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System Design Approach for Control of Differentially Private Dynamical Systems

Raman Goyal, Dhrubajit Chowdhury, Shantanu Rane

TL;DR

This paper introduces a novel approach to concurrently design dynamic controllers and correlated differential privacy noise in dynamic control systems that optimizes the noise distribution while shaping closed-loop system dynamics such that the privacy noise has the least impact on system performance and the most effect on system privacy.

Abstract

This paper introduces a novel approach to concurrently design dynamic controllers and correlated differential privacy noise in dynamic control systems. An increase in privacy noise increases the system's privacy but adversely affects the system's performance. Our approach optimizes the noise distribution while shaping closed-loop system dynamics such that the privacy noise has the least impact on system performance and the most effect on system privacy. We further add privacy noise to both control input and system output to privatize the system's state for an adversary with access to both communication channels and direct output measurements. The study also suggests tailored privacy bounds for different states, providing a comprehensive framework for jointly optimizing system performance and privacy in the context of differential privacy.

System Design Approach for Control of Differentially Private Dynamical Systems

TL;DR

This paper introduces a novel approach to concurrently design dynamic controllers and correlated differential privacy noise in dynamic control systems that optimizes the noise distribution while shaping closed-loop system dynamics such that the privacy noise has the least impact on system performance and the most effect on system privacy.

Abstract

This paper introduces a novel approach to concurrently design dynamic controllers and correlated differential privacy noise in dynamic control systems. An increase in privacy noise increases the system's privacy but adversely affects the system's performance. Our approach optimizes the noise distribution while shaping closed-loop system dynamics such that the privacy noise has the least impact on system performance and the most effect on system privacy. We further add privacy noise to both control input and system output to privatize the system's state for an adversary with access to both communication channels and direct output measurements. The study also suggests tailored privacy bounds for different states, providing a comprehensive framework for jointly optimizing system performance and privacy in the context of differential privacy.
Paper Structure (10 sections, 7 theorems, 53 equations, 5 figures, 1 table)

This paper contains 10 sections, 7 theorems, 53 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Review of Differential Privacy
  3. Problem Formulation
  4. Relationship between differential privacy and error in state estimates due to control input and output privacy noise
  5. Final Design Solution Development
  6. Adversary with access to communication channels
  7. Adversary with direct access to measurements
  8. Estimator for unstable systems
  9. Simulation Results
  10. Conclusion

Key Result

Lemma 1

(Gaussian mechanism; le2013differentially): Let us use privacy parameters $\epsilon>0$ and $\delta \in(0,1 / 2)$ and adjacency parameter $\beta>0$. Let $\mathcal{G}$ denote a dynamical system and $\Delta_2\mathcal{G}$ denote its 2-norm sensitivity. Then the Gaussian mechanism $\mathcal{M} = \mathcal

Figures (5)

  • Figure 1: Design architecture for making agent's state differentially private by adding privacy noise to both system inputs and output.
  • Figure 2: Interconnected four‐area power distribution system
  • Figure 3: Optimal input private noise for given values of differential privacy for (L) an adversary with access to communication channels ($y^a_k = \bar{y}_k$), and (R) an adversary with direct access to measurements ($y^a_k = y_k$).
  • Figure 4: Optimal output private noise for given values of differential privacy for (L) an adversary with access to communication channels ($y^a_k = \bar{y}_k$), and (R) an adversary with direct access to measurements ($y^a_k = y_k$).
  • Figure 5: Optimal system performance norm for given values of differential privacy for (L) an adversary with access to communication channels ($y^a_k = \bar{y}_k$), and (R) an adversary with direct access to measurements ($y^a_k = y_k$).

Theorems & Definitions (18)

  • Definition 1
  • Definition 2
  • Definition 3
  • Lemma 1
  • Lemma 2
  • Remark 1
  • Lemma 3
  • proof
  • Remark 2
  • Remark 3
  • ...and 8 more