Analysis and synthesis of safety-critical autonomous systems are carried out using models which are often dynamic. Two central features of these dynamic systems are parameters and unmodeled dynamics. Much of feedback control design is parametric in nature and as such, accurate and fast estimation of the parameters in the modeled part of the dynamic system is a crucial property for designing risk-aware autonomous systems. This paper addresses the use of a spectral lines-based approach for estimating parameters of the dynamic model of an autonomous system. Existing literature has treated all unmodeled components of the dynamic system as sub-Gaussian noise and proposed parameter estimation using Gaussian noise-based exogenous signals. In contrast, we allow the unmodeled part to have deterministic unmodeled dynamics, which are almost always present in physical systems, in addition to sub-Gaussian noise. In addition, we propose a deterministic construction of the exogenous signal in order to carry out parameter estimation. We introduce a new tool kit which employs the theory of spectral lines, retains the stochastic setting, and leads to non-asymptotic bounds on the parameter estimation error. Unlike the existing stochastic approach, these bounds are tunable through an optimal choice of the spectrum of the exogenous signal leading to accurate parameter estimation. We also show that this estimation is robust to unmodeled dynamics, a property that is not assured by the existing approach. Finally, we show that under ideal conditions with no deterministic unmodeled dynamics, the proposed approach can ensure a Õ(√t) Regret, matching existing literature. Experiments are provided to support all theoretical derivations, which show that the spectral lines-based approach outperforms the Gaussian noise-based method when unmodeled dynamics are present, in terms of both parameter estimation error and Regret obtained using the parameter estimates with a Linear Quadratic Regulator in feedback.

Link partitioning is a popular approach for discovering overlapping communities by identifying clusters of strongly connected links. Current link partitioning methods are specifically designed for networks modelled by graphs representing pairwise relationships. Therefore, these methods omit any higher-order information about group interactions in network data which is increasingly available. Simplicial complexes extend the dyadic model of graphs and can model polyadic relationships which are ubiquitous and crucial in many complex social and technological systems. In this paper, we introduce a link partitioning method that leverages higher-order (i.e. triadic and higher) information in simplicial complexes for better community detection. Our method utilizes a novel random walk on links of simplicial complexes defined by the higher-order Laplacian-a generalization of the graph Laplacian that incorporates polyadic relationships of the network. We transform this random walk into a graph-based random walk on a lifted line graph-a dual graph in which links are nodes while nodes and higher-order connections are links-and optimize for the standard notion of modularity. We show that our method is guaranteed to provide interpretable link partitioning results under mild assumptions. We also offer new theoretical results on the spectral properties of simplicial complexes by studying the spectrum of the link random walk. Experiment results on real-world community detection tasks show that our higher-order approach significantly outperforms existing graph-based link partitioning methods.