Related papers: Fast convolution algorithm for state space models
Linear Time Invariant (LTI) systems are ubiquitous in control applications. Unbounded-time reachability analysis that can cope with industrial-scale models with thousands of variables is needed. To tackle this problem, we use abstract…
This paper delves into designing stabilizing feedback control gains for continuous linear systems with unknown state matrix, in which the control is subject to a general structural constraint. We bring forth the ideas from reinforcement…
Achieving optimal steady-state performance in real-time is an increasingly necessary requirement of many critical infrastructure systems. In pursuit of this goal, this paper builds a systematic design framework of feedback controllers for…
We propose a principled method for projecting an arbitrary square matrix to the non-convex set of asymptotically stable matrices. Leveraging ideas from large deviations theory, we show that this projection is optimal in an…
We consider linear time invariant systems with exogenous stochastic disturbances, and in feedback with structured stochastic uncertainties. This setting encompasses linear systems with both additive and multiplicative noise. Our concern is…
Transient computational fluid dynamics (CFD) remains expensive when long horizons and multi-scale turbulence are involved. Data-driven surrogates promise relief, yet many degrade over multiple steps or drift from physical behavior. This…
We give an algorithm to compute $N$ steps of a convolution quadrature approximation to a continuous temporal convolution using only $O(N \log N)$ multiplications and $O(\log N)$ active memory. The method does not require evaluations of the…
In this paper, we address the problem of computing the maximal admissible robust positive invariant (MARPI) set for discrete-time linear time-varying systems with parametric uncertainties and additive disturbances. The system state and…
Linear time-periodic (LTP) dynamical systems frequently appear in the modeling of phenomena related to fluid dynamics, electronic circuits, and structural mechanics via linearization centered around known periodic orbits of nonlinear…
Stabilization is a key dependability property for dealing with unanticipated transient faults, as it guarantees that even in the presence of such faults, the system will recover to states where it satisfies its specification. One of the…
We approach designing a state-space model for deep learning applications through its dual representation, the transfer function, and uncover a highly efficient sequence parallel inference algorithm that is state-free: unlike other proposed…
We present an algorithm to study mixed-state dynamics in one-dimensional quantum lattice systems. The algorithm can be used, e.g., to construct thermal states or to simulate real time evolutions given by a generic master equation. Its two…
Multivariate spatio-temporal data arise more and more frequently in a wide range of applications; however, there are relatively few general statistical methods that can readily use that incorporate spatial, temporal and variable…
This paper considers the problem of linear time-invariant (LTI) system identification using input/output data. Recent work has provided non-asymptotic results on partially observed LTI system identification using a single trajectory but is…
We introduce and demonstrate two linear inverse modelling methods for systems of stochastic ODE's with accuracy that is independent of the dimensionality (number of elements) of the state vector representing the system in question.…
The self-attention mechanism is the key to the success of transformers in recent Large Language Models (LLMs). However, the quadratic computational cost $O(n^2)$ in the input sequence length $n$ is a notorious obstacle for further…
Preserving stability is a central problem in data-driven model order reduction of dynamical systems. For linear systems whose dynamics depend on geometric or physical parameters, multivariate rational approximation algorithms such as the…
The singular values of convolutional mappings encode interesting spectral properties, which can be used, e.g., to improve generalization and robustness of convolutional neural networks as well as to facilitate model compression. However,…
State-space models (SSMs) that utilize linear, time-invariant (LTI) systems are known for their effectiveness in learning long sequences. To achieve state-of-the-art performance, an SSM often needs a specifically designed initialization,…
The aim of this paper is to address two related estimation problems arising in the setup of hidden state linear time invariant (LTI) state space systems when the dimension of the hidden state is unknown. Namely, the estimation of any finite…