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It is very common in chemical engineering applications to find optimal control problems whose optimality conditions do not provide information about the control over an interval. This type of problems is called partially singular, as the control switches between nonsingular and singular arcs. When direct transcription is applied, the resulting nonlinear programming problem is ill conditioned. Some mesh refinement and rigorous iterative methods have been developed to determine the control profile and switching points. This work presents a practical alternative that quickly produces accurate state and control profiles without adding nonconvex terms. The problem is first solved with a large number of equally spaced finite elements. Then, unnecessary elements are removed while keeping the solution structure. Finally, direct and indirect approaches are combined to apply a regularization scheme only to the singular part. Seven examples were solved to test our strategy. Results provide good approximations to the analytical switching points.

The competitive, profitable, and safe operation of chemical plants depends on tight and effective coordination among the different decision making levels of the enterprise, including planning, scheduling, and control. The optimal integration of these functions has become critical given the disruptive effects of the recent COVID-19 pandemic on the supply chains and the current trends in climate change. However, integrating multiple decision making levels creates modelling and computational challenges. In this study, we review the progress made in the integration of two and three decisions levels using mathematical programming and control theory tools. We highlight the model reduction and decomposition techniques that have been applied, as well as the main issues that remain unsolved. Perspectives on emergent areas of application and novel computing solutions are also discussed.

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.

Computer-aided molecular design as a mixed-integer nonlinear programming problem under uncertainty in group contribution parameters has been addressed. A set of new low-temperature organic compounds, for heat recovery purposes, was obtained by solving the mixed-integer nonlinear programming problem with nominal values from a previous work. Monte Carlo simulations with Latin hypercube sampling were carried out to asses the effect of uncertain group contributions on thermo-physical properties. Furthermore, a set-based robust counterpart was formulated by taking into account uncertainty only in linear constraints. The results show that even small uncertainty in group contribution parameters can lead to significant variations in thermo-physical properties of the compounds analyzed. Therefore, it is necessary to consider uncertainty in the Computer-aided molecular design formulation. Solutions of the robust counterpart became more conservative as the uncertainty set size increased, producing organic compounds different from the nominal case.

In this work, a large-scale modeling framework for the Mexican electricity system is developed based on the energy hub concept. The hub consists of nine smaller hubs, each one describing a control region of the country. The interface between energy carriers and loads is modeled as the product of coupling matrices. Natural gas, fuel oil, diesel, uranium, and coal were regarded as inputs, which are converted into electricity by available technologies. Power outputs are used mainly to meet the demand. We also considered hydroelectric, wind, and geothermal power contributions as well as export, import, and internal power transmission. A nonlinear programming problem was formulated and solved with real data for a 1 h scenario. Constraints on clean technologies’ participation and operation limits were taken into consideration. Results provide optimal flows and dispatch of the inputs such that an economic objective function is minimized while the demand of each region is satisfied. The combined cycle working with natural gas was the predominant process to produce electricity. Renewable sources played an important role in the fulfillment of the country’s energy demand. The nationwide energy hub developed in this work is a potential tool for planning and renewable resource integration studies.