticated optimization tools. The methodology is applied to two benchmark chemical processes: (i) biodiesel production in a batch reactor, aimed at maximizing the concentration of ethyl esters at the final time t f, and (ii) a fed-batch fermentation process involving two control actions, where the objective is to maximize the concentration of extracellular xylitol at the final time t f. Results demonstrate that high-quality control trajectories can be obtained with a small number of parameters, yielding better or comparable performance indices than previously reported methods while ensuring continuous and implementable control profiles, without requiring any smoothing stage.
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