Optimal State Estimation Synthesis over Unreliable Network in Presence of Denial-of-Service Attack: an Operator Framework Approach

TL;DR

This paper develops an operator-based framework for designing optimal state estimators resilient to DoS attacks, ensuring minimal worst-case estimation error through convex optimization.

Contribution

It introduces a novel operator framework for state estimation under DoS attacks, enabling tractable convex optimization for optimal estimator design.

Findings

The estimator can be represented as a generalized Luenberger observer with an operator gain.

Optimal estimation error can be minimized via a linear programming approach.

The framework handles unbounded operator gains, extending classical observer design.

Abstract

In this paper, we consider the problem of state-estimation in the presence of Denial-of-Service (DoS) attack. We formulate this problem as an state estimation problem for a plant with switching measured outputs. In the absence of attack, the state-estimator has access to all measured outputs, however, in the presence of attack, only a subset of all measurements are made available to the state-estimator. We seek to find an state-estimator that results in the minimum estimation error for the worst-case attack strategy. First, we parameterize the set of all state-estimators that result in stable estimation error for the worst-case attack scenario. Then, we will show that any state-estimator in this set can be written as a generalized Luenberger observer with an appropriately defined observer-gain. This observer-gain, in general, can be an operator and possibly unbounded as opposed to the classical static observer-gain. Furthermore, we will show that finding the optimal state-estimator that results in the minimum estimation error can be cast as a convex program over the set of stable factors of the observer operator-gain. This optimization in, in fact, linear programming and tractable.