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Andrés-Martínez O, Ricardez-Sandoval LA. A switched system approach for the direct solution of singular optimal control problems. Comput Chem Eng 2022. [DOI: 10.1016/j.compchemeng.2022.108058] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Andrés‐Martínez O, Palma‐Flores O, Ricardez‐Sandoval LA. Optimal control and the Pontryagin's principle in chemical engineering: History, theory and challenges. AIChE J 2022. [DOI: 10.1002/aic.17777] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Affiliation(s)
| | - Oscar Palma‐Flores
- Department of Chemical Engineering University of Waterloo Waterloo Ontario Canada
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Abstract
In this paper, we investigate the problem of species separation in minimal time. Droop model is considered to describe the evolution of two distinct populations of microorganisms that are in competition for the same resource in a photobioreactor. We focus on an optimal control problem (OCP) subject to a five-dimensional controlled system in which the control represents the dilution rate of the chemostat. The objective is to select the desired species in minimal-time and to synthesize an optimal feedback control. This is a very challenging issue, since we are are dealing with a ten-dimensional optimality system. We provide properties of optimal controls allowing the strain of interest to dominate the population. Our analysis is based on the Pontryagin Maximum Principle (PMP), along with a thorough study of singular arcs that is crucial in the synthesis of optimal controls. These theoretical results are also extensively illustrated and validated using a direct method in optimal control (via the Bocop software for numerically solving optimal control problems). The approach is illustrated with numerical examples with microalgae, reflecting the complexity of the optimal control structure and the richness of the dynamical behavior.
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Mall K, Taheri E, Prabhu P. Solving singular control problems using uniform trigonometrization method. AIChE J 2021. [DOI: 10.1002/aic.17209] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Kshitij Mall
- Department of Aerospace Engineering Auburn University Auburn Alabama USA
| | - Ehsan Taheri
- Department of Aerospace Engineering Auburn University Auburn Alabama USA
| | - Prathamesh Prabhu
- School of Chemical Engineering Purdue University West Lafayette Indiana USA
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