Exploring a multi-objective approach for optimal control problems via a direct multiple shooting method

This paper explores the use of a multi-objective approach through the implementation of a numerical direct multiple shooting (MS) method to solve optimal control problems (OCP). When a direct MS method is used to solve the OCP, a set of ‘continuity constraints’ emerges and should be satisfied together with the other algebraic mixed states and control constraints. To minimize the objective function and satisfy all the constraint conditions, the finite-dimensional optimization problem is reformulated as a multi-objective problem with three objectives to be optimized. An illustrative example is included to show that the present methodology is worth pursuing.CIDEM, R&D unit funded by the FCT - Portuguese Foundation for the Development of Science and Technology, Ministry of Science, Technology and Higher Education, under the Project UID/EMS/0615/2016, and FCT within the Projects Scope: UID/CEC/00319/2019 and UID/MAT/00013/201