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Articles 1 - 3 of 3
Full-Text Articles in Control Theory
Largest 2-Regular Subgraphs In Complete S-Partite Graphs, Yiyang Jiang
Largest 2-Regular Subgraphs In Complete S-Partite Graphs, Yiyang Jiang
McKelvey School of Engineering Graduate Student Theses & Dissertations
In this thesis, we focus on the class of complete $S$-partite graphs, for $S$ an undirected graph possibly with self-loops, and address the problem of finding largest $2$-regular subgraphs of these graphs, which can be formulated as an integer linear program. Roughly speaking, a complete $S$-partite graph is obtained by replacing every single node of $S$ with a number of nodes, preserving the edge/non-edge relations of $S$. Our motivation in studying largest $2$-regular subgraphs is rooted in the structural systems theory, particularly in the problem of finding largest subnetworks that can sustain controllability or asymptotic stability of the corresponding subsystems. …
On The H-Property For Step-Graphons: Residual Case, Wanting Gao
On The H-Property For Step-Graphons: Residual Case, Wanting Gao
McKelvey School of Engineering Graduate Student Theses & Dissertations
We investigate the H-property for step-graphons. Specifically, we sample graphs Gn on n nodes from a step-graphon and evaluate the probability that Gn has a Hamiltonian decomposition in the asymptotic regime as n → ∞. It has been shown in Belabbas and Chen (2023); Belabbas et al. (2021) that for almost all step-graphons, this probability converges to either zero or one. We focus in this paper on the residual case where the zero-one law does not apply. We show that the limit of the probability still exists and provide an explicit expression of it. We present a complete proof of …
Safety And Optimality Monitors For Learning-Enabled Systems Using Conformal Prediction, Jackson Cox
Safety And Optimality Monitors For Learning-Enabled Systems Using Conformal Prediction, Jackson Cox
McKelvey School of Engineering Graduate Student Theses & Dissertations
The use of machine learning to create data-driven plant models and controllers has led to an increased need for safety and optimality monitors for model-based systems. System plant models are subject to uncertainty due to learning constraints such as unseen data and overfitting or physical constraints such as unknown dynamics and noise. This uncertainty is detrimental to safety-critical systems and must be properly regulated. To curb this uncertainty, we create prediction sets using the guarantees provided by Conformal Prediction. With a user-specified high probability, these prediction sets contain the true plant system states for an entire prediction horizon, which we …