Tracking-in-range Formulations for Numerical Optimal Control

In contrast to set-point tracking which aims to reduce the tracking error between the tracker and the reference, tracking-in-range problems only focus on whether the tracker is within a given range around the reference, making it more suitable for the mission specifications of many practical applications. In this work, we present novel optimal control formulations to solve tracking-in-range problems, for both problems requiring the tracker to be always in range, and problems allowing the tracker to go out of range to yield overall better outcomes. As the problem naturally involves discontinuous functions, we present alternative formulations and regularisation strategies to improve the performance of numerical solvers. The extension to in-range tracking with multiple trackers and in-range tracking in high dimensional space are also discussed and illustrated with numerical examples, demonstrating substantial increases in mission duration in comparison to traditional set-point tracking.