An iterative method for suboptimal control of linear time-delayed systems

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.     

Optimal Spectral-Galerkin Methods Using Generalized Jacobi Polynomials

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     

推广的Kantorovi多项式的L_p保持Lipschitz条件性

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。     

Brittle detachment of a stiffener bonded to an elastic plate

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.     

An introduction to Wu's method for mechanical theorem proving in geometry

Wu's algebraic method for mechanically proving geometry theorems is presented at a level as elementary as possible with sufficient examples for further understanding the complete method.The work reported here was supported by NSF Grant DCR-8503498.     

零点位于左扇区的多项式菱形族

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。     

Finding nondegenerate Hopf bifurcation points for four-dimensional two-parametric systems

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.     

On stability of second-order quasi-polynomials with a single delay

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).     

核磁共振测井在致密含气砂岩中的应用

通过对核磁共振测井的T₂谱及其T₂截至值的合理选取，解释并获得了鄂尔多斯盆地西缘上古生界山西组、石盒子组致密砂岩储集层的总孔隙度、有效孔隙度、毛细管束缚水体积、可动水体积及渗透率等参数，据此预测的储集层孔隙结构特征与岩心分析测试结果很吻合。研究还发现，致密含气砂岩的T₂谱具有分布范围窄-中等，波形及差谱分析谱位置明显后移、分布中等、呈单峰的典型特征。结合常规测井资料，综合研究了致密砂岩储层特征及其含气层的测井响应。经测试验证，致密含气砂岩储层的核磁共振测井解释结果十分可靠，表明核磁共振测井可用于该区致密含气砂岩复杂储集层评价。     

Analysis of nonlinear electrical circuits using bernstein polynomials

In electrical circuit analysis, it is often necessary to find the set of all direct current (d.c.) operating points (either voltages or currents) of nonlinear circuits. In general, these nonlinear equations are often represented as polynomial systems. In this paper, we address the problem of finding the solutions of nonlinear electrical circuits, which are modeled as systems of n polynomial equations contained in an n-dimensional box. Branch and Bound algorithms based on interval methods can give guaranteed enclosures for the solution. However, because of repeated evaluations of the function values, these methods tend to become slower. Branch and Bound algorithm based on Bernstein coefficients can be used to solve the systems of polynomial equations. This avoids the repeated evaluation of function values, but maintains more or less the same number of iterations as that of interval branch and bound methods. We propose an algorithm for obtaining the solution of polynomial systems, which includes a pruning step using Bernstein Krawczyk operator and a Bernstein Coefficient Contraction algorithm to obtain Bernstein coefficients of the new domain. We solved three circuit analysis problems using our proposed algorithm. We compared the performance of our proposed algorithm with INTLAB based solver and found that our proposed algorithm is more efficient and fast.