arXiv research

The OLS estimator optimally identifies stable linear systems with a finite number of samples.

New mathematical foundations for stable RKHSs improve system identification.

Study learns dynamics of linear systems from multiple short trajectories.

New algorithm learns stable LDSs with lower error and better control performance.

A new Bayesian approach to linear system identification has been proposed in a series of recent papers. The main idea is to frame linear system identification as predictor estimation in an infinite dimensional space, with the aid of regularization/Bayesian techniques. This approach guarantees the identification of stab…

The classical approach to linear system identification is given by parametric Prediction Error Methods (PEM). In this context, model complexity is often unknown so that a model order selection step is needed to suitably trade-off bias and variance. Recently, a different approach to linear system identification has been…

We consider the problem of online prediction in a marginally stable linear dynamical system subject to bounded adversarial or (non-isotropic) stochastic perturbations. This poses two challenges. Firstly, the system is in general unidentifiable, so recent and classical results on parameter recovery do not apply. Secondl…

Algorithm learns dynamics from past observations.

Study non-asymptotic bounds on correlation in high-dimensional linear systems, revealing invariant subspaces and bottlenecks.

Regularized least-squares approaches have been successfully applied to linear system identification. Recent approaches use quadratic penalty terms on the unknown impulse response defined by stable spline kernels, which control model space complexity by leveraging regularity and bounded-input bounded-output stability. T…

Regularized approaches have been successfully applied to linear system identification in recent years. Many of them model unknown impulse responses exploiting the so called Reproducing Kernel Hilbert spaces (RKHSs) that enjoy the notable property of being in one-to-one correspondence with the class of positive semidefi…

This paper focuses on using the first curvature $κ(t)$ of trajectory to describe the stability of linear time-invariant system. We extend the results for two and three-dimensional systems [Y. Wang, H. Sun, Y. Song et al., arXiv:1808.00290] to $n$-dimensional systems. We prove that for a system $\dot{r}(t)=Ar(t)$, (i) i…

This paper proposes a new approach to describe the stability of linear time-invariant systems via the torsion $τ(t)$ of the state trajectory. For a system $\dot{r}(t)=Ar(t)$ where $A$ is invertible, we show that (1) if there exists a measurable set $E_1$ with positive Lebesgue measure, such that $r(0)\in E_1$ implies t…

Proposes LAE-EnKF for improved nonlinear data assimilation.

The paper tackles long-context linear system identification with improved sample complexity bounds.

Develops inverse unscented Kalman filter for non-linear systems.

We investigate random complex dynamics of rational or polynomial maps on the Riemann sphere. We show that regarding random complex dynamics of polynomials, generically, the chaos of the averaged system disappears at any point in the Riemann sphere due to the automatic coopeartion of many kinds of maps in the system, ev…

Paper solves tracking control for $(x,u)$-flat systems using classical states.

Stability of recurrent models is closely linked with trainability, generalizability and in some applications, safety. Methods that train stable recurrent neural networks, however, do so at a significant cost to expressibility. We propose an implicit model structure that allows for a convex parametrization of stable mod…

We study the problem of controlling linear time-invariant systems with known noisy dynamics and adversarially chosen quadratic losses. We present the first efficient online learning algorithms in this setting that guarantee $O(\sqrt{T})$ regret under mild assumptions, where $T$ is the time horizon. Our algorithms rely …

Bayesian regularization tackles collinearity in large-scale systems with correlated inputs.

Estimates multiple linear systems on a graph with smoothness constraints.

Improves numerical solution of ill-conditioned linear systems for machine learning.

New insights into spectral statistics of sample covariance matrix for stable linear systems.

The paper develops a convex parameterization for robust RNNs ensuring stability and robustness.

Classifies non-linear Fredholm maps linking to stable homotopy groups of spheres.

This paper improves system identification by reducing sample complexity for high-dimensional linear dynamical systems.

In this paper we provide some stability criteria for systems of linear subspaces of $V \otimes W$ and for systems of quotient coherent sheaves, using, respectively, the Hilbert-Mumford numerical criterion and moment map. Along the way, we generalize the Gelfand-MacPherson correspondence [11] from point sets to sets of …

Paper tackles SMPC for linear systems with unknown noise distribution.

Research on long-range memory in financial and social systems using various models.

For dynamical systems that can be modelled as asymptotically stable linear systems forced by Gaussian noise, this paper develops methods to infer or estimate their modes from observations in real time. The modes can be real or complex. For a real mode, we wish to infer its damping rate and mode shape. For a complex mod…

An estimate on the number of distinct relative periodic orbits around a stable relative equilibrium in a Hamiltonian system with continuous symmetry is given. This result constitutes a generalization to the Hamiltonian symmetric framework of a classical result by Weinstein and Moser on the existence of periodic orbits …

PAC-Bayes bound for stable RNNs in time-series data.

Estimates time-varying parameters from two OLS estimates.

Study of deep Stable neural networks with various activation functions.

Noise can stabilize systemic risk models with uncertain robustness.

Efficient algorithm predicts unknown linear systems with long-term memory.

We provide a sufficient condition for polarisations of Fano varieties to be K-stable in terms of Tian's alpha invariant, which uses the log canonical threshold to measure singularities of divisors in the linear system associated to the polarisation. This generalises a result of Odaka-Sano in the anti-canonically polari…

Probabilistic solvers improve stability for stiff systems.

This paper studies when particle filtering is efficient for planning in partially observed systems.

Study on stable torsion length in groups, showing it vanishes in crystallographic groups and providing algorithms for computation.

New bounds quantify estimation error in kernel-based system identification with unknown hyperparameters.

Identifying the location of a disturbance and its magnitude is an important component for stable operation of power systems. We study the problem of localizing and estimating a disturbance in the interconnected power system. We take a model-free approach to this problem by using frequency data from generators. Specific…

In this paper we introduce a novel method for linear system identification with quantized output data. We model the impulse response as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential stability. This s…

Study identifies stable configurations of intertwined threads with repulsive interactions.

Using the mechanics of creep in material sciences as a metaphor, we present a general framework to understand the evolution of financial, economic and social systems and to construct scenarios for the future. In a nutshell, highly non-linear out-of-equilibrium systems subjected to exogenous perturbations tend to exhibi…

Statistic dynamics of financial systems is investigated, basing on a model of randomly coupled equation system driven by stochastic Langevin force. It is found that in stable regime the noise power spectrum of the system is of 1/f^alpha form, with the exponent alpha=3/2 in case of Hermitian coupling matrices, or slight…

The paper proves stability of certain singularities in integrable systems.