Formal Methods for the Analysis of Critical Control Systems Models: Combining Non-linear and Linear Analyses

Abstract

Critical control systems are often built as a combination of a control core with safety mechanisms allowing to recover from failures. For example a PID controller used with triplicated inputs and voting. Typically these systems would be designed at the model level in a synchronous language like Lustre or Simulink, and their code automatically generated from these models. We present a new analysis framework combining the analysis of open-loop stable controllers with safety constructs (redundancy, voters, ...). We introduce the basic analysis approaches: abstract interpretation synthesizing quadratic invariants and backward analysis based on quantifier elimination and convex hull computation synthesizing linear invariants. Then we apply it on a simple but representative example that no other available state-of-the-art technique is able to analyze. This contribution is another step towards early use of formal methods for critical embedded software such as the ones of the aerospace industry.

Formal Analysis of Robustness at Model and Code Level

“…These numerical analyses work on the model level representation of the systems, i.e., without complex pointers and memory issues, but they consider floating-point semantics. A more detailed explanation of these interactions between solvers is presented in [6].…”

Verification and Validation of Convex Optimization Algorithms for Model Predictive Control

“…As well, no formal verification is performed. On the other hand, some contributions have been made concerning formal verification of control systems [7][8][9][10], but they mainly focus on formal verification and code generation for linear control systems.…”