Static performance of functionally graded cantilever nanobeams exposed to lateral and axial loads from the end was examined by applying Pseudospectral Chebyshev Method. A solution is given for bending analysis using Euler-Bernoulli beam theory. The nonlocal elasticity theory first introduced Eringen used represent effect on a small scale. Using aforementioned theory, governing differential equa...

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...

This paper presents discrete Galerkin method for obtaining the numerical solution of higher even-order integro-differential equations with variable coefficients. We use the generalized Jacobi polynomials with indexes corresponding to the number of homogeneous initial conditions as natural basis functions for the approximate solution. Numerical results are presented to demonstrate the effectiven...

Recent convergence results with pseudospectral methods are exploited to design a robust, multigrid, spectral algorithm for computing optimal controls. The design of the algorithm is based on using the pseudospectral differentiation matrix to locate switches, kinks, corners, and other discontinuities that are typical when solving practical optimal control problems. The concept of pseudospectral ...

We present a formulation and implementation of MBller-Plesset perturbation theory in a pseudospectral framework. At the second-order level, the pseudospectral formulation is a formally a factor of N/n faster than conventional approaches, while the third order is formally faster by a factor of n, where Nis the number of atomic orbitals and n is the number of occupied orbitals. The accuracy of th...

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...

In this paper a generalization of the indirect pseudo-spectral method, presented in [17], for numerical solution budget-constrained infinite horizon optimal control problems is presented. Consideration problem statement framework weighted functional spaces allows to arrive at good approximation initial value adjoint variable, which inevitable obtaining solutions. The method illustrated by apply...