Pseudospectral methods PMs for solving general optimal control problems OCPs attract an increasing amount of research and application in engineering. It is challenging to improve the convergence rate, the solution accuracy, and the applicability of PMs, especially for nonsmooth problems. Existing hp-adaptive PMs consider only one heuristic criterion, which cannot produce satisfactory performanc...

A convergence theory is presented for approximations of continuous-time optimal control problems based on a Gauss pseudospectral discretization. Under assumptions of coercivity and smoothness, the Gauss pseudospectral method has a local minimizer that converges exponentially fast in the sup-norm to a local minimizer of the continuous-time optimal control problem. The convergence theorem is pres...

An initial value problem with piecewise constant coefficients is considered. The accuracies for both finite difference methods and the pseudospectral method are analyzed, and a modification of the initial value problem is suggested. The modified problem is shown to have the same temporal period as the original problem does, and a second order accuracy is obtained for the pseudospectral method a...

The problem of determining minimum-fuel maneuver sequences for a four-spacecraft formation is considered. The objective of this paper is to determine fuel-optimal configuration trajectories that transfer a four spacecraft formation from an initial parking orbit to a desired terminal reference orbit while satisfying particular formation constraints. In this paper, the configuration problem is so...

We extend the application of Legendre-Galerkin algorithms for sixth-order elliptic problems with constant coefficients to sixth-order elliptic equations with variable polynomial coefficients. The complexities of the algorithm are O(N) operations for a one-dimensional domain with N − 5 unknowns. An efficient and accurate direct solution for algorithms based on the LegendreGalerkin approximations...

By systematically altering the in-plane flight path and velocity of an aircraft and the rate at which the cable is deployed, the tip of a cable being towed behind an aircraft is shown to rendezvous with a ground-based surface location in minimum time, with minimum control effort required. This is achieved through optimal control, formulated as a nonlinear programming problem using the Legendre-...