On data-driven controller synthesis with regular language specifications

Data-driven control design for general systems with regular language specifications is addressed. We consider a discrete-time control system described as an abstract system i.e. as a collection of input-state functions. The abstract system is assumed to be suffix and concatenation closed, causal, deterministic and time-invariant. State variables are known but their dynamics are not, apart from a 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, we design a controller based on the finite set of experiments, that guarantees that the specification is met, up to an error that can be chosen as small as desired. We also present results on maximality, convergence and adaptivity of the controller as the set of experiments increases. Copyright (C) 2020 The Authors.