Optimal Trajectories for Drones with Limited Observability Constraints

The dynamic output stabilization problem is a central and important topic in control theory. A compelling example is the control of a drone where the only measurable output is its distance to a target. This scenario presents unique challenges, as the drone’s coordinates are not always observable, even after symmetry reductions. From a practical point of view, minimizing the time required to reach the target—closely tied to fuel efficiency—is critical, particularly in military applications. Interestingly, the optimal trajectories that achieve minimum time, typically straight line paths, coincide with trajectories where the system is unobservable. This paper introduces a novel methodology to reconcile these seemingly conflicting objectives: ensuring observability while minimizing travel time.