On an agile temporal discretization for abstraction-based control: applied to the optimal control of continuous-time systems

Details

Supervisors

Jungers, Raphaël M.

Faculty

Ecole polytechnique de Louvain

Degree label

Master [120] : ingénieur civil en mathématiques appliquées, à finalité spécialisée

Abstract

enAs control systems grow in complexity, abstraction-based methods have become essential for designing controllers with formal guarantees of success. These methods involve the construction of a finite-state mathematical object, called the abstraction, which approximates the real system. On this mathematical object, the control problem becomes a simple combinatorial problem. However, a key limitation of these methods is their reliance on discrete-time models, typically obtained by discretizing continuous-time systems with a fixed timestep. This discretization leads to two major problems: when the timestep is small, the abstraction includes numerous stuttering and spurious trajectories, making controller synthesis suboptimal or even infeasible; conversely, a large timestep may also render control design infeasible due to a lack of flexibility. In this thesis, drawing inspiration from Reinforcement Learning concepts, we introduce temporal abstractions-abstractions with an agile temporal discretization, which allow for a flexible timestep. We provide a method for constructing such abstractions and formally establish their correctness in controller design. Furthermore, we show how to apply these to optimal control under reachability specifications. Finally, we present and compare our methods on two numerical examples, highlighting that our approach leads to better controllers.