Encrypted optimization-based control for networked systems
Developing the foundations for optimization-based encrypted control.
Due to more complex system structures, future control strategies will increasingly rely on cloud-computing and distributed computing. The related transmission of sensitive data via public networks and processing of data on third party hardware platforms require new security concepts for the controller evaluation. In an ideal setup, the process data would be permanently encrypted on its way from the sensor, through the controller in the cloud, to the actuator. The realization of such a setup requires the encrypted evaluation of the control algorithm based on encrypted process data (e.g., system states). In this context, it is remarkably that the encrypted evaluation of algorithms can, in principle, be realized based on homomorphic encryption schemes (such as the Paillier cryptosystem). Unfortunately, in practice, the encryption only works for simple algorithms since solely encrypted sums or multiplications can be carried out (with a reasonable numerical effort). Yet, these operations already allow the encrypted evaluation of simple control laws such as linear state feedback. The research project addresses the encrypted evaluation of more complex and powerful networked control schemes. In this context, a key aspect is the encryption of model predictive control (MPC) schemes. MPC requires the recurring solution of an optimal control problem (OCP) during runtime. This fact raises the question of how encrypted MPC can be implemented based on the limited selection of encrypted operations. In two preliminary works of this project, it has been shown that encrypted MPC can be realized based on the explicit solution of the multiparametric OCP or based on real-time-iterations of projected gradient schemes. However, both approaches build on restrictive assumptions and lead to suboptimal controller architectures. The elimination of these restrictions is one of the main goals of the project. Achieving this goal requires efficient procedures for the encrypted solution of OCPs. A promising strategy to solve this task builds on the combination of modern cryptographic methods (such as leveled homomorphic encryption) with elaborated control schemes (based on real-time-ADMM or neural networks). Another focus of the research project lies on extensions of the novel security concept through the consideration of realistic attack models and the inclusion of authentication (via digital signatures).
Related publications
J. Adamek, P. Binfet, N. Schlüter, and M. Schulze Darup, Encrypted system identification as-a-service via reliable encrypted matrix inversion, 63rd IEEE Conference on Decision and Control (CDC), 2024 (accepted). Preprint: arxiv.org/abs/2410.20575
N. Schlüter, J. Kim, M. Schulze Darup, A Code-Driven Tutorial on Encrypted Control: From Pioneering Realizations to Modern Implementations. European Control Conference (ECC), 2024. DOI: 10.23919/ECC64448.2024.10590948, Preprint: https://arxiv.org/html/2404.04727v1
N. Schlüter, P. Binfet and M. Schulze Darup, A brief survey on encrypted control: From the first to the second generation and beyond, Annual Reviews in Control, 2023. DOI: 10.1016/j.arcontrol.2023.100913
P. Binfet, J. Adamek, N. Schlüter and M. Schulze Darup, Towards privacy-preserving cooperative control via encrypted distributed optimization, at - Automatisierungstechnik, vol. 71, no. 9, pp. 736-747, 2023. DOI: 10.1515/auto-2023-0082
P. Binfet, N.Schlüter and M. Schulze Darup. On the security of randomly transformed quadratic programs related to privacy-preserving cloud-based control, 62nd IEEE Conference on Decision and Control (CDC), 2023. Preprint: arXiv.2311.05215
P. Binfet, N. Schlüter, and M. Schulze Darup. Cryptanalysis of Random Affine Transformations for Encrypted Control, 22nd IFAC World Congress, pp. 11209-11216, 2023. DOI: 10.1016/j.ifacol.2023.10.848, Preprint: arXiv.2304.06582
N. Schlüter and M. Schulze Darup, On the stability of linear dynamic controllers with integer coefficients, IEEE Transactions on Automatic Control, 67(10): pp. 5610-5613, 2022. DOI: 10.1109/TAC.2021.3131126
N. Schlüter, P. Binfet, J. Kim, and M. Schulze Darup, Encrypted distributed state estimation via affine averaging, in Proc. of the 61st IEEE Conference on Decision and Control (CDC), pp. 7754-7761, 2022. DOI: 10.1109/CDC51059.2022.9992840, Preprint: arXiv:2209.07206
J. Kim, M. Schulze Darup, and H. Sandberg, and K. H. Johansson, Asymptotic stabilization over encrypted data with limited controller capacity and time-varying quantizer, in Proc. of the 61st IEEE Conference on Decision and Control (CDC), pp. 7762-7767, 2022. DOI: 10.1109/CDC51059.2022.9993215
N. Schlüter, M. Neuhaus, and M. Schulze Darup, Encrypted extremum seeking for privacy-preserving PID tuning as-a-Service, in Proc. of the 2022 European Control Conference (ECC), pp. 1288-1293, 2022. DOI: 10.23919/ECC55457.2022.9838380, Preprint: arXiv.2207.04442
M. Schulze Darup, A. B. Alexandru, G. J. Pappas, and D. Quevedo, Encrypted control for networked systems - An illustrative introduction and current challenges, IEEE Control Systems Magazine, 41(3): pp. 58–78, 2021. DOI: 10.1109/MCS.2021.3062956, Preprint: arXiv:2010.00268
M. Schulze Darup, A. Redder, and D. Quevedo, Encrypted cooperative control based on structured feedback, IEEE Control System Letters, 3(1): pp. 37-42, 2019. DOI: 10.1109/LCSYS.2018.2851152
M. Schulze Darup, A. Redder, I. Shames, F. Farokhi, and D. Quevedo, Towards encrypted MPC for linear constrained systems, IEEE Control System Letters, 2(2): pp. 195-200, 2018. DOI: 10.1109/LCSYS.2017.2779473