(Un)ambiguous optimal control

The phenomenon of using control actions to communicate is called signaling. Signaling is often beneficial in decentralized control problems with imperfect communication between agents. Seemingly simple control problems with signaling are often mathematically challenging. Humans, however, lack high-speed communication channels and routinely employ signaling strategies during cooperative movements. This paper presents a computationally tractable two-player problem that models several salient features of signaling problems arising in both decentralized control and human experiments. The problem consists of a signaler that reaches towards one of two possible targets, and an observer that decides on the target location based on noisy measurements of the movement. The signaler trades off control costs, such as energy, with informativeness for the observer. Two variants, the unambiguous case and the ambiguous case, are presented. In the unambiguous case, the signaler makes movements that are easy to distinguish, while in the ambiguous case, the signaler maximizes similarity of the movements. An approximation method for nonlinear systems is presented. When applied to a three-link arm model, the control scheme reproduces qualitative signaling phenomena observed in human reaching experiments.