arXiv research

The paper tackles joint learning of linear systems, improving accuracy with pooled data.

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

The paper introduces a new method to assess system stability using torsion of state trajectories.

Paper derives an error bound for stochastic LTI systems.

We prove that stochastic gradient descent efficiently converges to the global optimizer of the maximum likelihood objective of an unknown linear time-invariant dynamical system from a sequence of noisy observations generated by the system. Even though the objective function is non-convex, we provide polynomial running …

Efficiently designs distributed controllers for sparse systems with sub-linear sample complexity.

AR model forecasts partially observed dynamical time series by estimating evolution function and imputing missing variables.

New model stabilizes asynchronous LTI systems, independent of synchronous stability.

The paper describes solutions for linear control systems on Lie groups.

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

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…

Safety filter for unknown discrete-time systems with learned models and noise covariance.

Solves parameter non-identifiability in Bayesian LTI system identification.

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 …

Study online control of unknown time-varying systems with negative and positive results.

We provide a brief tutorial on the use of concentration inequalities as they apply to system identification of state-space parameters of linear time invariant systems, with a focus on the fully observed setting. We draw upon tools from the theories of large-deviations and self-normalized martingales, and provide both d…

Study shows exponential sample complexity for stabilizing certain linear systems.

Unified Bayesian framework for LTV system identification using neural networks and Gaussian Processes.

Proposes local coordinate frames for improving model performance in complex dynamical systems.

dynoGP uses deep Gaussian processes for dynamic system identification.

It is shown that in the multivariate case the orders p, of the AR part, and q, of the MA part, are not invariants of the time series. Thus, it is concluded that it only makes sense to define the class of ARMA(p,p)- irreducible models, where p is the biggest of the system's Kronecker indices. This class is shown not to …

Polynomial-time reachability for LTI systems with TLL NN controllers is achieved.

New measure EC assesses node contributions in nonlinear, time-varying systems.

We consider the problem of learning a realization for a linear time-invariant (LTI) dynamical system from input/output data. Given a single input/output trajectory, we provide finite time analysis for learning the system's Markov parameters, from which a balanced realization is obtained using the classical Ho-Kalman al…

We find the complete set of fundamental invariants for systems of ordinary differential equations of order $\ge 4$ under the group of point transformations generalizing similar results for contact invariants of a single ODE and point invariants of systems of the second and the third order. It turns out that starting fr…

Overview of high-dimensional dynamical systems and their applications to machine learning.

A new real-time method estimates system matrices and states using Kalman filter.

Improved stability analysis of neural network systems using Zames-Falb multipliers.

The paper proves that linearization along trajectories preserves flatness in discrete-time systems.

We show that classical Wilczynski--Se-ashi invariants of linear systems of ordinary differential equations are generalized in a natural way to contact invariants of non-linear ODEs. We explore geometric structures associated with equations that have vanishing generalized Wilczynski invariants and establish relationship…

The aim of this paper is to prove that a control affine system on a manifold is equivalent by diffeomorphism to a linear system on a Lie group or a homogeneous space if and only the vector fields of the system are complete and generate a finite dimensional Lie algebra. A vector field on a connected Lie group is linear …

New algorithm optimizes linear system estimation from single trajectory.

In this paper we propose a new identification scheme for Hammerstein systems, which are dynamic systems consisting of a static nonlinearity and a linear time-invariant dynamic system in cascade. We assume that the nonlinear function can be described as a linear combination of $p$ basis functions. We reconstruct the $p$…

Complex frequency generalizes eigenvalues in LTI systems.

We derive a system of equations governing the coupled gravitational and electromagnetic perturbations of Reissner-Nordström spacetime. The equations are derived in the context of global non-linear stability of Reissner-Nordström under axially symmetric polarized perturbations, as a generalization of the recent work on …

The paper develops robust tests for detecting independence in synchronous stochastic systems with finite sample guarantees.

Geometric framework for dynamic feedback linearization of control systems with symmetry.

Lower bounds for delta invariant of weighted hypersurfaces proved for K-stability.

BP fails to find sparsest solution for structured matrices.

Algorithm learns linear systems from partial observations with near-optimal rate.

The paper studies symmetry reduction of control systems and its implications for feedback linearization.

Efficiently controls unknown linear systems with black-box interactions.

New insights into cascade feedback linearization of control systems.

Gaussian processes for dynamical systems with Koopman equivariance.

ESNs trained with Tikhonov least squares approximate ergodic dynamical systems in L2(μ) norm.

New model preserves symmetry in multivariate time series, improving performance.

A distributed system identification method for LTI systems using reverse experience replay.

We provide a physical definition of new homological invariants $\mathcal{H}_a (M_3)$ of 3-manifolds (possibly, with knots) labeled by abelian flat connections. The physical system in question involves a 6d fivebrane theory on $M_3$ times a 2-disk, $D^2$, whose Hilbert space of BPS states plays the role of a basic build…