(299e) Quantum Technologies and Model Predictive Control

Quantum computation is becoming more widespread, and as a result, it is being investigated for what its potential benefits might be within process systems engineering. Already, works has been done to relate quantum computing to, for example, machine learning and optimization related to faults in industrial systems [1-4]. However, there are relatively few works considering the relationship of control and quantum computing. For example, a model predictive controller for a linear system was implemented on a quantum annealer [5], and there have also been works exploring, for example, preliminary reinforcement learning algorithms within a quantum computing framework [6-8].

We have recently begun to introduce quantum computation within the process control context [9]. Our premise is that, because it is currently unknown whether there exist quantum computing algorithms which might speed up control law execution (particularly for advanced controllers) compared to classical computers, it is necessary to explore the conditions under which algorithms on a quantum computer could even be considered for potential use in control. For example, part of what can enable quantum computers to have special properties compared to their classical counterparts is the ability to put a qubit, the quantum equivalent of a bit of information, into a superposition state [10]. However, coming out of this superposition state could entail a probabilistic operation where the result of the algorithm may not be certain. Understanding whether such a phenomenon could be acceptable in a control-theoretic context, or under what scenarios it might be acceptable, could be beneficial.

Motivated by this, we will present a discussion of the relationship between control theory and quantum computing algorithms. We will discuss our first methodology from [9], which explores how the impacts of non-determinism in control action selection can be discussed in the context of advanced control designs like Lyapunov-based economic model predictive control (LEMPC) [11] by considering the discrete nature of solutions to such problems on computers where binary logic is important, as it is in quantum computing. The LEMPC is implemented as a lookup table searched by an (inefficient) quantum algorithm that returns the desired result with probability. Using the concept that the probability of obtaining a desired solution from this LEMPC relates to whether the closed-loop state is guaranteed to stay in a defined region of operation, we can develop the probability that the closed-loop state stays in a defined region of operation for a subsequent sampling period. A backup stabilizing controller could also be included that can be executed whenever the closed-loop state leaves a defined region of state-space. This backup control algorithm could be implemented using deterministic policies if it is desired to only use a quantum computer for the control logic, and not a hybrid of quantum and classical computers. However, the fact that the control-theoretic guarantees of LEMPC cannot be satisfied in a given region of state-space does not necessarily mean that the closed-loop state will exit a defined region; it only means that a set of sufficient (but not necessary) conditions for stability was not met. Therefore, we use a continuous stirred tank reactor example to analyze how many inputs from a variety of points in state-space would meet the stability requirements of LEMPC over a subsequent sampling period, and use this to better understand how even a probabilistic algorithm might be stabilizing over all time through creative coding implementations (e.g., potentially limiting the input space at certain states in state-space) or otherwise enforcing the backup control law. We close by discussing several extensions, such as how control theory is not enough to make entanglement a viable communication means in next-generation manufacturing and how the discussions in this work are related to other concepts in our group about cyberattack detection and handling [9].

[1] Ajagekar, A., Humble, T., You, F., 2020. “Quantum computing based hybrid solution strategies for large-scale discrete-continuous optimization problems.” Computers & Chemical Engineering 132, 106630.

[2] Ajagekar, A., You, F., 2019. “Quantum computing for energy systems optimization: Challenges and opportunities.” Energy 179, 76-89.

[3] Ajagekar, A., You, F., 2020. “A deep learning approach for fault detection and diagnosis of industrial processes using quantum computing.” 2020 IEEE International Conference on Systems, Man, and Cybernetics (SME), IEEE, Toronto, Ontario, Canada. pp. 2345-2350.

[4] Ajagekar, A., You, F., 2020. “Quantum computing assisted deep learning for fault detection and diagnosis in industrial process systems.” Computers & Chemical Engineering 143, 107119.

[5] Inoue, D., Yoshida, H., 2020. “Model predictive control for finite input systems using the D-Wave quantum annealer.” Scientific Reports 10(1), pp. 1-10.

[6] Dong, D., Chen, C., Li, H., Tarn, T.J., 2008. “Quantum reinforcement learning.” IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics) 38, pp. 1207-1220.

[7] Lamata, L., 2017. “Basic protocols in quantum reinforcement learning with superconducting circuits.” Scientific Reports 7, pp. 1-10.

[8] Wu, S., Jin, S., Wen, D., Wang, X., 2020. “Quantum reinforcement learning in continuous action space.” arXiv preprint arXiv:2012.10711.

[9] Nieman, K., Rangan, K. K., and Durand, H., submitted. “Control Implemented on Quantum Computers: Effects of Noise, Non-Determinism, and Entanglement.” Industrial & Engineering Chemistry Research.

[10] Yanofsky, N.S., Mannucci, M.A., 2008. Quantum computing for computer scientists. Cambridge University Press.

[11] Heidarinejad, M., Liu, J., Christofides, P.D., 2012. “Economic model predictive control of nonlinear process systems using Lyapunov techniques.” AIChE Journal 58, pp. 855-870.