Optimal control problems (OCP) have an underlying symplectic structure that can be exploited for the design and application of robust time-integration algorithms [1]. OCPs are in general written as the minimisation of an objective function on a given time interval [0, T]. However, in practical problems, this time-interval is not known, and should be considered as an additional variable of the optimisation problem [2]. In doing that, though, the algebraic constraints of the optimality conditions are modified, and the constrain of the symplectic structure is also in turn modified. In this work we present the application of recent algorithms that preserve the symplectic structure in the discretised solution [3], and apply them to some illustrative OCPs with no prescribed end-time. We show that indeed that solution may be further optimised, and that it still preserves the symplectic structure. REFERENCES [1] J. M. Sanz-Serna, Symplectic Runge–Kutta Schemes for Adjoint Equations, Automatic Differentiation, Optimal Control, and More SIAM Review 58, no. 1: 3–33, 2016. [2] J. T. Betts, Practical Methods for Optimal Control and Estimation Using Nonlinear Programming, 2nd ed. Society for Industrial and Applied Mathematics (SIAM), 2010. [3] N Armengou-Riera, N Rabiei, A Bijalwan, A Rodr´ıguez-Ferran and J.J. Mu˜noz. On the convergence of Conjugate Gradient and GMRES algorithms in the Forward Backward Sweep Method for optimal control. Opt. Contr. Appl. Meth. Online. 2026