Representing Symbolic Controllers with Deep Neural Networks

Abstract

Controller synthesis techniques based on symbolic models or discrete abstractions are becoming increasingly attractive as they allow for synthesizing correct-by-design controllers of general nonlinear systems under complex behavioral requirements. However, its immense size as the consequence of the state-space explosion prohibits the approach to be widely used in real-life applications. The explosion of state space is mainly caused by the discretization in the abstraction step, and the redundancy of control inputs resulted in from the synthesis. Compression methods and determinization techniques have been developed to tackle the size problem of the resulting controller. Neural networks capabilities at approximating function and substituting look-up tables in broad applications, such as flight-critical system and deep reinforcement learning, motivate us to suggest utilizing neural networks as an alternative approach to represent the controller. In this work, the evaluation of the capability of neural networks as a viable approach to store a symbolic controller is presented. We present the utilization of neural networks to store deterministic controllers. We also propose a determinization technique based on the multiclass classification task in neural networks to determinize the controller. Additionally, we employ neural networks to store non-deterministic controllers by preserving the redundancy of the control inputs. Comparisons between binary decision diagrams (BDDs) and neural networks as compact representations of symbolic controllers are performed. Results show that neural networks are able to represent symbolic controllers in a more compact way compared to BDDs considering the size overhead produced by the CUDD package as its manipulation library.