Observers in Language-based Control *

This work discusses the construction of an observer for language-driven control systems. Such systems accept symbolic inputs corresponding to feedback control laws together with logical conditions which determine when each control law is to be applied. Here, we explore the problem of how to identify the symbolic string driving the system through observation of its output. We discuss the identification of individual “instructions” from which inputs are composed, as well as the recovery of more global features of the input. These features can be quite complex depending on the richness of the grammar. Our approach is motivated by settings where language-driven systems (e.g., mobile robots) must cooperate “silently”, so that a newcomer who wants to be useful must first determine what others in the team are trying to accomplish. Our ideas are illustrated in a series of numerical experiments involving symbolic control of linear systems using the motion description language MDLe.