Numerical Optimal Control with Periodicity Constraints in the Presence of Invariants

Journal article, 2018

Periodic optimal control problems (POCPs) based on dynamic models holding invariants are challenging due to possible failure of standard constraint qualifications. This paper analyses this issue and proposes three simple and computationally inexpensive modifications of the formulation that allow for a recovery of Linear Independence Constraint Qualification, while preserving the Second-Order Sufficient Conditions for optimality. The resulting POCP can be tackled via standard solvers. Application is detailed for the case of POCPs holding index-reduced DAEs and representations of the SO (3) Lie group.