Learning-based Symbolic Abstractions for Nonlinear Control Systems

Symbolic models or abstractions are known to be powerful tools towards the control design of cyber-physical systems (CPSs) with logic specifications. In this paper, we investigate a novel learning-based approach towards the construction of symbolic models for nonlinear control systems. In particular, the symbolic model is constructed based on learning the un-modeled part of the dynamics from training data based on state-space exploration, and the concept of an alternating simulation relation that represents behavioral relationships with respect to the original control system. Moreover, we aim at achieving safe exploration, meaning that the trajectory of the system is guaranteed to be in a safe region for all times while collecting the training data. In addition, we provide some techniques to reduce the computational load of constructing the symbolic models and the safety controller synthesis, so as to make our approach practical. Finally, a numerical simulation illustrates the effectiveness of the proposed approach.