Efficient Representation and Approximation of Model Predictive Control Laws via Deep Learning

• Published in: IEEE transactions on cybernetics Vol. 50; no. 9; pp. 3866 - 3878
• Main Authors: Karg, Benjamin, Lucia, Sergio
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01.09.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Approximation; Artificial neural networks; Biological neural networks; Computer simulation; Control theory; Cyber-physical systems; Decision making; Deep learning; Electronic devices; Embedded systems; Error correction; Machine learning; Mathematical analysis; Memory management; Neural networks; Neurons; Optimization; Predictive control; Storage capacity; Time invariant systems
• ISSN: 2168-2267; 2168-2275; 2168-2275
• DOI: 10.1109/TCYB.2020.2999556

We show that artificial neural networks with rectifier units as activation functions can exactly represent the piecewise affine function that results from the formulation of model predictive control (MPC) of linear time-invariant systems. The choice of deep neural networks is particularly interesting as they can represent exponentially many more affine regions compared to networks with only one hidden layer. We provide theoretical bounds on the minimum number of hidden layers and neurons per layer that a neural network should have to exactly represent a given MPC law. The proposed approach has a strong potential as an approximation method of predictive control laws, leading to a better approximation quality and significantly smaller memory requirements than previous approaches, as we illustrate via simulation examples. We also suggest different alternatives to correct or quantify the approximation error. Since the online evaluation of neural networks is extremely simple, the approximated controllers can be deployed on low-power embedded devices with small storage capacity, enabling the implementation of advanced decision-making strategies for complex cyber-physical systems with limited computing capabilities.