Speaker
Description
In optimal control, Pontryagin's maximum principle provides necessary conditions for optimality of a solution. Generally, however, solutions satisfying these cannot be found analytically, and instead, we need to rely on numerical methods. The convergence rate of the resulting approximations is not the only important measure of the quality of the method. The preservation of qualitative features such as conservation laws is also crucial. In an earlier work, we proposed a new way of stating optimal control problems for second order differential equations as a Lagrangian system in the space of states and costates. This provides a novel way deriving discrete necessary conditions for optimality by discretising these new Lagrangians and applying a variational principle. In this work, we investigate these discrete new Lagrangians and the resulting discrete optimality conditions, which are symplectic by construction. A comparison is performed with standard approaches, concerning e.g. conservation of symmetries, by solving, among others, the low-thrust orbital transfer problem.
