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Privacy-Preserving Nonlinear Cloud-based Model Predictive Control via Affine Masking

Kaixiang Zhang, Zhaojian Li, Yongqiang Wang, Nan Li

TL;DR

This work tackles privacy in cloud-based nonlinear MPC by introducing an affine masking scheme that transforms states and inputs via invertible maps, yielding an equivalent transformed MPC problem that preserves performance. It formalizes an $\ ty$-diversity with unbounded diameter privacy notion and proves that external eavesdroppers or honest-but-curious clouds cannot infer private signals from the transformed data. The approach extends to output-feedback MPC and is validated through simulations (e.g., quadrotor) showing identical control performance while significantly obscuring private information, with favorable comparisons to encryption-based and other transformation-based methods. The method offers computationally light privacy preservation suitable for real-time cloud-assisted control and opens avenues for further refinement of privacy metrics and robustness.

Abstract

With the advent of 5G technology that presents enhanced communication reliability and ultra low latency, there is renewed interest in employing cloud computing to perform high performance but computationally expensive control schemes like nonlinear model predictive control (MPC). Such a cloud-based control scheme, however, requires data sharing between the plant (agent) and the cloud, which raises privacy concerns. This is because privacy-sensitive information such as system states and control inputs has to be sent to/from the cloud and thus can be leaked to attackers for various malicious activities. In this paper, we develop a simple yet effective affine masking strategy for privacy-preserving nonlinear MPC. Specifically, we consider external eavesdroppers or honest-but-curious cloud servers that wiretap the communication channel and intend to infer the plant's information including state information and control inputs. An affine transformation-based privacy-preservation mechanism is designed to mask the true states and control signals while reformulating the original MPC problem into a different but equivalent form. We show that the proposed privacy scheme does not affect the MPC performance and it preserves the privacy of the plant such that the eavesdropper is unable to identify the actual value or even estimate a rough range of the private state and input signals. The proposed method is further extended to achieve privacy preservation in cloud-based output-feedback MPC. Simulations are performed to demonstrate the efficacy of the developed approaches.

Privacy-Preserving Nonlinear Cloud-based Model Predictive Control via Affine Masking

TL;DR

This work tackles privacy in cloud-based nonlinear MPC by introducing an affine masking scheme that transforms states and inputs via invertible maps, yielding an equivalent transformed MPC problem that preserves performance. It formalizes an -diversity with unbounded diameter privacy notion and proves that external eavesdroppers or honest-but-curious clouds cannot infer private signals from the transformed data. The approach extends to output-feedback MPC and is validated through simulations (e.g., quadrotor) showing identical control performance while significantly obscuring private information, with favorable comparisons to encryption-based and other transformation-based methods. The method offers computationally light privacy preservation suitable for real-time cloud-assisted control and opens avenues for further refinement of privacy metrics and robustness.

Abstract

With the advent of 5G technology that presents enhanced communication reliability and ultra low latency, there is renewed interest in employing cloud computing to perform high performance but computationally expensive control schemes like nonlinear model predictive control (MPC). Such a cloud-based control scheme, however, requires data sharing between the plant (agent) and the cloud, which raises privacy concerns. This is because privacy-sensitive information such as system states and control inputs has to be sent to/from the cloud and thus can be leaked to attackers for various malicious activities. In this paper, we develop a simple yet effective affine masking strategy for privacy-preserving nonlinear MPC. Specifically, we consider external eavesdroppers or honest-but-curious cloud servers that wiretap the communication channel and intend to infer the plant's information including state information and control inputs. An affine transformation-based privacy-preservation mechanism is designed to mask the true states and control signals while reformulating the original MPC problem into a different but equivalent form. We show that the proposed privacy scheme does not affect the MPC performance and it preserves the privacy of the plant such that the eavesdropper is unable to identify the actual value or even estimate a rough range of the private state and input signals. The proposed method is further extended to achieve privacy preservation in cloud-based output-feedback MPC. Simulations are performed to demonstrate the efficacy of the developed approaches.
Paper Structure (11 sections, 3 theorems, 28 equations, 5 figures, 1 table)

This paper contains 11 sections, 3 theorems, 28 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Cloud-based MPC
  4. Attack Model
  5. Main Results
  6. Affine masking and problem reformulation
  7. Privacy Preservation
  8. Discussion on Privacy Notion and Protection Scheme
  9. Extension to Output-feedback MPC
  10. Simulation Results
  11. Conclusion

Key Result

Lemma 1

Under the affine transformation mechanism, the optimization problem $\textbf{P-2}$ is equivalent to $\textbf{P-1}$, i.e., if $\bar{\bm{U}}^{*}_{k}=^{\top}$ is a local (resp. global) minimizer of $\textbf{P-2}$, then the transformed control via inverse mapping $\bm{U}^{*}_{k} =^{\top} = ^{\top}$ is a

Figures (5)

  • Figure 1: Cloud-based conventional MPC architecture.
  • Figure 2: Cloud-based privacy-preserving MPC architecture with affine masking.
  • Figure 3: System state evolution of conventional and privacy-preserving state-feedback MPC. C-MPC refers to conventional MPC and PP-MPC refers to privacy-preserving MPC.
  • Figure 4: System input evolution of conventional and privacy-preserving state-feedback MPC.
  • Figure 5: Trajectory evolution of the quadrotor, resulting from Method 1 DarupIFAC2018, Method 2 SultangazinTAC2021, and the proposed method.

Theorems & Definitions (11)

  • Remark 1
  • Lemma 1
  • proof
  • Definition 1: $\infty$-Diversity with Unbounded Diameter
  • Theorem 1
  • proof
  • Remark 2
  • Remark 3
  • Theorem 2
  • proof
  • ...and 1 more