Justin P. Koeln

Joseph M. Pisani, Christopher T. Aksland, Philip M. Renkert et al.

Modern energy systems in vehicles and built infrastructure are governed by high-dimensional dynamics spanning multiple physical domains (e.g., electrical, thermal, mechanical) and timescales. This tutorial paper presents a graph-based modeling approach created to facilitate the modeling, analysis, control, estimation, optimization, and design of these systems. Matured and validated through more than a decade of research spanning multiple academic institutions and companies, the graph-based approach combines transient energy conservation with an explicit mathematical representation of the network by which energy is stored and transferred within a system. Following a mathematical overview of graph-based models, examples of multi-domain component and system models from the recent literature are presented, including single-phase thermal systems, two-phase thermal systems, and electro-mechanical systems. This is followed by a survey of recent applications for decentralized and hierarchical model predictive control, design optimization, and control co-design. Lastly, the paper describes an open-source toolbox created to facilitate the generation and analysis of graph-based models.

Joshua Ortiz, Alyssa Vellucci, Justin Koeln et al.

We show that hybrid zonotopes offer an equivalent representation of feed-forward fully connected neural networks with ReLU activation functions. Our approach demonstrates that the complexity of binary variables is equal to the total number of neurons in the network and hence grows linearly in the size of the network. We demonstrate the utility of the hybrid zonotope formulation through three case studies including nonlinear function approximation, MPC closed-loop reachability and verification, and robustness of classification on the MNIST dataset.