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Nonlinear Data-Driven Approximation of the Koopman Operator
Dan Wilson
Koopman analysis provides a general framework from which to analyze a nonlinear dynamical system in terms of a linear operator acting on an infinite-dimensional observable space. T…
Optimal Control of Oscillation Timing and Entrainment Using Large Magnitude Inputs: An Adaptive Phase-Amplitude-Coordinate-Based Approach
Dan Wilson
Given the high dimensionality and underlying complexity of many oscillatory dynamical systems, phase reduction is often an imperative first step in control applications where oscil…
Data-Driven Inference of High-Accuracy Isostable-Based Dynamical Models in Response to External Inputs
Dan Wilson
Isostable reduction is a powerful technique that can be used to characterize behaviors of nonlinear dynamical systems in a basis of slowly decaying eigenfunctions of the Koopman op…
An Adaptive Phase-Amplitude Reduction Framework Without Constraints on Inputs
Dan Wilson
Phase reduction is a well-established technique used to analyze the timing of oscillations in response to weak external inputs. In the preceding decades, a wide variety of results…