In this paper, an optimal trajectory guidance law is developed for a free-floating space manipulator through a combination of a Gaussian pseudospectral collocation scheme with a Non-Linear Problem solver. Specifically, the resulting nonlinear optimal guidance problem with path constraints is defined with the general pseudospectral optimal software and numerically solved by the sparse nonlinear ...

The pseudospectral abscissa and the stability radius are well-established tools for quantifying the stability of a matrix under unstructured perturbations. Based on first-order eigenvalue expansions, Guglielmi and Overton [SIAM J. Matrix Anal. Appl., 32 (2011), pp. 1166-1192] recently proposed a linearly converging iterative method for computing the pseudospectral abscissa. In this paper, we pr...

We consider the optimal control of feedback linearizable dynamic systems subject to mixed state and control constraints. The optimal controller is allowed to be discontinuous including bang-bang control. Although the nonlinear system is assumed to be feedback linearizable, in general, the optimal control does not linearize the dynamics. The continuous optimal control problem is discretized usin...

In this paper, error estimates for generalized Laguerre–Gauss-type interpolations are derived in nonuniformly weighted Sobolev spaces weighted with ωα,β(x) = x αe−βx, α > −1, β > 0. Generalized Laguerre pseudospectral methods are analyzed and implemented. Two model problems are considered. The proposed schemes keep spectral accuracy and, with suitable choice of basis functions, lead to sparse a...

Different discretization and trust-region methods are compared for the low-thrust fuel-optimal trajectory optimization problem using successive convex programming. In particular, differential integral formulations of adaptive pseudospectral Legendre–Gauss–Radau method, an arbitrary-order Legendre–Gauss–Lobatto technique based on Hermite interpolation, a first-order-hold considered. The number p...

Over the last decade, pseudospectral (PS) computational methods for nonlinear constrained optimal control have been applied to many industrial-strength problems, notably the recent zero-propellant-maneuvering of the International Space Station performed by NASA. 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 conv...

Pseudospectral methods are investigated for singularly perturbed boundary value problems for ordinary diierential equations which possess boundary layers. It is well known that if the boundary layer is very small then a very large number of spectral collocation points is required to obtain accurate solutions. We introduce here a new eeective procedure, based on coordinate stretching and the Che...

An improved optimal drug scheduling model with considering two control drugs is proposed and the Gauss pseudospectral-based optimization method studied to decrease tumor size toxicity in this work. Firstly, Dexrazoxane drug, which has significant clinical effect reduce of anticancer introduced. By analyzing growth kinetics cancer chemotherapy, reduction regarded as second input dynamic equation...

We present two new algorithms for investigating the stability of large and sparse matrices subject to real perturbations. The first algorithm computes the real structured pseudospectral abscissa and is based on the algorithm for computing the pseudospectral abscissa proposed by Guglielmi and Overton [SIAM J. Matrix Anal. Appl., 32 (2011), pp. 1166-1192]. It entails finding the rightmost eigenva...