Constructing Symbolic Abstractions From Data Without Model Assumptions

Research at the interface between formal methods and control theory has given rise to symbolic control [1], [2], [3], which deals with control of dynamical systems with logic specifications. A key ingredient of symbolic control is a finite abstraction, i.e. a dynamical system with a finite number of states and inputs, also called symbolic model, constructed from the original system. When the concrete and abstract systems are related by a behavioral relation, such as an approximate alternating simulation relation [1], showing that the trajectories of the abstraction mimic the ones of the original system, the discrete controller synthesized for the abstraction can be refined into a hybrid controller for the original system.