In the mid-1950s, Pontryagin et al. published a principle that became a fundamental concept in optimal control (OC) theory. The principle provides theoretical and practical methods to find the solution of OC problems, in particular, open-loop control problems. In chemical engineering, the principle has played an important role as a decision making framework for more than 60 years. This study gathers the main contributions on the application of the Pontryagin's principle to the dynamic optimization of chemical processes. A concise overview of the optimality conditions for a wide class of constrained OC problems is provided. Numerical methods to solve the necessary conditions and strategies to address inequality constraints are summarized. The information and illustrative case study presented in this work can be used as a guide to implement the principle in different settings. Opportunities for further application of the principle in relevant chemical engineering problems are also discussed.

中文翻译：

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化学工程中的最优控制和庞特里亚金原理：历史、理论和挑战

在 1950 年代中期，Pontryagin 等人。发表了一项原则，该原则成为最佳控制（OC）理论的基本概念。该原理为解决 OC 问题，特别是开环控制问题提供了理论和实践方法。在化学工程中，该原则作为决策框架发挥了 60 多年的重要作用。本研究收集了 Pontryagin 原理在化学过程动态优化中的应用的主要贡献。提供了针对各种受约束的 OC 问题的最优条件的简明概述。总结了解决不平等约束的必要条件和策略的数值方法。本工作中提供的信息和说明性案例研究可用作在不同环境中实施该原则的指南。还讨论了在相关化学工程问题中进一步应用该原理的机会。