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

Abstract

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.