Related papers: Fast convolution algorithm for state space models
We propose a transformation algorithm for a class of Linear Parameter-Varying (LPV) systems with functional affine dependence on parameters, where the system matrices depend affinely on nonlinear functions of the scheduling varable, into…
Objectives involving bilinear forms $u^\top f(A(\theta))v$ for Hermitian $A$ arise widely in scientific computing and probabilistic machine learning. For large matrices, Lanczos efficiently approximates these quantities, but differentiating…
Time domain identification is studied in this paper for parameters of a continuous-time multi-input multi-output descriptor system, with these parameters affecting system matrices through a linear fractional transformation. Sampling is…
In this paper we describe spectral transformation algorithms for the computation of eigenvalues with positive real part of sparse nonsymmetric matrix pencils $(J,L)$, where $L$ is of the form $\pmatrix{M&0\cr 0&0}$. For this we define a…
This paper presents a low-dimensional observer design for stable, single-input single-output, continuous-time linear time-invariant (LTI) systems. Leveraging the model reduction by moment matching technique, we approximate the system with a…
We investigate integral formulations and fast algorithms for the steady-state radiative transfer equation with isotropic and anisotropic scattering. When the scattering term is a smooth convolution on the unit sphere, a model reduction step…
We derive finite time error bounds for estimating general linear time-invariant (LTI) systems from a single observed trajectory using the method of least squares. We provide the first analysis of the general case when eigenvalues of the LTI…
Linear time invariant (LTI) systems are widely used for modeling system dynamics in science and engineering problems. Harmonic oscillation of LTI systems are widely used for modeling and analyses of periodic physical phenomenon. This study…
Fast time-domain algorithms have been developed in signal processing applications to reduce the multiplication complexity. For example, fast convolution structures using Cook-Toom and Winograd algorithms are well understood. Short length…
When using reinforcement learning (RL) algorithms to evaluate a policy it is common, given a large state space, to introduce some form of approximation architecture for the value function (VF). The exact form of this architecture can have a…
A new concept, called the spatio-temporal transfer function (STTF), is introduced to characterise a class of linear time-invariant (LTI) spatio-temporal dynamical systems. The spatio-temporal transfer function is a natural extension of the…
Likelihood-free inference (LFI) has been successfully applied to state-space models, where the likelihood of observations is not available but synthetic observations generated by a black-box simulator can be used for inference instead.…
We study the capability of the Fast Fourier Transform (FFT) to accelerate exact and approximate matrix multiplication without using Strassen-like divide-and-conquer. We present a simple exact algorithm running in $O(n^{2.89})$ time, which…
Under-approximations of reachable sets and tubes have been receiving growing research attention due to their important roles in control synthesis and verification. Available under-approximation methods applicable to continuous-time linear…
Long Short-Term Memory (LSTM) is a special class of recurrent neural network, which has shown remarkable successes in processing sequential data. The typical architecture of an LSTM involves a set of states and gates: the states retain…
We study the problem of learning to stabilize unknown noisy Linear Time-Invariant (LTI) systems on a single trajectory. It is well known in the literature that the learn-to-stabilize problem suffers from exponential blow-up in which the…
We address the global stabilization of linear time-invariant (LTI) systems when the magnitude of the control input and its successive time derivatives, up to an order $p\in\mathbb N$, are bounded by prescribed values. We propose a static…
We present a framework for learning of modeling uncertainties in Linear Time Invariant (LTI) systems. We propose a methodology to extend the dynamics of an LTI (without uncertainty) with an uncertainty model, based on measured data, to…
In these lectures notes, we review our recent works addressing various problems of finding the nearest stable system to an unstable one. After the introduction, we provide some preliminary background, namely, defining Port-Hamiltonian…
Reinforcement learning with function approximation can be unstable and even divergent, especially when combined with off-policy learning and Bellman updates. In deep reinforcement learning, these issues have been dealt with empirically by…