The post-optimality analysis of a tetrahedral formation flying optimal control problem is considered. In particular, this four-spacecraft orbit insertion problem is transcribed to a nonlinear programming problem (NLP) using a direct method called the Gauss pseudospectral method. The Karush-Kuhn-Tucker (KKT) conditions for this NLP are then derived and are compared to the conditions obtained via...

properties of the hybrid of block-pulse functions and lagrange polynomials based on the legendre-gauss-type points are investigated and utilized to define the composite interpolation operator as an extension of the well-known legendre interpolation operator. the uniqueness and interpolating properties are discussed and the corresponding differentiation matrix is also introduced. the applicabili...

Nonplanar trajectory optimization problem with advanced variable specific impulse magnetoplasma rocket (VASIMR) engine is studied. A newly developed method called Gauss Pseudospectral method is applied to the nonplanar trajectory optimization problem with VASIMR engine. Three representative trajectory optimization problems are solved. The first is an orbit raising problem from LEO to GEO; the s...

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...

Acentral computational issue in solving infinite-horizonnonlinear optimal control problems is the treatment of the horizon. In this paper, we directly address this issue by a domain transformation technique that maps the infinite horizon to a finite horizon. The transformed finite horizon serves as the computational domain for an application of pseudospectral methods. Although any pseudospectra...

In this paper, we investigate a new pseudospectral method for mixed boundary value problems defined on quadrilaterals. We introduce a new Legendre-Gauss type interpolation and establish the basic approximation results, which play important roles in pseudospectral method for partial differential equations defined on quadrilaterals. We propose pseudospectral method for two model problems and prov...

properties of the hybrid of block-pulse functions and lagrange polynomials based on the legendre-gauss-type points are investigated and utilized to define the composite interpolation operator as an extension of the well-known legendre interpolation operator. the uniqueness and interpolating properties are discussed and the corresponding differentiation matrix is also introduced. the appli...

This paper presents the use of Legendre pseudospectral method for the optimization of finite-thrust orbital transfer for spacecrafts. In order to get an accurate solution, the System’s dynamics equations were normalized through a dimensionless method. The Legendre pseudospectral method is based on interpolating functions on Legendre-Gauss-Lobatto (LGL) quadrature nodes. This is used to transfor...

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...