Related papers: Parameter estimation, nonlinearity and Occam's raz…
While the identification of nonlinear dynamical systems is a fundamental building block of model-based reinforcement learning and feedback control, its sample complexity is only understood for systems that either have discrete states and…
Data-driven methods for modeling dynamic systems have received considerable attention as they provide a mechanism for control synthesis directly from the observed time-series data. In the absence of prior assumptions on how the time-series…
We present a method that allows to distinguish between nearly periodic and strictly periodic time series. To this purpose, we employ a conservative criterion for periodicity, namely that the time series can be interpolated by a periodic…
A method for detecting possible non-deterministic dynamics underlying a time series is introduced. Non-deterministic dynamics may arise due to the failure of the Lipschitz condition in the equations of motion. At a singular point, the phase…
Before we apply nonlinear techniques, for example those inspired by chaos theory, to dynamical phenomena occurring in nature, it is necessary to first ask if the use of such advanced techniques is justified "by the data". While many…
This paper considers a general class of nonparametric time series regression models where the regression function can be time-dependent. We establish an asymptotic theory for estimates of the time-varying regression functions. For this…
Statistical mechanics can provide a versatile theoretical framework for investigating the collective dynamics of weakly nonlinear waves-settings that can be utterly complex to describe otherwise. In optics, composite systems arise due to…
This paper introduces a novel parameterization to characterize unknown linear time-invariant systems using noisy data. The presented parameterization describes exactly the set of all systems consistent with the available data. We then…
We examine the time-dependent behavior of a nonlinear system driven by a two-frequency forcing. By using a non-perturbative approach, we are able to derive an asymptotic expression, valid in the long-time limit, for the time average of the…
We characterise the evolution of a dynamical system by combining two well-known complex systems' tools, namely, symbolic ordinal analysis and networks. From the ordinal representation of a time-series we construct a network in which every…
Non-autonomous dynamical systems help us to understand the implications of real systems which are in contact with their environment as it actually occurs in nature. Here, we focus on systems where a parameter changes with time at small but…
Computers are nonlinear dynamical systems that exhibit complex and sometimes even chaotic behavior. The models used in the computer systems community, however, are linear. This paper is an exploration of that disconnect: when linear models…
A new method is introduced for analysis of interactions between time-dependent coupled oscillators, based on the signals they generate. It distinguishes unsynchronized dynamics from noise-induced phase slips, and enables the evolution of…
In this paper, we present a data-driven controller design method for continuous-time nonlinear systems, using no model knowledge but only measured data affected by noise. While most existing approaches focus on systems with polynomial…
We extend the phase field crystal method for nonequilibrium patterning to stochastic systems with external source where transient dynamics is essential. It was shown that at short time scales the system manifests pattern selection…
We propose a moving horizon estimation scheme to estimate the states and the unknown constant parameters of general nonlinear uncertain discrete-time systems. The proposed framework and analysis explicitly do not involve the a priori…
A systematic procedure to synthesize interval observers for nonlinear discrete-time systems is proposed. The feedback gains and other matrices are found from the solutions to semidefinite feasibility programs. Two cases are considered: (1)…
Complex systems are characterized by a huge number of degrees of freedom often interacting in a non-linear manner. In many cases macroscopic states, however, can be characterized by a small number of order parameters that obey stochastic…
The resonances of forced dynamical systems occur when either the amplitude of the frequency response undergoes a local maximum (amplitude resonance) or phase lag quadrature takes places (phase resonance). This study focuses on the phase…
Natural systems are typically nonlinear and complex, and it is of great interest to be able to reconstruct a system in order to understand its mechanism, which can not only recover nonlinear behaviors but also predict future dynamics. Due…