Related papers: Fast Mesh Refinement in Pseudospectral Optimal Con…
Over the last two decades, pseudospectral methods based on Lagrange interpolants have flourished in solving trajectory optimization problems and their flight implementations. In a seemingly unjustified departure from these highly successful…
This paper details a methodology to transcribe an optimal control problem into a nonlinear program for generation of the trajectories that optimize a given functional by approximating only the highest order derivatives of a given system's…
An adaptive mesh refinement and error estimation method for numerically solving optimal control problems is developed using Legendre-Gauss-Radau direct collocation. In regions of the solution where the desired accuracy tolerance has not…
We study strategies for increasing the precision in the blurring models by maintaining a complexity in the related numerical linear algebra procedures (matrix-vector product, linear system solution, computation of eigenvalues etc.) of the…
In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…
Multi-revolution low-thrust trajectory optimization problems are important and challenging in space mission design. In this paper, an efficient, accurate, and widely applicable pseudospectral method is proposed to solve multi-revolution…
A mesh refinement method is described for solving optimal control problems using Legendre-Gauss-Radau collocation. The method detects discontinuities in the control solution by employing an edge detection scheme based on jump function…
A method for performing high order mesh refinement multigrid computations is presented. The Full Approximation Scheme (FAS) multigrid technique is utilized for a sequence of nested patches of increasing resolution. Conservation forms are…
Solving inverse and optimization problems over solutions of nonlinear partial differential equations (PDEs) on complex spatial domains is a long-standing challenge. Here we introduce a method that parameterizes the solution using spectral…
This paper presents a Fourier integral pseudospectral (FIPS) method for a general class of nonlinear, periodic optimal control (OC) problems with equality and/or inequality constraints and sufficiently smooth solutions. In this scheme, the…
The local refinement of PHT-splines (polynomial splines over hierarchical T-meshes) is achieved by a simple cross insertion, which may introduce superfluous control points or coefficients. By allowing split-in-half in mesh refinement,…
It has now become customary in the field of numerical relativity to couple high order finite difference schemes to mesh refinement algorithms. To this end, different modifications to the standard Berger-Oliger adaptive mesh refinement…
We present a refinement of the Spectral Method by incorporating an optimization method into it and generalize it to two space dimensions. We then apply this Refined Spectral Method as an extremely accurate technique for finding the bound…
In this paper, a well-conditioned collocation method is constructed for solving general $p$-th order linear differential equations with various types of boundary conditions. Based on a suitable Birkhoff interpolation, we obtain a new set of…
Highly accurate simulation of plasma transport is needed for the successful design and operation of magnetically confined fusion reactors. Unfortunately, the extreme anisotropy present in magnetized plasmas results in thin boundary layers…
Reconstruction of the point spread function (PSF) is a critical process in weak lensing measurement. We develop a real-data based and galaxy-oriented pipeline to compare the performances of various PSF reconstruction schemes. Making use of…
Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…
A mesh refinement method is developed for solving bang-bang optimal control problems using direct collocation. The method starts by finding a solution on a coarse mesh. Using this initial solution, the method then determines automatically…
In this paper, we prove a theorem on the rate of convergence for the optimal cost computed using PS methods. It is a first proved convergence rate in the literature of PS optimal control. In addition to the high-order convergence rate, two…
In this paper, we propose a meshfree approximation method for the implicit filter developed in [2], which is a novel numerical algorithm for nonlinear filtering problems. The implicit filter approximates conditional distributions in the…