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Department of Mechanical Engineering
TRUELEAP

Tailored Neural Networks for Learning-based Predictive Control

Aligning machine learning models with the mathematical structures of predictive control.

Machine learning has long been used in the context of automatic control, but the rapid progress of deep learning in recent years has enabled fundamentally new and more powerful approaches. A particularly promising direction is learning-based control, where machine learning methods are applied to approximate control policies or value functions in a computationally efficient manner. However, control applications pose unique challenges that go far beyond standard machine learning problems. Real-time requirements, computational limitations, and strict process constraints demand function approximators that are at once lightweight, accurate, and reliable.

Fortunately, optimal controllers obtained from MPC are not arbitrary functions, but exhibit well-understood mathematical structures. For instance, control policies for linear systems with polyhedral constraints are known to be piecewise affine (PWA), while the corresponding optimal value functions and Q-functions are piecewise quadratic (PWQ) and convex. This structural knowledge allows to make learning-based MPC more efficient by designing neural networks (NN) that harmonize with these properties. In fact, NNs with rectified linear unit (ReLU) or maxout activations naturally generate PWA mappings, making them particularly suitable candidates for representing MPC control policies. Yet, despite this close match, it remains largely an open question how to exploit such structures in practice and how to extend them to the approximation of convex PWQ functions.

This project therefore pursues three closely connected research goals. First, we seek to design less conservative NN architectures for efficiently representing PWA control policies. Second, we aim to identify suitable network types and topologies for approximating convex PWQ value functions and Q-functions. Finally, we will investigate and substantiate the claim that such tailored NNs are indeed beneficial for learning, implementation, and real-time evaluation of modern controllers.

Related publications

D. Teichrib and M. Schulze Darup, Reachability analysis for piecewise affine systems with neural network-based controllers, Proc. of the 63rd IEEE Conference on Decision and Control (CDC), pp. 894-900, 2024. DOI: 10.1109/CDC56724.2024.10886414, Preprint: arXiv:2411.03834

D. Teichrib and M. Schulze Darup, Piecewise regression via mixed-integer programming for MPC, Proc. of the 6th Annual Learning for Dynamics & Control Conference, pp. 337-348, 2024, available at: https://proceedings.mlr.press/v242/teichrib24a.html

D. Teichrib and M. Schulze Darup, Error bounds for maxout neural network approximations of model predictive control, IFAC-PapersOnLine, 56(2): pp. 10113-10119, 2023. DOI: 10.1016/j.ifacol.2023.10.883. Preprint: arXiv:2304.08779.

D. Teichrib and M. Schulze Darup, Tailored max-out networks for learning convex PWQ functions, in Proc. of the 2022 European Control Conference (ECC), pp. 2272-2278, 2022. DOI: 10.23919/ECC55457.2022.9838225, Preprint: arXiv.2206.06826

D. Teichrib and M. Schulze Darup, Tailored neural networks for learning optimal value functions in MPC, in Proc. of the 60th IEEE Conference on Decision and Control (CDC), pp. 5281-5287, 2021. DOI: 10.1109/CDC45484.2021.9683528, Preprint: arXiv:2112.03975

M. Schulze Darup, Exact representation of piecewise affine functions via neural networks, in Proc. of the 2020 European Control Conference (ECC), pp. 1073-1078, 2020. DOI: 10.23919/ECC51009.2020.9143957