Related papers: Parameter Inference in Non-linear Dynamical System…

In this study, we consider the experimentally-obtained, periodically-forced response of a nonlinear structure in the presence of process noise. Control-based continuation is used to measure both the stable and unstable periodic solutions…

In this paper, we propose and study several inverse problems of determining unknown parameters in nonlocal nonlinear coupled PDE systems, including the potentials, nonlinear interaction functions and time-fractional orders. In these coupled…

A semi-parametric, non-linear regression model in the presence of latent variables is applied towards learning network graph structure. These latent variables can correspond to unmodeled phenomena or unmeasured agents in a complex system of…

Deep sequence models are receiving significant interest in current machine learning research. By representing probability distributions that are fit to data using maximum likelihood estimation, such models can model data on general…

Learning-based control methods typically assume stationary system dynamics, an assumption often violated in real-world systems due to drift, wear, or changing operating conditions. We study reinforcement learning for control under…

Recurrent Neural Networks excel at predicting and generating complex high-dimensional temporal patterns. Due to their inherent nonlinear dynamics and memory, they can learn unbounded temporal dependencies from data. In a Machine Learning…

We present a novel, model-free, and data-driven methodology for controlling complex dynamical systems into previously unseen target states, including those with significantly different and complex dynamics. Leveraging a parameter-aware…

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…

Summary: Errors in gradient trajectories introduce significant artifacts and distortions in magnetic resonance images, particularly in non-Cartesian imaging sequences, where imperfect gradient waveforms can greatly reduce image quality.…

The coupled problems of selecting control nodes and designing control actions for nonlinear network dynamics are fundamental scientific problems with applications in many diverse fields. These problems are thoroughly studied for linear…

A common pipeline in learning-based control is to iteratively estimate a model of system dynamics, and apply a trajectory optimization algorithm - e.g.~$\mathtt{iLQR}$ - on the learned model to minimize a target cost. This paper conducts a…

Large scale dynamical systems (e.g. many nonlinear coupled differential equations) can often be summarized in terms of only a few state variables (a few equations), a trait that reduces complexity and facilitates exploration of behavioral…

This paper provides a unified framework connecting dynamical systems with tools from topological data analysis and geometric topology and inspires new interactions among dynamical systems, topology, and nonlinear analysis. To this end, we…

Limit cycle oscillations are phenomena arising in nonlinear dynamical systems and characterized by periodic, locally-stable, and self-sustained state trajectories. Systems controlled in a closed loop along a periodic trajectory can also be…

When designing controllers for safety-critical systems, practitioners often face a challenging tradeoff between robustness and performance. While robust control methods provide rigorous guarantees on system stability under certain…

Model inference for dynamical systems aims to estimate the future behaviour of a system from observations. Purely model-free statistical methods, such as Artificial Neural Networks, tend to perform poorly for such tasks. They are therefore…

We propose a technique for the design and analysis of adaptation algorithms in dynamical systems. The technique applies both to systems with conventional Lyapunov-stable target dynamics and to ones of which the desired dynamics around the…

An artificial neural network architecture, parameterization networks, is proposed for simulating extrapolated dynamics beyond observed data in dynamical systems. Parameterization networks are used to ensure the long term integrity of…

Recurrence plots provide a graphical representation of the recurrent patterns in a timeseries, the quantification of which is a relatively new field. Here we derive analytical expressions which relate the values of key statistics, notably…

The vast majority of systems of practical interest are characterised by nonlinear dynamics. This renders the control and optimization of such systems a complex task due to their nonlinear behaviour. Additionally, standard methods such as…