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Learning-based predictive control is a promising alternative to optimization-based MPC. However, efficiently learning the optimal control policy, the optimal value function, or the Q-function requires suitable function approximators. Often,…

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 of linear time-invariant systems. The…

Although artificial neural networks have shown great promise in applications including computer vision and speech recognition, there remains considerable practical and theoretical difficulty in optimizing their parameters. The seemingly…

Online model predictive control (MPC) for piecewise affine (PWA) systems requires the online solution to an optimization problem that implicitly optimizes over the switching sequence of PWA regions, for which the computational burden can be…

It is shown that any continuous piecewise affine (CPA) function $\mathbb{R}^2\to\mathbb{R}$ with $p$ pieces can be represented by a ReLU neural network with two hidden layers and $O(p)$ neurons. Unlike prior work, which focused on convex…

In exchange for large quantities of data and processing power, deep neural networks have yielded models that provide state of the art predication capabilities in many fields. However, a lack of strong guarantees on their behaviour have…

We present a novel layerwise optimization algorithm for the learning objective of Piecewise-Linear Convolutional Neural Networks (PL-CNNs), a large class of convolutional neural networks. Specifically, PL-CNNs employ piecewise linear…

Piecewise regression is a versatile approach used in various disciplines to approximate complex functions from limited, potentially noisy data points. In control, piecewise regression is, e.g., used to approximate the optimal control law of…

Recently, the interpretability of deep learning has attracted a lot of attention. A plethora of methods have attempted to explain neural networks by feature visualization, saliency maps, model distillation, and so on. However, it is hard…

We investigate the problem of fitting piecewise affine functions (PWA) to data. Our algorithm divides the input domain into finitely many polyhedral regions whose shapes are specified using a user-defined template such that the data points…

We introduce an optimal and nearly parameter-free algorithm for minimizing piecewise smooth (PWS) convex functions under the quadratic growth (QG) condition, where the locations and structure of the smooth regions are entirely…

Infinite-horizon optimal control of constrained piecewise affine (PWA) systems has been approximately addressed by hybrid model predictive control (MPC), which, however, has computational limitations, both in offline design and online…

In this paper, the disjunctive and conjunctive lattice piecewise affine (PWA) approximations of explicit linear model predictive control (MPC) are proposed. The training data are generated uniformly in the domain of interest, consisting of…

Rectifier (ReLU) deep neural networks (DNN) and their connection with piecewise affine (PWA) functions is analyzed. The paper is an effort to find and study the possibility of representing explicit state feedback policy of model predictive…

This work formally introduces Y-wise Affine Neural Networks (YANNs), a fully-explainable network architecture that continuously and efficiently represent piecewise affine functions with polytopic subdomains. Following from the proofs, it is…

Many feedforward neural networks (NNs) generate continuous and piecewise-linear (CPWL) mappings. Specifically, they partition the input domain into regions on which the mapping is affine. The number of these so-called linear regions offers…

The increasing penetration of renewables in distribution networks calls for faster and more advanced voltage regulation strategies. A promising approach is to formulate the problem as an optimization problem, where the optimal reactive…

This paper introduces an adaptive convolutional neural network (CNN) architecture capable of automating various topology optimization (TO) problems with diverse underlying physics. The proposed architecture has an encoder-decoder-type…

As a powerful modelling method, PieceWise Linear Neural Networks (PWLNNs) have proven successful in various fields, most recently in deep learning. To apply PWLNN methods, both the representation and the learning have long been studied. In…

We introduce a new class of neural networks designed to be convex functions of their inputs, leveraging the principle that any convex function can be represented as the supremum of the affine functions it dominates. These neural networks,…