Related papers: A Mathematical Framework for Linear Response Theor…
The problem of estimating an unknown force driving a linear oscillator is revisited. When using linear measurement, feedback is often cited as a mechanism to enhance bandwidth or sensitivity. We show that as long as the oscillator dynamics…
We study the problem of modeling a non-linear dynamical system when given a time series by deriving equations directly from the data. Despite the fact that time series data are given as input, models for dynamics and estimation algorithms…
We address the problem of learning to control an unknown nonlinear dynamical system through sequential interactions. Motivated by high-stakes applications in which mistakes can be catastrophic, such as robotics and healthcare, we study…
The classical fluctuation-dissipation theorem predicts the average response of a dynamical system to an external deterministic perturbation via time-lagged statistical correlation functions of the corresponding unperturbed system. In this…
Forecasting the evolution of complex systems is one of the grand challenges of modern data science. The fundamental difficulty lies in understanding the structure of the observed stochastic process. In this paper, we show that every…
We show a linear response statement for fixed points of a family of Markov operators which are perturbations of mixing and regularizing operators. We apply the statement to random dynamical systems on the interval given by a deterministic…
We present a novel approach to control design for nonlinear systems which leverages model-free policy optimization techniques to learn a linearizing controller for a physical plant with unknown dynamics. Feedback linearization is a…
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…
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…
Basing on the theory of Feynman's influence functional and its hierarchical equations of motion, we develop a linear response theory for quantum open systems. Our theory provides an effective way to calculate dynamical observables of a…
This paper proposes a framework for adaptively learning a feedback linearization-based tracking controller for an unknown system using discrete-time model-free policy-gradient parameter update rules. The primary advantage of the scheme over…
A technique is introduced for estimating unknown parameters when time series of only one variable from a multivariate nonlinear dynamical system is given. The technique employs a combination of two different control methods, a linear…
This work establishes a quenched (trajectory-wise) linear response formula for random intermittent dynamical systems, consisting of Liverani-Saussol-Vaienti maps with varying parameters. This result complements recent annealed (averaged)…
The sensitivity of climate models to increasing CO2 concentration and the climate response at decadal time scales are still major factors of uncertainty for the assessment of the long and short term effects of anthropogenic climate change.…
The classical theory of linear response applies to statistical mechanics close to equilibrium. Away from equilibrium, one may describe the microscopic time evolution by a general differentiable dynamical system, identify nonequilibrium…
We propose an approach for learning the causal structure in stochastic dynamical systems with a $1$-step functional dependency in the presence of latent variables. We propose an information-theoretic approach that allows us to recover the…
A fundamental concept in control theory is that of controllability, where any system state can be reached through an appropriate choice of control inputs. Indeed, a large body of classical and modern approaches are designed for controllable…
The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems…
A methodology is developed to learn a feedback linearization (i.e., nonlinear change of coordinates and input transformation) using a data-driven approach for a single input control-affine nonlinear system with unknown dynamics. We employ…
We present a learning theory for the training of a linear system operator having an input compositional variable and propose a Bayesian inversion method for inferring the unknown variable from an output of a noisy linear system. We assume…