arXiv subjects

Zachary Morrison

Publications and source records attributed to Zachary Morrison.

4 recordsLinked to original sources

arXiv2023

Dynamic Mode Decomposition of Control-Affine Nonlinear Systems using Discrete Control Liouville Operators

Representation of nonlinear dynamical systems as infinite-dimensional linear operators over Hilbert spaces enables analysis of nonlinear systems via pseudo-spectral operator analysis. In this paper, we provide a novel representation for discrete-time control-affine nonlinear dynamical systems as linear operators acting on a Hilbert space. We also demonstrate that this representation can be used to predict the behavior of the closed-loop system given a known feedback law using recorded snapshots of the system state resulting from arbitrary, potentially open-loop control inputs. We thereby extend the predictive capabilities of dynamic mode decomposition to discrete-time nonlinear systems that are affine in control. We validate the method using two numerical experiments by predicting the response of a controlled Duffing oscillator to a known feedback law, as well as demonstrating the advantage of the developed method relative to existing techniques in the literature.

math.OC↗

arXiv2023

Pilot Performance modeling via observer-based inverse reinforcement learning

The focus of this paper is behavior modeling for pilots of unmanned aerial vehicles. The pilot is assumed to make decisions that optimize an unknown cost functional, which is estimated from observed trajectories using a novel inverse reinforcement learning (IRL) framework. The resulting IRL problem often admits multiple solutions. In this paper, a recently developed novel IRL observer is adapted to the pilot modeling problem. The observer is shown to converge to one of the equivalent solutions of the IRL problem. The developed technique is implemented on a quadcopter where the pilot is a linear quadratic supervisory controller that generates velocity commands for the quadcopter to travel to and hover over a desired location. Experimental results demonstrate the robustness of the method and its ability to learn equivalent cost functionals.

eess.SY↗

arXiv2023

Fault Detection via Occupation Kernel Principal Component Analysis

The reliable operation of automatic systems is heavily dependent on the ability to detect faults in the underlying dynamical system. While traditional model-based methods have been widely used for fault detection, data-driven approaches have garnered increasing attention due to their ease of deployment and minimal need for expert knowledge. In this paper, we present a novel principal component analysis (PCA) method that uses occupation kernels. Occupation kernels result in feature maps that are tailored to the measured data, have inherent noise-robustness due to the use of integration, and can utilize irregularly sampled system trajectories of variable lengths for PCA. The occupation kernel PCA method is used to develop a reconstruction error approach to fault detection and its efficacy is validated using numerical simulations.

stat.ML↗

arXiv2022

Nonuniqueness and Convergence to Equivalent Solutions in Observer-based Inverse Reinforcement Learning

A key challenge in solving the deterministic inverse reinforcement learning (IRL) problem online and in real-time is the existence of multiple solutions. Nonuniqueness necessitates the study of the notion of equivalent solutions, i.e., solutions that result in a different cost functional but same feedback matrix, and convergence to such solutions. While offline algorithms that result in convergence to equivalent solutions have been developed in the literature, online, real-time techniques that address nonuniqueness are not available. In this paper, a regularized history stack observer that converges to approximately equivalent solutions of the IRL problem is developed. Novel data-richness conditions are developed to facilitate the analysis and simulation results are provided to demonstrate the effectiveness of the developed technique.

eess.SY↗