Sparse Sensing and Optimal Precision: An Integrated Framework for H₂/H_∞ Optimal Observer Design

Abstract

We present a framework which incorporates three aspects of the estimation problem, namely, sparse sensor configuration, optimal precision, and robustness in the presence of model uncertainty. The problem is formulated in the H∞ optimal observer design framework. We consider two types of uncertainties in the system, i.e. structured affine and unstructured uncertainties. The objective is to design an observer with a given H∞ performance index with minimal number of sensors and minimal precision values, while guaranteeing the performance for all admissible uncertainties. The problem is posed as a convex optimization problem subject to linear matrix inequalities. Numerical simulations demonstrate the application of the theoretical results presented in this work.

Sensor Placement with Optimal Precision for Temperature Estimation of Battery Systems

“…Following the notation in [15], we define an output vector of interest, z(t), that we wish to estimate…”

“…Therefore, we seek to determine the sensor precisions p such that G(s) H∞ < γ, and l 1 -norm of the precision vector p 1 is minimized. To this end, we adopt the result from [15] for H ∞ observer design with the optimal precisions to write the inequality G(s) H∞ < γ as a matrix inequality.…”

“…In particular, the following holds [15], [17] G(s) H∞ < γ ⇐⇒ ∃X > 0 such that M (p, X, Y ) < 0 where M (p, X, Y ) is a matrix defined as follows…”

“…. Remark 1: The cost function in the optimization problem (11) can be trivially replaced with the weighted l 1 -norm of the sensor precisions [15]. In a complex battery model where different kinds of sensors are used for battery health monitoring, weighted l 1 -norm can penalize different sensor precisions to different extents accounting for the difference in sensors' economic cost.…”

Sensor Selection and Optimal Precision in $\mathcal{H}_2/\mathcal{H}_{\infty}$ Estimation Framework: Theory and Algorithms

“…Adopting the idea of variable sensor precisions from [19], our recent work [22] addressed the problem of observer design with given performance bound in both H 2 and H ∞ frameworks while simultaneously minimizing the required sensor precisions and promoting sparseness in the sensor configuration. We also discussed an extension of this work for uncertain models in an H ∞ framework in our most recent paper [23].…”