We consider nonlinear optimal control problems with mixed statecontrol constraints. A discretization of the Bolza problem by a Legendre pseudospectral method is considered. It is shown that the operations of discretization and dualization are not commutative. A set of Closure Conditions are introduced to commute these operations. An immediate consequence of this is a Covector Mapping Theorem (C...

Abstract The main aim presented in this article is to provide an efficient transferred Legendre pseudospectral method for solving pantograph delay differential equations. At the first step, we transform problem into a continuous-time optimization and then utilize discretize problem. By discrete problem, can attain pointwise continuous estimated solutions major equation. convergence of has been ...

In this paper, we present a unified computational method based on pseudospectral approximations for the design of optimal pulse sequences in open quantum systems. The proposed method transforms the problem of optimal pulse design, which is formulated as a continuous-time optimal control problem, to a finite-dimensional constrained nonlinear programming problem. This resulting optimization probl...

We examine the merits of using prolate spheroidal wave functions (PSWFs) as basis functions when solving hyperbolic PDEs using pseudospectral methods. The relevant approximation theory is reviewed and some new approximation results in Sobolev spaces are established. An optimal choice of the band-limit parameter for PSWFs is derived for single-mode functions. Our conclusion is that one might gai...

by the pseudospectral Legendre method, which shows that in order to maintain spectral accuracy the grids on which a physical problem is to be solved must also be obtained by spectrally accurate techniques. This paper presents an alternative spectrally accurate computational method of solving the nonlinear controlled Duffing oscillator. The method is based upon constructing the Afth-degree inter...

An important aspect of numerically approximating the solution of an infinite-horizon optimal control problem is the manner in which the horizon is treated. Generally, an infinite-horizon optimal control problem is approximated with a finite-horizon problem. In such cases, regardless of the finite duration of the approximation, the final time lies an infinite duration from the actual horizon at ...