Abstraction-Based Data-Driven Control

Our world is living a paradigm shift in technology policy, often referred to as the Cyber-Physical Revolution or Industry 4.0. Nowadays, Cyber-Physical Systems are ubiquitous in modern control engineering, including automobiles, aircraft, building control systems, chemical plants, transportation systems, and so on. The interactions of the physical processes with the machines that control them are becoming increasingly complex, and in a growing number of situations either the model of the system is unavailable, or it is too difficult to describe accurately. Therefore, embedded computers need to "learn" the optimal way to control the systems by the mere observation of data. What seems the best approach to control these complex systems is often by discretizing the different variables, thus transforming the model into a combinatorial problem on a finite-state automaton, which is called an abstraction of the real system. Until now, this approach, often referred to as "abstraction-based control" or "symbolic control", has not been proved useful beyond small academic examples. In this project I aim to show the potential of this approach by implementing a novel data-driven approach based on a probabilistic interpretation of the discretization error. I have developed a toolbox (github.com/davidedl-ucl/master-thesis) implementing this kind of control with the aim of integrating it in the Dionysos software github.com/dionysos-dev). With this software, I succeeded in efficiently solving problems for non-linear control systems such as a path planning for an autonomous vehicle and a cart-pole balancing problem. The long-term objective of this project is to improve the methods implemented in my current software by employing a variable discretization of the state space and to consider complex specifications such as LTL formulas.