State-Robust Observability Measures for Sensor Selection in Nonlinear Dynamic Systems

TL;DR

This paper introduces a robust sensor selection method for nonlinear dynamical systems using modified observability measures and efficient algorithms, improving robustness to initial state uncertainties.

Contribution

It proposes a novel state-averaged observability measure and demonstrates that sensor selection retains submodularity, enabling efficient and robust sensor placement in nonlinear systems.

Findings

Method is validated on a combustion reaction network.

Sensor selection retains submodular properties for efficient optimization.

Approach shows increased robustness to initial state uncertainties.

Abstract

This paper explores the problem of selecting sensor nodes for a general class of nonlinear dynamical networks. In particular, we study the problem by utilizing altered definitions of observability and open-loop lifted observers. The approach is performed by discretizing the system's dynamics using the implicit Runge-Kutta method and by introducing a state-averaged observability measure. The observability measure is computed for a number of perturbed initial states in the vicinity of the system's true initial state. The sensor node selection problem is revealed to retain the submodular and modular properties of the original problem. This allows the problem to be solved efficiently using a greedy algorithm with a guaranteed performance bound while showing an augmented robustness to unknown or uncertain initial conditions. The validity of this approach is numerically demonstrated on a $H_{2}/O_{2}$ combustion reaction network.