Reach Avoid Games With Output Observer Mixed Monotone Reachable Set Estimation

We consider the problem of overestimating the reachable set of a partially observable dynamical agent with unknown disturbance dynamics. We use the framework of mixed-monotonicity to obtain a conservative estimate of the reachable set with respect to bounds on the uncertain dynamics. High-gain observers are used to produce states of the estimates and collapse the reachable set estimate error. Analysis shows that the reachable set estimate can be bounded through careful gain design. The results are validated in simulation and on a real ballistic dynamical systems. The results are used to show capture can be achieved by a team of slow pursuers against a fast evader in a reach-avoid game.