Distributed and Asynchronous Algorithm for Smooth High-dimensional Function Approximation using Orthotope B-splines

Distributed and Asynchronous Algorithm for Smooth High-dimensional Function Approximation using Orthotope B-splines

Meyer, Johann (TU Delft Electrical Engineering, Mathematics and Computer Science; TU Delft Aerospace Engineering)

de Visser, C.C. (mentor)
Al-Ars, Z. (graduation committee)
Mulder, M. (graduation committee)

Delft University of Technology

2021-02-24

Aircraft are complex systems with, in some cases, high-dimensional nonlinear interactions between control surfaces. When a failure occurs, adaptive flight control methods can be utilised to stabilise and make the aircraft controllable. Adaptive flight control methods, however, require accurate aerodynamic models - where first-order continuity is necessary for estimating the control derivatives and mitigating chattering that can reduce the longevity of components. Additionally, high-dimensional offline model identification with current approaches can take several hours for a few dimensions and this means model iterating and hyper-parameter tuning is often not feasible. Current approaches to smooth high-dimensional functional approximation are not scalable, require global communication between iteration steps, and are ill-conditioned in higher dimensions. This research develops the Distributed Asynchronous B-spline (DAB) algorithm that is more robust to ill-conditioning, due to low data coverage, by using first-order methods with acceleration and weighted constraint application. This algorithm is also suitable for continuous state-spaces. Smooth aerodynamic models can be determined in exactly n·r iterations, where r is the number of continuity equations in a single dimension and n is the number of dimensions. Moreover, memory reorganisation is proposed to avoid false sharing and conflict-free use of shared memory on the GPU to ensure that the algorithm runs efficiently in parallel.

Smooth High-dimensional Linear Function Approximation
Linearly-constrained Convex Quadratic Programming
Asynchronous Algorithms
Parallel Algorithms
Multivariate B-spline
System Identification
GPU
Cache-aware

http://resolver.tudelft.nl/uuid:e418ca00-6aa1-4255-9eb2-a837f155871f

2026-02-24

Double degree in Aerospace and Computer Engineering

Student theses

master thesis

© 2021 Johann Meyer