Related papers: Fourier-Gegenbauer Pseudospectral Method for Solvi…
We introduce the tensor numerical method for solving optimal control problems that are constrained by fractional 2D and 3D elliptic operators with variable coefficients. We solve the governing equation for the control function which…
We present PANOC, a new algorithm for solving optimal control problems arising in nonlinear model predictive control (NMPC). A usual approach to this type of problems is sequential quadratic programming (SQP), which requires the solution of…
This study presents the Fourier-Gegenbauer Integral-Galerkin (FGIG) method, a novel and efficient numerical framework for solving the one-dimensional advection-diffusion equation with periodic boundary conditions. The FGIG method uniquely…
Solving optimal control problems (OCPs) of autonomous agents operating under spatial and temporal constraints fast and accurately is essential in applications ranging from eco-driving of autonomous vehicles to quadrotor navigation. However,…
We introduce the tensor numerical method for solution of the $d$-dimensional optimal control problems with fractional Laplacian type operators in constraints discretized on large $n^{\otimes d}$ tensor-product Cartesian grids. The approach…
In its simplest form, a chemostat consists of microorganisms or cells that grow continually in a specific phase of growth while competing for a single limiting nutrient. Under certain conditions of the cell growth rate, substrate…
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…
We propose and analyze an extended Fourier pseudospectral (eFP) method for the spatial discretization of the Gross-Pitaevskii equation (GPE) with low regularity potential by treating the potential in an extended window for its discrete…
We present a method to solve fractional optimal control problems, where the dynamic depends on integer and Caputo fractional derivatives. Our approach consists to approximate the initial fractional order problem with a new one that involves…
Accurate prediction of rarefied gas flows is important for space vehicle design, particularly in rarefied regimes where the Navier-Stokes equations are no more valid. While the direct simulation Monte Carlo (DSMC) method acts as a numerical…
We propose two efficient numerical approaches for solving variable-order fractional optimal control-affine problems. The variable-order fractional derivative is considered in the Caputo sense, which together with the Riemann-Liouville…
Fourier ptychographic microscopy (FPM) is a novel computational coherent imaging technique for high space-bandwidth product imaging. Mathematically, Fourier ptychographic (FP) reconstruction can be implemented as a phase retrieval…
We present a combination technique based on mixed differences of both spatial approximations and quadrature formulae for the stochastic variables to solve efficiently a class of Optimal Control Problems (OCPs) constrained by random partial…
Integer-order calculus often falls short in capturing the long-range dependencies and memory effects found in many real-world processes. Fractional calculus addresses these gaps via fractional-order integrals and derivatives, but…
An adaptive direct collocation method is developed for solving optimal control problems constrained by parabolic partial differential equations. The partial differential equation is first reformulated in a variational setting, where the…
Two key challenges in optimal control include efficiently solving high-dimensional problems and handling optimal control problems with state-dependent running costs. In this paper, we consider a class of optimal control problems whose…
A general-purpose C++ software program called $\mathbb{CGPOPS}$ is described for solving multiple-phase optimal control problems using adaptive Gaussian quadrature collocation. The software employs a Legendre-Gauss-Radau direct orthogonal…
This chapter presents some numerical methods to solve problems in the fractional calculus of variations and fractional optimal control. Although there are plenty of methods available in the literature, we concentrate mainly on approximating…
In this article, we first introduce a singular fractional Sturm-Liouville eigen-problems (SFSLP) on unbounded domain. The associated fractional differential operators in these problems are both Weyl and Caputo type . The properties of…
Recently, the numerical schemes of the Fokker-Planck equations describing anomalous diffusion with two internal states have been proposed in [Nie, Sun and Deng, arXiv: 1811.04723], which use convolution quadrature to approximate the…