Related papers: Learning Stable and Robust Linear Parameter-Varyin…
Nonlinear dynamical behaviours in engineering applications can be approximated by linear-parameter varying (LPV) representations, but obtaining precise model knowledge to develop a control algorithm is difficult in practice. In this paper,…
This paper studies the parameter tuning problem of positive linear systems for optimizing their stability properties. We specifically show that, under certain regularity assumptions on the parametrization, the problem of finding the…
Grad's moment models for Boltzmann equation were recently regularized to globally hyperbolic systems, and thus the regularized models attain local well-posedness for Cauchy data. The hyperbolic regularization is only related to the…
We present a sample-based Learning Model Predictive Controller (LMPC) for constrained uncertain linear systems subject to bounded additive disturbances. The proposed controller builds on earlier work on LMPC for deterministic systems.…
High-dimensional predictive models, those with more measurements than observations, require regularization to be well defined, perform well empirically, and possess theoretical guarantees. The amount of regularization, often determined by…
Many modern datasets don't fit neatly into $n \times p$ matrices, but most techniques for measuring statistical stability expect rectangular data. We study methods for stability assessment on non-rectangular data, using statistical learning…
Declines in cost and concerns about the environmental impact of traditional generation have boosted the penetration of renewables and non-conventional distributed energy resources into the power grid. The intermittent availability of these…
The goal of this paper is to analyze Long Short Term Memory (LSTM) neural networks from a dynamical system perspective. The classical recursive equations describing the evolution of LSTM can be recast in state space form, resulting in a…
In this work, we investigate the problem of simultaneously learning and controlling a system subject to adversarial choices of disturbances and system parameters. We study the problem for a scalar system with $l_\infty$-norm bounded…
This paper introduces a new parameterization of deep neural networks (both fully-connected and convolutional) with guaranteed $\ell^2$ Lipschitz bounds, i.e. limited sensitivity to input perturbations. The Lipschitz guarantees are…
Scientific machine learning for inferring dynamical systems combines data-driven modeling, physics-based modeling, and empirical knowledge. It plays an essential role in engineering design and digital twinning. In this work, we primarily…
This work primarily focuses on an operator inference methodology aimed at constructing low-dimensional dynamical models based on a priori hypotheses about their structure, often informed by established physics or expert insights. Stability…
Stability is a key property of both forward models and inverse problems, and depends on the norms considered in the relevant function spaces. For instance, stability estimates for hyperbolic partial differential equations are often based on…
Recently there has been substantial interest in spectral methods for learning dynamical systems. These methods are popular since they often offer a good tradeoff between computational and statistical efficiency. Unfortunately, they can be…
This paper proposes an active learning method for designing experiments to identify quasi-Linear Parameter-Varying (qLPV) models. Since informative experiments are costly, input signals must be selected to maximize information content based…
In this paper, we consider the analysis and control of continuous-time nonlinear systems to ensure universal shifted stability and performance, i.e., stability and performance w.r.t. each forced equilibrium point of the system. This…
The principal task to control dynamical systems is to ensure their stability. When the system is unknown, robust approaches are promising since they aim to stabilize a large set of plausible systems simultaneously. We study linear…
When neural networks are used to model dynamics, properties such as stability of the dynamics are generally not guaranteed. In contrast, there is a recent method for learning the dynamics of autonomous systems that guarantees global…
Deep sequence models are receiving significant interest in current machine learning research. By representing probability distributions that are fit to data using maximum likelihood estimation, such models can model data on general…
The vector autoregression (VAR) has been widely used in system identification, econometrics, natural science, and many other areas. However, when the state dimension becomes large the parameter dimension explodes. So rank reduced modelling…