Public Thesis defense - ICTEAM

Abstraction Relations over Dynamical Systems: Theory and Algorithms by Julien Calbert

The increasing complexity of modern control systems—spanning applications from smart grids to autonomous vehicles—has underscored the limitations of traditional control techniques. These cyber-physical systems (CPS) require advanced frameworks to ensure both efficiency and safety. This thesis explores abstraction-based control as a promising approach for CPS, where system behaviors are captured by finite-state models, transforming control tasks into combinatorial problems that enable systematic, correct-by-design controller synthesis.

First, we develop a theoretical framework to systematically classify and characterize system relations according to their concretization procedure. We demonstrate how the abstraction relation can be tailored based on the desired properties of the control architecture of the original system, irrespective of the specification we aim to enforce. Meanwhile, we introduce key system relations, highlighting their impact on control design and their role in mitigating the inherent non-determinism caused by discretization.

Second, we introduce algorithms to co-design the abstraction and abstract controller, focusing on relevant regions of the state space specific to the control task and thereby reducing computational complexity. For that, we integrate dynamic programming techniques within the abstraction framework, providing methods to transfer value functions from the abstract system to the original system, and we propose a framework for constructing non-uniform cells optimized for the system dynamics and control objectives. Finally, we implement these algorithms in Dionysos.jl, a modular package that solves control problems using advanced techniques from symbolic control, optimization, and learning.

Jury’s members:

Prof. Raphaël Jungers (UCLouvain), supervisor

Prof. Pierre-Antoine Absil (UCLouvain), chairperson

Prof. Julien Hendrickx (UCLouvain), secretary

Prof. Antoine Girard (L2S-CNRS, CentraleSupélec – France)

Prof. Majid Zamani (University of Colorado Boulder, USA)

Pay attention:

The public defense of Julien Calbert scheduled for Tuesday December 3 at 04:15p.m. will also take place in the form of a video conference.

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