An indirect approach for singular optimal control problems

In singular optimal control problems, the control is not explicitly defined by the optimality conditions. As a consequence, both direct and indirect methods may fail to find a proper solution. This situation is common when optimizing the operation of some process systems, such as batch and continuous reactors. Some direct strategies that rely on regularization and rigorous or heuristic mesh refinement have been recently proposed. In this work, a simple but flexible nonlinear programing formulation is presented, with moving finite elements based on an indirect approach. It is shown that, despite previously reported drawbacks, indirect methods, when properly formulated, are efficient to solve challenging problems. The proposed formulation strictly satisfies the optimality and Weierstrass-Erdmann corner conditions at dis-crete points and provides accurate results with short CPU times. Heuristics or sophisticated regularization schemes are not required. Two sets of problems were solved to assess the performance of this strategy. (c) 2020 Elsevier Ltd. All rights reserved.