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We extend slow manifolds near a transcritical singularity in a fast-slow system given by the explicit Euler discretization of the corresponding continuous-time normal form. The analysis uses the blow-up method and direct trajectory-based…
We propose a general strategy to discretize the Dyson series without applying direct numerical quadrature to high-dimensional integrals, and extend this framework to open quantum systems. The resulting discretization can also be interpreted…
Hyper-differential sensitivity analysis with respect to model discrepancy was recently developed to enable uncertainty quantification for optimization problems. The approach consists of two primary steps: (i) Bayesian calibration of the…
We introduce an algorithm based on a method of snapshots for computing approximate balanced truncations for discrete-time, stable, linear time-periodic systems. By construction, this algorithm is applicable to very high-dimensional systems,…
Optimization is an important module of modern machine learning applications. Tremendous efforts have been made to accelerate optimization algorithms. A common formulation is achieving a lower loss at a given time. This enables a…
To quantify the fundamental evolution of time-varying networks, and detect abnormal behavior, one needs a notion of temporal difference that captures significant organizational changes between two successive instants. In this work, we…
Control laws for continuous-time dynamical systems are most often implemented via digital controllers using a sample-and-hold technique. Numerical discretization of the continuous system is an integral part of subsequent analysis. Feedback…
We employ reachability analysis in designing dynamic quantization schemes for the remote state estimation of linear systems over a finite date rate communication channel. The quantization region is dynamically updated at each transmission…
The estimation of covariance operators of spatio-temporal data is in many applications only computationally feasible under simplifying assumptions, such as separability of the covariance into strictly temporal and spatial factors.Powerful…
Inner-approximate reachability analysis involves calculating subsets of reachable sets, known as inner-approximations. This analysis is crucial in the fields of dynamic systems analysis and control theory as it provides a reliable…
Classification in the dissimilarity space has become a very active research area since it provides a possibility to learn from data given in the form of pairwise non-metric dissimilarities, which otherwise would be difficult to cope with.…
We present two semidiscretizations of the Camassa-Holm equation in periodic domains based on variational formulations and energy conservation. The first is a periodic version of an existing conservative multipeakon method on the real line,…
We compare two approaches to the predictive modeling of dynamical systems from partial observations at discrete times. The first is continuous in time, where one uses data to infer a model in the form of stochastic differential equations,…
Reachability analysis is at the core of many applications, from neural network verification, to safe trajectory planning of uncertain systems. However, this problem is notoriously challenging, and current approaches tend to be either too…
We propose and study an algorithm for computing a nearest passive system to a given non-passive linear time-invariant system (with much freedom in the choice of the metric defining `nearest', which may be restricted to structured…
Iterative imperative programs can be considered as infinite-state systems computing over possibly unbounded domains. Studying reachability in these systems is challenging as it requires to deal with an infinite number of states with…
Distributed model predictive control (DMPC) has attracted extensive attention as it can explicitly handle system constraints and achieve optimal control in a decentralized manner. However, the deployment of DMPC strategies generally…
This work proposes a unifying probabilistic framework for the design of robustly asymptotically stable moving-horizon estimators (MHE) for discrete-time nonlinear systems, and a mechanism to incorporate differential privacy in…
The iterative consensus problem requires a set of processes or agents with different initial values, to interact and update their states to eventually converge to a common value. Protocols solving iterative consensus serve as building…
We propose a data-driven method to learn the time-dependent probability density of a multivariate stochastic process from sample paths, assuming that the initial probability density is known and can be evaluated. Our method uses a novel…