Optimal control and the Pontryagin's principle in chemical engineering: History,theory, and challenges

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.