Data-driven controller synthesis for abstract systems with regular language specifications

In this paper we address data-driven control design with regular language specifications for plants described as abstract systems, i.e. as collections of input-state functions. The abstract system is assumed to be suffix and concatenation closed, causal, deterministic and time-invariant. The system is unknown, apart from a collected finite set of experiments. Given a specification expressed as a regular language defined over an alphabet consisting of a finite set of states of the plant, a controller based on the finite set of experiments is designed, which guarantees that the specification is met up to an arbitrarily small error. Maximality, convergence and adaptivity of the controller as the set of experiments gets bigger are discussed. Controller performance on trajectories of the plant different from those in the set of experiments and in the presence of state measurement errors is analyzed. An example related to the artificial pancreas illustrates the results.