Comparison and performance analysis of dynamic encrypted control approaches

TL;DR

Recent approaches to dynamic encrypted control, such as bootstrapping, periodic resets of the controller state, integer reformulations, and FIR controllers are reviewed and equipped with a stability and performance analysis to evaluate their suitability.

Abstract

Encrypted controllers using homomorphic encryption have proven to guarantee the privacy of measurement and control signals, as well as system and controller parameters, while regulating the system as intended. However, encrypting dynamic controllers has remained a challenge due to growing noise and overflow issues in the encoding. In this paper, we review recent approaches to dynamic encrypted control, such as bootstrapping, periodic resets of the controller state, integer reformulations, and FIR controllers, and equip them with a stability and performance analysis to evaluate their suitability. We complement the analysis with a numerical performance comparison on a benchmark system.

Figures (4)

• Figure 3: The modulo function and its polynomial approximation for bootstrapping.
• Figure 4: Relative error of the polynomial approximation to the modulo function for bootstrapping. The figure shows multiple error functions since the bootstrapping polynomial in Fig. \ref{['fig:modPoly']} is evaluated at different intervals depending on the offset $rq$.
• Figure 5: Pole shift by $K x_c$ (and transformation) such that $A_{\mathbb{Z}}$ is an integer matrix.
• Figure 6:

Theorems & Definitions (5)

• Theorem 1
• Lemma 1
• Theorem 2
• Theorem 3
• Theorem 4