Encrypted Model Predictive Control of a Nonlinear Chemical Process Network

Abstract

This work focuses on developing and applying Encrypted Lyapunov-based Model Predictive Control (LMPC) in a nonlinear chemical process network for Ethylbenzene production. The network, governed by a nonlinear dynamic model, comprises two continuously stirred tank reactors that are connected in series and is simulated using Aspen Plus Dynamics. For enhancing system cybersecurity, the Paillier cryptosystem is employed for encryption–decryption operations in the communication channels between the sensor–controller and controller–actuator, establishing a secure network infrastructure. Cryptosystems generally require integer inputs, necessitating a quantization parameter d, for quantization of real-valued signals. We utilize the quantization parameter to quantize process measurements and control inputs before encryption. Through closed-loop simulations under the encrypted LMPC scheme, where the LMPC uses a first-principles nonlinear dynamical model, we examine the effect of the quantization parameter on the performance of the controller and the overall encryption to control the input calculation time. We illustrate that the impact of quantization can outweigh those of plant/model mismatch, showcasing this phenomenon through the implementation of a first-principles-based LMPC on an Aspen Plus Dynamics process model. Based on the findings, we propose a strategy to mitigate the quantization effect on controller performance while maintaining a manageable computational burden on the control input calculation time.