Recursive Binary Identification under Data Tampering and Non-Persistent Excitation with Application to Emission Control

TL;DR

This paper introduces recursive algorithms for online parameter estimation in cyber-physical systems with binary outputs under data tampering, achieving convergence and robustness without persistent excitation, and demonstrates their effectiveness in emission control.

Contribution

It develops first- and second-order recursive algorithms for tampering-resilient online estimation, extending to adaptive control and validating through simulations and a vehicle emission application.

Findings

Algorithms converge almost surely under tampering.

Second-order method achieves faster convergence without persistent excitation.

Effective in detecting excess-emission events in vehicle control.

Abstract

This paper studies the problem of online parameter estimation for cyber-physical systems with binary outputs that may be subject to adversarial data tampering. Existing methods are primarily offline and unsuitable for real-time learning. To address this issue, we first develop a first-order gradient-based algorithm that updates parameter estimates recursively using incoming data. Considering that persistent excitation (PE) conditions are difficult to satisfy in feedback control scenarios, a second-order quasi-Newton algorithm is proposed to achieve faster convergence without requiring the PE condition. For both algorithms, corresponding versions are developed to handle known and unknown tampering strategies, and their parameter estimates are proven to converge almost surely over time. In particular, the second-order algorithm ensures convergence under a signal condition that matches the minimal excitation required by classical least-squares estimation in stochastic regression models. The second-order algorithm is also extended to an adaptive control framework, providing an explicit upper bound on the tracking error for binary-output FIR systems under unknown tampering. Three numerical simulations verify the theoretical results and show that the proposed methods are robust against data tampering. Finally, the approach is validated via a vehicle emission control problem, where it effectively improves the detection accuracy of excess-emission events.