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/00013/2013