Higher order variational time discretization of optimal control problems
For researchers in computational optimal control and mechanics, this provides a more efficient variational integrator that maintains essential system invariants.
The paper develops higher-order variational time discretizations for optimal control problems by discretizing the Lagrange-d'Alembert principle with polynomial collocation, achieving reduced computational effort while preserving structural properties like momentum and energy behavior.
We reconsider the variational integration of optimal control problems for mechanical systems based on a direct discretization of the Lagrange-d'Alembert principle. This approach yields discrete dynamical constraints which by construction preserve important structural properties of the system, like the evolution of the momentum maps or the energy behavior. Here, we employ higher order quadrature rules based on polynomial collocation. The resulting variational time discretization decreases the overall computational effort.