A multiple shooting descent-based filter method for optimal control problems

A direct multiple shooting (MS) method is implemented to solve optimal control problems (OCP) in the Mayer form. The use of an MS method gives rise to the so-called ‘continuity conditions’ that must be satisfied together with general algebraic equality and inequality constraints. The resulting finite nonlinear optimization problem is solved by a first-order descent method based on the filter methodology. In the equivalent tri-objective problem, the descent method aims to minimize the objective function, the violation of the ‘continuity conditions’ and the violation of the algebraic constraints simultaneously. The numerical experiments carried out with different types of benchmark OCP are encouraging.We acknowledge the financial support of 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/0615/2019, and FCT within the Projects Scope: UID/CEC/00319/2019 and UID/MAT/00013/2013