Formal Analysis of Robustness at Model and Code Level

Abstract

Robustness analyses play a major role in the synthesis and analysis of controllers. For control systems, robustness is a measure of the maximum tolerable model inaccuracies or perturbations that do not destabilize the system. Analyzing the robustness of a closed-loop system can be performed with multiple approaches: gain and phase margin computation for single-input single-output (SISO) linear systems, mu analysis, IQC computations, etc. However, none of these techniques consider the actual code in their analyses.The approach presented here relies on an invariant computation on the discrete system dynamics. Using semi-definite programming (SDP) solvers, a Lyapunov-based function is synthesized that captures the vector margins of the closedloop linear system considered. This numerical invariant expressed over the state variables of the system is compatible with code analysis and enables its validation on the code artifact.This automatic analysis extends verification techniques focused on controller implementation, addressing validation of robustness at model and code level. It has been implemented in a tool analyzing discrete SISO systems and generating over-approximations of phase and gain margins. The analysis will be integrated in our toolchain for Simulink and Lustre models autocoding and formal analysis.

Verifying fragility in digital systems with uncertainties using DSVerifier v2.0

“…Earth [70]. The eighth benchmark, which is represented by controller C 8 and plant G 8 , with a sample time of 0.001s, considers a discrete model for a simple spring-mass damper plant [71].…”

Program Synthesis for Program Analysis

“…The first set of benchmarks uses the discrete plant of a cruise control model for a car, and accounts for rolling friction, aerodynamic drag, and the gravitational disturbance force [5]. The second set of benchmarks considers a simple spring-mass damper [81]. A third set of benchmarks uses a physical plant for satellite applications [41].…”

Preserving Functional Correctness of Cyber-Physical System Controllers: From Model to Code

“…numerical invariants over state variables. As an example, we have revisited the computation of phase and gain margin using this lemma and characterized the appropriate numerical property [36].…”