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Explicit Model Predictive Control with Quantum Encryption

Yingjie Mi, Zihao Ren, Lei Wang, Daniel E. Quevedo, Guodong Shi

Abstract

This paper studies quantum-encrypted explicit MPC for constrained discrete-time linear systems in a cloud-based architecture. A finite-horizon quadratic MPC problem is solved offline to obtain a piecewise-affine controller. Shared quantum keys generated from Bell pairs and protected by quantum key distribution are used to encrypt the online control evaluation between the sensor and actuator. Based on this architecture, we develop a lightweight encrypted explicit MPC protocol, prove exact recovery of the plaintext control action, and characterize its computational efficiency. Numerical results demonstrate lower online complexity than classical encrypted MPC, while security is discussed in terms of confidentiality of plant data and control inputs.

Explicit Model Predictive Control with Quantum Encryption

Abstract

This paper studies quantum-encrypted explicit MPC for constrained discrete-time linear systems in a cloud-based architecture. A finite-horizon quadratic MPC problem is solved offline to obtain a piecewise-affine controller. Shared quantum keys generated from Bell pairs and protected by quantum key distribution are used to encrypt the online control evaluation between the sensor and actuator. Based on this architecture, we develop a lightweight encrypted explicit MPC protocol, prove exact recovery of the plaintext control action, and characterize its computational efficiency. Numerical results demonstrate lower online complexity than classical encrypted MPC, while security is discussed in terms of confidentiality of plant data and control inputs.
Paper Structure (16 sections, 3 theorems, 37 equations, 3 figures, 4 tables, 1 algorithm)

This paper contains 16 sections, 3 theorems, 37 equations, 3 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background
  3. Linear-Quadratic MPC
  4. Explicit MPC
  5. Explicit MPC with Encryption for Networked Systems
  6. Quantum Encrypted MPC
  7. Quantum Encrypted Explicit MPC
  8. Effectiveness
  9. Quantization and Computational Efficiency
  10. Bit-cost model
  11. Numerical Example
  12. Simulation Setup
  13. Effectiveness
  14. Computational Efficiency
  15. Confidentiality
  16. ...and 1 more sections

Key Result

Theorem 1

Under standard nondegeneracy conditions, there exists a finite polyhedral partition $\{\mathcal{P}^{(\sigma)}\}_{\sigma=1}^{s}$ of the feasible state set such that the explicit MPC feedback is piecewise affine where $\sigma\in\{1,\ldots,s\}$ denotes the region index, $s\in\mathbb{N}$ is the number of regions, and $K^{(\sigma)}\in\mathbb{R}^{m\times n}$, $b^{(\sigma)}\in\mathbb{R}^{m}$.

Figures (3)

  • Figure 1: Architecture of the proposed quantum-encrypted explicit MPC. The sensor identifies the active region and encrypts the state and affine offset, the cloud evaluates the encrypted affine law, and the actuator decrypts the control input using shared keys generated via a quantum channel.
  • Figure 2: Effectiveness of QE-MPC. Top: closed-loop tracking responses of plaintext explicit MPC and QE-MPC under the same reference signal. Bottom: per-step input mismatch $|u_{\mathrm{QE-MPC}}-u_{\mathrm{plain}}|$, showing machine-precision agreement between encrypted and plaintext evaluations.
  • Figure 3: Tracking error $\mathrm{RMSE}(y-r)$ versus payload bits per cycle for plaintext, Paillier, RSA, AES, and QE-MPC. QE-MPC attains the same low-error regime with a substantially smaller payload than the classical encrypted baselines.

Theorems & Definitions (5)

  • Theorem 1
  • Theorem 2
  • proof
  • Theorem 3
  • proof