Optimization based control for target estimation and tracking via highly observable trajectories

This paper presents a Model Predictive Control (MPC) scheme to solve the target estimation and tracking problem. The objective is to derive a feedback law that drives a follower vehicle to a target vehicle using on-line estimation of the target position and velocity. In this scenario, when the target is observed through a nonlinear observation model, e.g., bearing only or range only sensors, it is possible to show that solving the tracking problem independently from the estimation problem can lead to an unsatisfactory result where the follower-target system is driven by the controller through unobservable or weekly observable trajectories and, as result, the target position and velocity cannot be recovered or cannot be recovered with high accuracy. In this paper, we propose a strategy that embeds, in a seamless way, an index of observability in design of the target tracking controller resulting in a closed-loop behavior that balances the objective of target tracking with the competing objective of maintaining a good estimate of the target's position and velocity. Numerical results are presented that illustrate this type of behavior.