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- Conflict of Interest
- In relation to this article, we declare that there is no conflict of interest.
- Publication history
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Received April 25, 2022
Revised January 10, 2023
Accepted February 9, 2023
- Acknowledgements
- This work is supported by the National Natural Science Foundation of China (61673349), Basic Public Welfare research Plan of Zhejiang Province (LGG19F030006) and Huzhou Key Laboratory of Intelligent Sensing and Optimal Control for Industrial Systems (2022-17).
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Sigma-point and stochastic gradient descent approach to solving global self-optimizing controlled variables
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Abstract
Direct numerical optimization for the global self-optimizing control (gSOC) problem has been recently
attempted in the rigorous nonlinear programming (NLP) framework. Compared with the previous perturbation-based
SOC approaches, the global scheme is of potential to obtain solutions with better performances, as the economics are
evaluated via the rigorous nonlinear process model, rather than approximations using the Taylor expansion. The main
obstacles for solving the NLP are, however, difficulties for the statistical computations for the cost and constrained variables. In this paper, we firstly introduce the sigma-point approach, which generates less and more efficient sampling
points with linear complexity with respect to the uncertain variables, such that the computational load is eased. Furthermore, we incorporate the stochastic gradient descent algorithm to accelerate the search of optimal combination
matrix, which can be carried out upon evaluations of only a few, rather than all, sampling points. The scheme, therefore, makes it possible to deal with problems that have high dimensional uncertain parameters and/or when a single
evaluation of the cost is time-consuming. A batch reactor and a batch distillation column are investigated to show the
usefulness of the presented ideas.
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