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2.
This article presents a new approach for solving the Optimal Control Problem (OCP) of linear time-delay systems with a quadratic cost functional. The proposed method can also be used for designing optimal control time-delay systems with disturbance. In this study, the Variational Iteration Method (VIM) is employed to convert the original Time-Delay Optimal Control Problem (TDOCP) into a sequence of nonhomogeneous linear two-point boundary value problems (TPBVPs). The optimal control law obtained consists of an accurate linear feedback term and a nonlinear compensation term which is the limit of an adjoint vector sequence. The feedback term is determined by solving Riccati matrix differential equation. By using the finite-step iteration of a nonlinear compensation sequence, we can obtain a suboptimal control law. Finally, Illustrative examples are included to demonstrate the validity and applicability of the technique. 相似文献
3.
We extend the definition of the classical Jacobi polynomials withindexes α, β>−1 to allow α and/or β to be negative integers. We show that the generalized Jacobi polynomials, with indexes corresponding to the number of boundary conditions in a given partial differential equation, are the natural basis functions for the spectral approximation of this partial differential equation. Moreover, the use of generalized Jacobi polynomials leads to much simplified analysis, more precise error estimates and well conditioned algorithms.Mathematics subject classification 1991. 65N35, 65N22, 65F05, 35J05 相似文献
4.
混合Hermite-Lagrange插值之同时逼近 总被引:1,自引:1,他引:0
谢庭藩 《中国计量学院学报》1993,(2)
对于(-1,1)中的结点组{X_k}_(k=1)~n,记l_k(x)为相应的Lagrange插值基本多项式,又记A_n=‖∑(2-x~2-x_k~2)(1-x_k~2)~-1丨l_k(x)‖。对于f∈C_([-1,1)~q与r=[q+2/2],本文证明满足条件H_n(f,x_k)=f(x_k)(k=1,2,…,n),H_n~(s)(f,±1)=f~(s)(±1)(s=0,1,…,n-1)的n+2r-1次代数多项式H_n(f,x)有逼近性质H_n~(s)(f,x)-f~(s)(x)=(?)其中δ_n(x)=n~(-1)(1-x~2)~(1/2),△_n(x)=δ_n(x)+n~(-2).作为证明的重要工具,本文还对n次代数多项式P_n(x),建立了另一形式的Bernstein不等武:若 P_n(x)=O(1)δ_n~q(x)ω(δ_n(x)),则p_n~(S)(X)=O(1)δ_n~(q-2S)(X)ω(δ_n(X))△_n~s(X)。 相似文献
5.
J. C. Sevy 《Calcolo》1993,30(1):41-68
Explicit error estimates are given for the iterated Boolean sum of a sequence of simultaneous approximants; the rate of convergence
is shown to be improved for smooth functions. The general results are applied in the case of the Bernstein, Durrmeyer and
Stancu operators. 相似文献
6.
姜功建 《云南工业大学学报》1993,(4)
本文研究推广的Kantorovi多项式P_n~*(f, x)在L_p[0,1]空间中的保持Lipschitz条件性质。 相似文献
7.
Piero Villaggio 《Journal of Engineering Mathematics》2003,46(3-4):409-416
The diffusion of contact stresses between an elastic bar, bonded to an elastic half-plane and loaded longitudinally, requires the integration of a singular integral equation. The solution of this equation is not available in closed form, but only by a series expansion of the contact tangential force mutually transmitted between the stiffener and the plate. Since forty years it has been realized that the expansion of the solution in terms of Chebyshev polynomials is its most convenient method of representation. The procedure can also be extended to treat the brittle detachments of the tips of the stiffener when, according to Griffith's criterion of fracture, a balance can be virtually established between the increase of strain energy due to a propagation of cracks and the surface energy created. 相似文献
8.
零点位于左扇区的多项式菱形族 总被引:1,自引:1,他引:0
本文考虑多项式菱形族的左扇区稳定性,证明了多项式族左扇区稳定的充分必要条件是的至多4q(q—1)条特殊棱边左扇区稳定;进一步,在一定条件下,只要检验的4q个顶点多项式就可确定的左扇区稳定性。 相似文献
9.
We establish a numerically feasible algorithm to find a simplicial approximation A to a certain part
of the boundary of the set
of stable (or Hurwitz) polynomials of degree 4. Moreover, we have that
. Using this, we build an algorithm to find a piecewise-linear approximation to the intersection curve of a given surface contained in
4 with
. We have also devised an efficient computer program to perform all these operations. The main motivation is to find the curve of nondegenerate bifurcation points in parameter space for a given 2-parametric Hopf bifurcation problem of dimension 4. 相似文献
10.
In this note the stability of a second-order quasi-polynomial with a single delay is studied. Although there is a vast literature on this problem, most available solutions are limited to some particular cases. Moreover, some published results on this subject appear to contain imprecise, or even wrong, conditions. The purpose of this note is to show that by accurate application of known theories, a complete explicit characterization of stability regions can be derived in a most general case. As a byproduct of the proposed analysis, we show that in the high-order case the quasi-polynomial is delay-independent unstable whenever its delay-free version has an odd number of unstable roots (or, equivalently, a negative static gain). 相似文献