Numerical solving of an optimal control problem in large time horizon: the aerial vehicle guidance
Veljko Askovic, Emmanuel Trélat, Hasnaa Zidani
TL;DR
The paper tackles long-horizon aerial-vehicle trajectory optimization in the vertical plane by formulating a Pontryagin maximum principle (PMP)–based indirect method augmented with continuation and turnpike concepts. A regularized, multi-stage strategy connects a simple Dubins Fuller type problem to the full 5D OCP, using parametrized dynamics and a ‘shooting from the middle’ technique to stabilize convergence and exploit the turnpike near cruise altitude. The authors analyze extremals, address singular arcs, and demonstrate that regularization improves the shooting method’s robustness, yielding accurate terminal conditions and cruise-altitude tracking under practical constraints. The approach offers a path toward efficient, potentially real-time re-planning for long-horizon flight trajectories, leveraging both theoretical guarantees and computational strategies to manage complexity in indirect optimal-control solvers.
Abstract
In this paper we consider an optimal control problem in large time horizon and solve it numerically. More precisely, we are interested in an aerial vehicle guidance problem: launched from a ground platform, the vehicle aims at reaching a ground/sea target under specified terminal conditions while minimizing a cost modelling some performance and constraint criteria. Our goal is to implement the indirect method based on the Pontryagin maximum principle (PMP) in order to solve such a problem. After modeling the problem, we implement continuations in order to ''connect'' a simple problem to the original one. Particularly, we exploit the turnpike property in order to enhance the efficiency of the shooting.