共查询到20条相似文献，搜索用时 125 毫秒
1.
Andrea L׳Afflitto 《Journal of The Franklin Institute》2017,354(1):456-478
In this paper, we develop a unified framework to find state-feedback control laws that solve two-player zero-sum differential games over the infinite time horizon and guarantee partial-state asymptotic stability of the closed-loop system. Partial-state asymptotic stability is guaranteed by means of a Lyapunov function that is positive definite and decrescent with respect to part of the system state. The existence of a saddle point for the system?s performance measure is guaranteed by the fact that this Lyapunov function satisfies a partial differential equation that corresponds to a steady-state form of the Hamilton–Jacobi–Isaacs equation. In the second part of this paper, we show how our differential game framework can be applied not only to solve pursuit-evasion and robust optimal control problems, but also to assess the effectiveness of a model reference adaptive control law. Specifically, the model reference adaptive control architecture is designed to guarantee satisfactory trajectory tracking for uncertain nonlinear dynamical systems, whose matched nonlinearities are captured by the regressor vector. By modeling matched and unmatched nonlinearities, which are not captured by the regressor vector, as the pursuer?s and evader?s control inputs in a differential game, we provide an explicit characterization of the system?s uncertainties that do not disrupt the trajectory tracking capabilities of the adaptive controller. Two numerical examples illustrate the applicability of our results. 相似文献
2.
《Journal of The Franklin Institute》2022,359(18):10628-10652
Control of a water hyacinth-fish ecological system is required for a healthy and sustainable environment. This paper aims to investigate the global dynamics of a water hyacinth fish ecological system under ratio-dependent state impulsive control. First, we study the positivity and boundedness of the solution of the controlled system. By studying the local stability of the equilibrium, we find that the system has two situations. One is that there are two equilibria, namely a saddle point and a boundary equilibrium. In the second case, there are four equilibria, namely, two saddle points, a boundary equilibrium, and a focus point. For the first case, when we select an appropriate ratio-dependent control threshold, the trajectory will globally converge to the boundary equilibrium. For the second case, when the control line is located below the focus point, by using Poincare mapping method, flip bifurcation theory, and vector field analysis techniques, we find that the solution of the controlled system either globally converges to the boundary equilibrium, order-1 periodic solution, or order-2 periodic solution under certain conditions. When the control line is located above the focus point, the solution of the controlled system either globally converges to the focus point, order-1 or order-2 periodic solution. Finally, we use examples to verify the correctness and validity of the theoretical results. 相似文献
3.
吴英毅 《中国科学院研究生院学报》2008,25(5):585-591
HCMU是一种在Riemann面上带奇点的extremal度量．在面积和Calabi能量有界的情况下, HCMU的Gauss曲率是Riemann面上的连续函数．本文得到一个在球面上没有Gauss曲率鞍点的HCMU的明显表达式,并进一步证明了在球面或环面上HCMU的Gauss曲率光滑的充要条件是度量的所有奇点的角度都是整数． 相似文献
4.
《Journal of The Franklin Institute》2022,359(17):9925-9951
This paper focuses on constructing a conjugate gradient-based (CGB) method to solve the generalized periodic coupled Sylvester matrix equations in complex space. The presented method is developed from a point of conjugate gradient methods. It is proved that the presented method can find the solution of the considered matrix equations within finite iteration steps in the absence of round-off errors by theoretical derivation. Some numerical examples are provided to verify the convergence performance of the presented method, which is superior to some existing numerical algorithms both in iteration steps and computation time. 相似文献
5.
结合模松弛SQP算法和强次可行方向算法思想,给出了初始点任意选取的新的拟强次可行方向算法。每步迭代,只需求解一个总有最优解的二次规划子问题来产生主搜索方向,引入一种新的非单调曲线搜索来产生步长,在较弱的条件下,可以得到算法的全局收敛性。 相似文献
6.
文章以天津子牙河大桥上部结构安装施工为例,说明自锚式悬索桥上部结构包括塔顶索鞍底板及索鞍安装;主缆施工工艺;吊杆安装的工艺及配套附属件的安装工艺。 相似文献
7.
Geyang Xiao Huaguang Zhang Qiuxia Qu He Jiang 《Journal of The Franklin Institute》2018,355(5):2610-2630
In this paper, a novel iterative approximate dynamic programming scheme is proposed by introducing the learning mechanism of value iteration (VI) to solve the constrained optimal control problem for CT affine nonlinear systems with utilizing only one neural network. The idea is to show the feasibility of introducing the VI learning mechanism to solve for the constrained optimal control problem from a theoretical point of view, and thus the initial admissible control can be avoided compared with most existing works based on policy iteration (PI). Meanwhile, the initial condition of the proposed VI based method can be more general than the traditional VI method which requires the initial value function to be a zero function. A general analytical method is proposed to demonstrate the convergence property. To simplify the architecture, only one critic neural network is adopted to approximate the iterative value function while implementing the proposed method. At last, two simulation examples are proposed to validate the theoretical results. 相似文献
8.
9.
提出了一种基于迭代自适应机制的改进算法,有效地缩减了分层置信传播算法(HBP)的计算时间.传统HBP计算时间随指定的迭代上限增加而线性增长.为此引入消息收敛的条件判断,在迭代上限相同情况下,减少算法的迭代次数,缩减整体迭代时间.实验表明,与传统HBP相比,该方法计算时间缩减了38％以上,计算时间对整体迭代上限不敏感.该方法可以应用于使用HBP算法的其他方法. 相似文献
10.
运用单调迭代法研究一类非线性三阶常微分方程三点边值问题,不仅获得其单调正解的存在性,还给出单调正解的两个迭代序列,并且迭代序列的初值是零函数或一次函数,这从计算的角度来说是非常有用和可行的。 相似文献
11.
Betzalel Avitzur Walter C. Hahn Samy Iscovici 《Journal of The Franklin Institute》1975,299(5):339-358
A variety of mathematical models may be used to analyse plastic deformation during a metal-forming process. One of these methods—limit analysis—places the estimate of required power between an upper bound and a lower bound. The upper and lower bound analyses are designed so that the actual power or forming stress requirement is less than that predicted by the upper bound and greater than that predicted by the lower bound. Finding a lower upper bound and a higher lower bound reduces the uncertainty of the actual power requirement. Upper and lower bounds will permit the determination of such quantities as required forces, limitations on the process, optimal die design, flow patterns, and prediction and prevention of defects.Fundamental to the development of both upper bound and lower bound solutions is the division of the body into zones. For each of the zones there is written either a velocity field (upper bound) or a stress field (lower bound). A better choice of zones and fields brings the calculated values closer to actual values.In the present work, both upper and lower bound solutions are presented for axisymmetric flow through conical converging dies. For the upper bound triangular velocity fields have been solved and compared to previously published work on spherical velocity fields. It is found that each type provides a lower solution over a part of the range of process variables. A previously published lower bound solution for axisymmetric flow is refined. 相似文献
12.
《Journal of The Franklin Institute》2022,359(2):1713-1731
Optimized extreme learning machine (OELM) has been shown to achieve high performance on classification problems due to its simple dual form. This paper presents a predictor-corrector affine scaling interior point method to exploit the dual problem of OELM. This method aims to combine a predictor step with a corrector step for determining the descent Newton direction. At each iteration, the predictor step focuses on the complementarity gap reduction and computes an affine scaling direction to estimate the extent of the reduction of complementarity gap, while the corrector step traces the central path towards the optimal solution by high order approximation, and computes the corresponding center direction. Then, the Newton direction is combined by using both two directions, and the iteration sequence of interior feasible points converges to the optimal solution. Extensive experimental evaluations on various benchmark datasets show that the proposed algorithms outperform other interior point-based or active set-based algorithms. Moreover, they are able to converge in fewer iterations, which are independent of kernel type, dataset size and dimensionality. 相似文献
13.
The paper is indicated to constructing a modified conjugate gradient iterative (MCG) algorithm to solve the generalized periodic multiple coupled Sylvester matrix equations. It can be proved that the proposed approach can find the solution within finite iteration steps in the absence of round-off errors. Furthermore, we provide a method for choosing the initial matrices to obtain the least Frobenius norm solution of the system. Some numerical examples are illustrated to show the performance of the proposed approach and its superiority over the existing method CG. 相似文献
14.
An impulsive reaction-diffusion periodic food-chain system with Holling type III functional response is presented and studied in this paper. Sufficient conditions for the ultimate boundedness and permanence of the food-chain system are established based on the upper and lower solution method and comparison theory of differential equation. By constructing appropriate auxiliary function, the conditions for the existence of a unique globally stable positive periodic solution are also obtained. Some numerical examples are shown to illustrate our results. A discussion is given in the end of the paper. 相似文献
15.
Maurice A. King 《Journal of The Franklin Institute》1980,309(4):195-213
Important problems exist in the field of communications theory whose solution is in the form of an expectation of a function of a random variable. Often it is not computationally feasible to evaluate these moments exactly. This paper presents a geometric bounding technique that yields tight upper and lower bounds to generalized moments of a broad class of random variables. This technique produces excellent results for these communications theory problems. 相似文献
16.
《Journal of The Franklin Institute》2023,360(3):1523-1539
This paper considers a trilayer Stackelberg game problem for nonlinear system with three players. A novel performance function is defined for each player, which depends on the coupling relationships with the other two players. The coupled Hamilton–Jacobi–Bellman (HJB) equations are built from the performance functions, and the optimal control polices of three players are obtained based on the Bellman’s principle of optimality. Because of the nonlinearity and coupling characteristics, a policy iteration (PI) algorithm with a three-layer decision-making framework is developed to online learn the coupled HJB equations. In order to implement the algorithm, we construct a critic-action neural network (NN) structure and design a NN approximation-based iteration algorithm. Finally, a simulation example is presented to verify the effectiveness of the proposed method. 相似文献
17.
用鞍点法导出了非均匀桂面波的复射线束展开系数公式，所得结果可用于研究非均匀柱面波在复杂环境中的传播、散射等问题。 相似文献
18.
In this paper, by constructing the equivalent form of the continuous algebraic Riccati equation and utilizing the eigenvalue and singular value inequalities of matrix's sum and product, we propose new lower and upper matrix bounds for the solution of the continuous algebraic Riccati equation. Finally, we give corresponding numerical examples to illustrate the effectiveness of our results. 相似文献
19.
GDP是目前衡量经济增长的重要和主要指标,但该指标既能不反映经济增长的质量,也不能全面反映社会的进步,更不能反映国民的富裕程度。而GPI(真实进步指标)系统涵盖了社会、经济和环境三个账户,被公认为是检验一个国家或一个地区可持续发展水平较有效的工具。中国GPI研究组建立的中国GPI系统,将有利于透过GDP所表现出来的繁荣的经济景象,检验我国经济发展质量以及在经济、社会、资源与生态环境等各个领域的实际进步。如果将GPI作为GDP的补充和完善,并作为考察各地业绩的补充指标,将有利于协助各级决策者适时地调整发展战略和措施,逐步达到真正落实科学发展观和构建和谐社会的目标。 相似文献
20.
Numerous upper bounds for the truncation error of the Shannon sampling expansion associated with the Fourier transforms are available in the literature. In this paper we derive an upper bound for the truncation error of the generalized sampling expansion associated with the Hankel (Bessel) transform. A clear example of the application of such series is in the analysis of optical systems with circular symmetry. A lower bound for the Bessel function Jm(j?,N+iy), which agrees with the known asymptotic one and is necessary to this analysis, is derived. The method, which employs complex contour integration, can be applied to other generalized sampling expansions. 相似文献