Formal Verification of Control Systems Properties with Theorem Proving

TL;DR

This paper introduces a formal verification methodology for control system properties like stability and robustness using theorem proving in Why3, integrating Simulink models through automatic translation and verification steps.

Contribution

It presents a novel approach combining Simulink modeling with automatic translation to Why3 for formal property verification using theorem provers.

Findings

Successfully verified Lyapunov stability of a discrete system

Developed a library of theories for Simulink blocks in Why3

Automated translation from Simulink to Why3 achieved

Abstract

This paper presents the deductive formal verification of high-level properties of control systems with theorem proving, using the Why3 tool. Properties that can be verified with this approach include stability, feedback gain, and robustness, among others. For the systems, modelled in Simulink, we propose three main steps to achieve the verification: specifying the properties of interest over the signals within the model using Simulink blocks, an automatic translation of the model into Why3, and the automatic verification of the properties with theorem provers in Why3. We present a methodology to specify the properties in the model and a library of relevant assertion blocks (logic expressions), currently in development. The functionality of the blocks in the Simulink models are automatically translated to Why3 as theories and verification goals by our tool implemented in MATLAB. A library of theories in Why3 corresponding to each supported block has been developed to facilitate the process of translation. The goals are automatically verified in Why3 with relevant theorem provers. A simple first-order discrete system is used to exemplify the specification of the Simulink model, the translation process from Simulink to the Why3 formal logic language, and the verification of Lyapunov stability.