Switching Controller Synthesis for Hybrid Systems Against STL Formulas

TL;DR

This paper presents a method for synthesizing switching controllers for hybrid systems to satisfy STL specifications with timing constraints, addressing a gap in existing safety and liveness-focused approaches.

Contribution

It introduces an iterative approach for controller synthesis that handles timing constraints in STL, applicable to both constant and non-constant hybrid systems.

Findings

Method is sound and relatively complete for a subclass of HSs.

Experimental results demonstrate the approach's effectiveness.

Supports synthesis for systems with complex timing requirements.

Abstract

Switching controllers play a pivotal role in directing hybrid systems (HSs) towards the desired objective, embodying a ``correct-by-construction'' approach to HS design. Identifying these objectives is thus crucial for the synthesis of effective switching controllers. While most of existing works focus on safety and liveness, few of them consider timing constraints. In this paper, we delves into the synthesis of switching controllers for HSs that meet system objectives given by a fragment of STL, which essentially corresponds to a reach-avoid problem with timing constraints. Our approach involves iteratively computing the state sets that can be driven to satisfy the reach-avoid specification with timing constraints. This technique supports to create switching controllers for both constant and non-constant HSs. We validate our method's soundness, and confirm its relative completeness for a certain subclass of HSs. Experiment results affirms the efficacy of our approach.