Agile Temporal Discretization for Symbolic Optimal Control

Abstract: As control systems grow in complexity, abstraction-based methods have become essential for designing controllers with formal guarantees. However, a key limitation of these methods is their reliance on discrete-time models, typically obtained by discretizing continuous-time systems with a fixed time step. This discretization leads to two major problems: when the time step is small, the abstraction includes numerous stuttering and spurious trajectories, making controller synthesis suboptimal or even infeasible; conversely, a large time step may also render control design infeasible due to a lack of flexibility. In this work, drawing inspiration from Reinforcement Learning concepts, we introduce temporal abstractions, which allow for a flexible time-step. 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 showcase our methods on two numerical examples, highlighting that our approach leads to better controllers.