ARX-Implementation of encrypted nonlinear dynamic controllers using observer form

TL;DR

This paper presents a method for implementing encrypted nonlinear dynamic controllers using an ARX model and observer form, enabling finite operations on encrypted data while maintaining control accuracy.

Contribution

It introduces a novel ARX-based reformulation of nonlinear controllers with observer form for encrypted control systems, ensuring finite operations and stability.

Findings

Finite-operations ARX model enables encrypted control.

Stable observer ensures control accuracy.

Simulation confirms effectiveness of the approach.

Abstract

While computation-enabled cryptosystems applied to control systems have improved security and privacy, a major issue is that the number of recursive operations on encrypted data is limited to a finite number of times in most cases, especially where fast computation is required. To allow for nonlinear dynamic control under this constraint, a method for representing a state-space system model as an auto-regressive model with exogenous inputs (ARX model) is proposed. With the input as well as the output of the plant encrypted and transmitted to the controller, the reformulated ARX form can compute each output using only a finite number of operations, from its several previous inputs and outputs. Existence of a stable observer for the controller is a key condition for the proposed representation. The representation replaces the controller with an observer form and applies a method similar to finite-impulse-response approximation. It is verified that the approximation error and its effect can be made arbitrarily small by an appropriate choice of a parameter, under stability of the observer and the closed-loop system. Simulation results demonstrate the effectiveness of the proposed method.