In this paper, a numerical method for solving the constrained optimal control of time-varying singular systems with quadratic performance index is presented. Presented method is based on Bernste in polynomials. Operational matrices of integration, differentiation and product are introduced and utilized to reduce the optimal control of time-varying singular problems to the solution of algebraic ...

Multiple-Scattering Theory Beyond The MutTm-Tin Approximation J. Molenaar Mathematics Consulting Department Katholieke Universiteit Toernooiveld 6525 ED Nijmegen We present a new derivation of multiple-scattering theory as applied in solid state physics. The present approach is a generalization of the well-known Korringa, Kohn and Rostoker (KKR) formalism and holds also in the case of overlappi...

The impacts of the fast growth renewable energy sources (RESs) and distribution static synchronous compensators (D-STATCOMs) on unbalanced radial networks (URDNs) are analyzed with three-phase power flow algorithms (PFAs). As URDNs unbalanced, they can experience voltage unbalance (VU). This paper proposes a novel PFA for multiple RES D-STATCOM device integrations. bus number matrix (BNM) branc...

In this paper, we introduce hybrid of block-pulse functions and Bernstein polynomials and derive operational matrices of integration, dual, differentiation, product and delay of these hybrid functions by a general procedure that can be used for other polynomials or orthogonal functions. Then, we utilize them to solve delay differential equations and time-delay system. The method is based upon e...

In this work, the convection-diffusion integro-differential equation with a weakly singular kernel is discussed. The  Legendre spectral tau method is introduced for finding the unknown function. The proposed method is based on expanding the approximate solution as the elements of a shifted Legendre polynomials. We reduce the problem to a set of algebraic equations by using operational matrices....

In this paper, a new shifted ultraspherical wavelets operational matrix of derivatives is introduced. The two wavelets operational matrices, namely Legendre and first kind Chebyshev operational matrices can be deduced as two special cases. Two numerical algorithms based on employing the shifted ultraspherical wavelets operational matrix of derivatives for solving linear and nonlinear differenti...

Within the process of European integrations in sphere defence, Republic Serbia is expected to adapt Common security and defence policy Union regarding strategic planning, normative legal conditions, as well construction appropriate operational capacities for completing tasks EU joint operations. This paper analyses policy, compatibility The Serbia's with that EU, capabilities Serbian Armed Forc...

this paper presents an approach for solving a nonlinear stochastic differential equations (nsdes) using a new basis functions (nbfs). these functions and their operational matrices areused for representing matrix form of the nbfs. with using this method in combination with the collocation method, the nsdes are reduced a stochastic nonlinear system of equations and unknowns. then, the error anal...