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A Control-Recoverable Added-Noise-based Privacy Scheme for LQ Control in Networked Control Systems

Xuening Tang, Xianghui Cao, Wei Xing Zheng

TL;DR

A secure control scheme for computing linear quadratic control in a networked control system utilizing two networked controllers, a privacy encoder, and a control restorer that effectively preserves the privacy of the control system's state without sacrificing the control performance.

Abstract

As networked control systems continue to evolve, ensuring the privacy of sensitive data becomes an increasingly pressing concern, especially in situations where the controller is physically separated from the plant. In this paper, we propose a secure control scheme for computing linear quadratic control in a networked control system utilizing two networked controllers, a privacy encoder and a control restorer. Specifically, the encoder generates two state signals blurred with random noise and sends them to the controllers, while the restorer reconstructs the correct control signal. The proposed design effectively preserves the privacy of the control system's state without sacrificing the control performance. We theoretically quantify the privacy-preserving performance in terms of the state estimation error of the controllers and the disclosure probability. Moreover, we extend the proposed privacy-preserving scheme and evaluation method to cases where collusion between two controllers occurs. Finally, we verify the validity of our proposed scheme through simulations.

A Control-Recoverable Added-Noise-based Privacy Scheme for LQ Control in Networked Control Systems

TL;DR

A secure control scheme for computing linear quadratic control in a networked control system utilizing two networked controllers, a privacy encoder, and a control restorer that effectively preserves the privacy of the control system's state without sacrificing the control performance.

Abstract

As networked control systems continue to evolve, ensuring the privacy of sensitive data becomes an increasingly pressing concern, especially in situations where the controller is physically separated from the plant. In this paper, we propose a secure control scheme for computing linear quadratic control in a networked control system utilizing two networked controllers, a privacy encoder and a control restorer. Specifically, the encoder generates two state signals blurred with random noise and sends them to the controllers, while the restorer reconstructs the correct control signal. The proposed design effectively preserves the privacy of the control system's state without sacrificing the control performance. We theoretically quantify the privacy-preserving performance in terms of the state estimation error of the controllers and the disclosure probability. Moreover, we extend the proposed privacy-preserving scheme and evaluation method to cases where collusion between two controllers occurs. Finally, we verify the validity of our proposed scheme through simulations.
Paper Structure (21 sections, 10 theorems, 71 equations, 5 figures, 1 table, 1 algorithm)

This paper contains 21 sections, 10 theorems, 71 equations, 5 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Linear Quadratic (LQ) Formulation
  4. Problem Statements
  5. Privacy Preserving Algorithm
  6. Privacy-preserving Performance Analysis
  7. State Estimation of Controller
  8. Privacy-Preserving Performance Analysis
  9. The Case When The Controllers Collude
  10. Privacy-Preserving Algorithm
  11. Privacy-Preserving Performance Analysis
  12. Discussion
  13. Simulation Study
  14. Conclusion
  15. Proof of Theorem \ref{['theorem:error bounds']}
  16. ...and 6 more sections

Key Result

Theorem 1

The error covariance matrix $P(k)$ of the state estimate is bounded as follows: where $P(k)$ is defined and given as in defpk and eq:KF:sigma, respectively.

Figures (5)

  • Figure 1: The proposed privacy preserving framework.
  • Figure 2: The trajectories of $x(k)$, $\tilde{x}(k)$, $\hat{x}(k)$ and the state estimation performance in the non-collusion case.
  • Figure 3: The trajectories of $\delta(k)$ and $\bar{\delta}$ and in the non-collusion case.
  • Figure 4: Comparison of the LQ control performance in terms of $\Delta J$ under different schemes in the non-collusion case.
  • Figure 5: The trajectories of the disclosure probability $\delta(k)$ and its upper bound $\bar{\delta}$ in the colluding case.

Theorems & Definitions (14)

  • Definition 1: he2018preserving
  • Remark 1
  • Remark 2
  • Theorem 1
  • Lemma 1
  • Theorem 2
  • Theorem 3
  • Remark 3
  • Corollary 1
  • Theorem 4
  • ...and 4 more