Data-Driven Observability Analysis for Nonlinear Stochastic Systems

IEEE Transactions on Automatic Control, vol. 69, pp. 4042–4049

Abstract

Distinguishability and, by extension, observability are key properties of dynamical systems. Establishing these properties is challenging, especially when no analytical model is available and they are to be inferred directly from measurement data. The presence of noise further complicates this analysis, as standard notions of distinguishability are tailored to deterministic systems. We build on distributional distinguishability, which extends the deterministic notion by comparing distributions of outputs of stochastic systems. We first show that both concepts are equivalent for a class of systems that includes linear systems. We then present a method to assess and quantify distributional distinguishability from output data. Specifically, our quantification measures how much data is required to tell apart two initial states, inducing a continuous spectrum of distinguishability. We propose a statistical test to determine a threshold above which two states can be considered distinguishable with high confidence. We illustrate these tools by computing distinguishability maps over the state space in simulation, then leverage the test to compare sensor configurations on hardware.

Authors 5

1. Pierre-François Massiani Aachen Institute for Data Science in Mechanical Engineering

   RWTH Aachen University

   Affiliation as printed

   Institute for Data Science in Mechanical Engineering, RWTH Aachen University, Aachen, Germany

2. Mona Buisson-Fenet Aachen Institute for Data Science in Mechanical Engineering

   Ansys (France) · RWTH Aachen University

   Affiliation as printed

   Institute for Data Science in Mechanical Engineering, RWTH Aachen University, Aachen, Germany

   Ansys Research Team, Ansys France, Villeurbanne, France

3. Friedrich Solowjow Aachen Institute for Data Science in Mechanical Engineering

   RWTH Aachen University

   Affiliation as printed

   Institute for Data Science in Mechanical Engineering, RWTH Aachen University, Aachen, Germany

4. Florent Di Meglio

   Université Paris Sciences et Lettres · Centre Automatique et Systèmes · École Nationale Supérieure des Mines de Paris

   Affiliation as printed

   Centre Automatique et Systèmes, Mines Paris—PSL University, Paris, France

5. Sebastian Trimpe Aachen Institute for Data Science in Mechanical Engineering

   RWTH Aachen University

   Affiliation as printed

   Institute for Data Science in Mechanical Engineering, RWTH Aachen University, Aachen, Germany