Global convergence of a class of smooth penalty methods for semi-infinite programming

For the semi-infinite programming (SIP) problem, the authors first convert it into an equivalent nonlinear programming problem with only one inequality constraint by using an integral function, and then propose a smooth penalty method based on a class of smooth functions. The main feature of this method is that the global solution of the penalty function is not necessarily solved at each iteration, and under mild assumptions, the method is always feasible and efficient when the evaluation of the integral function is not very expensive. The global convergence property is obtained in the absence of any constraint qualifications, that is, any accumulation point of the sequence generated by the algorithm is the solution of the SIP. Moreover, the authors show a perturbation theorem of the method and obtain several interesting results. Furthermore, the authors show that all iterative points remain feasible after a finite number of iterations under the Mangasarian-Fromovitz constraint qualification. Finally, numerical results are given.     

基于T-S模型的约束鲁棒保性能飞行控制律设计

对一类具有范数有界参数不确定Takagi-Sugeno (T-S)模糊模型系统,采用状态反馈并行分配补偿结构,综合考虑变量约束和多个性能指标,研究了约束鲁棒最优保性能飞行控制律设计问题。改进输入、输出及状态约束线性矩阵不等式,提出了带约束模糊最优保性能控制定理。在一般抗干扰控制基础上引入不确定性矩阵,证明了模糊鲁棒最优抗干扰定理。综合上述结论,推导出带约束模糊最优保性能抗干扰定理。最后,建立了飞机不确定T-S模糊模型,分别设计了满足上述3个定理的飞行控制律,并进行了仿真与对比分析,结果验证了该设计方法的有效性。     

非零和多准则合作型对策研究

讨论了非零和多准则合作型对策的若干问题．定义了Ｐａｒｅｔｏ最优安全策略与安全水平，研究了确定Ｐａｒｅｔｏ最优安全策略与安全水平的规划法，给出了协商可行集的约束条件，提出了改善的Ｎａｓｈ定理，对一类特殊问题研究了最优威胁集的确定方法，并且算例对上述内容进行了验证．     

Finite-time neural funnel control for motor servo systems with unknown input constraint

In this paper, a finite-time neural funnel control (FTNFC) scheme is proposed for motor servo systems with unknown input constraint. To deal with the non-smooth input saturation constraint problem, a smooth non-affine function of the control input signal is employed to approximate the saturation constraint, which is further transformed into an affine form according to the mean-value theorem. A fast terminal sliding mode manifold is constructed by using a novel funnel error variable to force the tracking error falling into a prescribe boundary within a finite time. Then, a simple sigmoid neural network is utilized to approximate the unknown system nonlinearity including the saturation. Different from the prescribed performance control (PPC), the proposed finite-time neural funnel control avoids using the inverse transformed function in the controller design, and could guarantee the prescribed tracking performance without knowing the saturation bounds in prior. The effectiveness and superior performance of the proposed method are verified by comparative simulation results.     

用线性系统理论分析相控阵天线

相控阵天线是一离散阵,它的波束控制采用了数字移相器。因所用的字长有限,必然对天线的性能有影响。本文用线性系统中的采样定理导出了阵元间距的约束条件,用付氏变换理论,计算出在有限字长时,对天线性能的影响,并在空间馈电的情形下,导出了方向图锐化等效于时域中脉冲压缩。     

An Exact Solution and its Extensions for Generalized Linear Least Squares Problems

ＡｎＥｘａｃｔＳｏｌｕｔｉｏｎａｎｄｉｔｓＥｘｔｅｎｓｉｏｎｓｆｏｒＧｅｎｅｒａｌｉｚｅｄＬｉｎｅａｒＬｅａｓｔＳｑｕａｒｅｓＰｒｏｂｌｅｍｓＬＩＵＸｉａｏｍｉｎＤｅｐｔｏｆＡｐｐｌｉｅｄＭａｔｈ．，ＢｅｉｊｉｎｇＵｎｉｖｅｒｓｉｔｙｏｆＡｅｒｏｎａ...     

GENERALIZED SUBCONVEXLIKE FUNCTIONS AND MULTIPLE OBJECTIVE OPTIMIZATION

ＧＥＮＥＲＡＬＩＺＥＤＳＵＢＣＯＮＶＥＸＬＩＫＥＦＵＮＣＴＩＯＮＳＡＮＤＭＵＬＴＩＰＬＥＯＢＪＥＣＴＩＶＥＯＰＴＩＭＩＺＡＴＩＯＮ￥ＹＡＮＧＸｉｎｍｉｎ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＣｈｏｎｇｑｉｎｇＮｏｒｍａｌＵｎｉｖｅｒｓｉｔ...     

利用遗传算法优化施工网络计划

从遗传算法基本原理出发,设计出带有修复算子的约束优化问题求解方法,用于网络计划资源优化,实践证明,该法解题速度快,结果的精确度也高,由此可以看出,遗传算法在解决大型工程的复杂优化问题中有很大优势．     

极大熵准则下n人非合作条件博弈的期望Nash均衡

设每个局中人的纯策略空间都是实数集上的Borel集，在实数集上有m个确定的Lebesgue可测集，并存在从这n个纯策略空间的笛卡尔乘积到实数集的m个n元Borel函数。这m个Borel函数在对应Lebesgue可测集下的逆像构成这n个纯策略空间的笛卡尔乘积的一个划分，并且每n-1个纯策略空间的笛卡尔乘积都具有有限正Lebesgue测度。纯策略空间的笛卡尔乘积的不同分块中的纯局势一般具有不同的博弈结果。每个局中人的效用都是自己所选纯策略的一元函数。在极大熵准则是每个局中人的共同知识的条件下，我们得到了求这类博弈的期望意义下的Nash均衡点的方法．给出这种Nash均衡点的存在定理和可交换定理。最后给出一个应用例子。     

Robust L_1 filtering with pole constraint in a disk via parameter-dependent Lyapunov functions

1.INTRODUCTION Filteringisaveryimportantissueinsystemsdiagno sis,surveillanceandcontrol.Byfiltering,wereferto theproblemwhichamountstoextracttheinformation fromthemeasuredoutputtoprovideanestimateof thestate(oralinearcombinationofthestate).Clas sicalworksinthisdomainaretheonesofKalmanin thestochasticframe work[1].Inthecasewherethere existsuncertaintyinthemodelandinsufficientstatis ticalinformationaboutthenoiseinput,theKalman filteringschemeisnolongerapplicable.Therefore, validstrategi…     

Optimal multi-asset investment with no-shorting constraint under mean-variance criterion for an insurer

This paper considers the optimal investment strategy for an insurer under the criterion of mean-variance. The risk process is a compound Poisson process and the insurer can invest in a risk-free asset and multiple risky assets. This paper obtains the optimal investment policy using the stochastic linear quadratic (LQ) control theory with no-shorting constraint. Then the efficient strategy (optimal investment strategy) and efficient frontier are derived explicitly by a verification theorem with the viscosity solution of Hamilton-Jacobi-Bellman (HJB) equation.     

混合滤波器组ADC系统的频响分析与量化噪声研究

根据带通采样定理对混合滤波器组ADC系统的抽取过程进行了系统理论分析,得到其失真/混迭函数。利用混合滤波器组ADC系统之综合滤波器组的多相结构,对混合滤波器组ADC系统量化噪声进行了详细研究。所得的理论结果为混合滤波器组ADC系统的失真/混迭函数与开关电容滤波器组ADC系统的失真/混迭函数一致,且混合滤波器组ADC系统的分辨率比其ADC提高了0.51og2M比特。     

High-resolution algorithm based on temporal-spatial extrapolation

To enhance the resolution of parameter estimation with limited samples received by a short passive array, an iterative nonparametric algorithm for estimating the frequencies and direction-of-arrivals (DOAs) of signals is proposed. The cost function is constructed using l2-norm Gaussian entropy combined with an additional constraint, l2-norm constraint or linear constraint. By minimizing the cost functions in the temporal and the spatial dimensions using corresponding iteration algorithms respectively, the s...     

一类纯反馈非仿射非线性系统的自适应神经网络变结构控制

研究了一类非仿射的纯反馈单输入单输出非线性系统。针对此系统,在中值定理、神经网络参数化和解耦Backstepping的基础上,提出了一种自适应变结构神经网络控制策略,而且所给出的定理证明闭环系统的所有信号在平衡点上是半全局一致有界的。通过对一个非仿射CSTR对象的仿真验证了该方法的有效性。     

MINIMAX PROGRAMMING UNDER GENERALIZED （p, r）-INVEXITY

Minimax programming problems involving generalized （p, r）-invex functions are consid- ered. Parametric sufficient optimality conditions and duality results are established under the aforesaid assumptions on the objective and constraint functions.     

CONVEXIFICATION AND CONCAVIFICATION METHODS FOR SOME GLOBAL OPTIMIZATION PROBLEMS

In this paper, firstly, we propose several convexification and concavification transformations to convert a strictly monotone function into a convex or concave function, then we propose several convexification and concavification transformations to convert a non-convex and non-concave objective function into a convex or concave function in the programming problems with convex or concave constraint functions, and propose several convexification and concavification transformations to convert a non-monotone objective function into a convex or concave function in some programming problems with strictly monotone constraint functions. Finally, we prove that the original programming problem can be converted into an equivalent concave minimization problem, or reverse convex programming problem or canonical D.C. programming problem. Then the global optimal solution of the original problem can be obtained by solving the converted concave minimization problem, or reverse convex programming problem or canonical D.C     

Cooperative Neuro Adaptive Control of Leader Following Uncertain Multi-Agent Systems with Unknown Hysteresis and Dead-Zone

In this paper, a cooperative adaptive control of leader-following uncertain nonlinear multiagent systems is proposed. The communication network is weighted undirected graph with fixed topology. The uncertain nonlinear model for each agent is a higher-order integrator with unknown nonlinear functions, unknown disturbances and unknown input actuators. Meanwhile, the gains of input actuators are unknown nonlinear functions with unknown sign. Two most common behaviors of input actuators in practical applications are hysteresis and dead-zone. In this paper, backlash-like hysteresis and dead-zone are used to model the input actuators. Using universal approximation theorem proved for neural networks, the unknown nonlinear functions are tackled. The unknown weights of neural networks are derived by proposing appropriate adaptive laws. To cope with modeling errors and disturbances an adaptive robust structure is proposed. Considering Lyapunov synthesis approach not only all the adaptive laws are derived but also it is proved that the closed-loop network is cooperatively semi-globally uniformly ultimately bounded(CSUUB). In order to investigate the effectiveness of the proposed method, it is applied to agents modeled with highly nonlinear mathematical equations and inverted pendulums. Simulation results demonstrate the effectiveness and applicability of the proposed method in dealing with both numerical and practical multi-agent systems.     

Distributed Algorithm for Robust Resource Allocation with Polyhedral Uncertain Allocation Parameters

This paper studies a distributed robust resource allocation problem with nonsmooth objective functions under polyhedral uncertain allocation parameters. In the considered distributed robust resource allocation problem, the (nonsmooth) objective function is a sum of local convex objective functions assigned to agents in a multi-agent network. Each agent has a private feasible set and decides a local variable, and all the local variables are coupled with a global affine inequality constraint, which is subject to polyhedral uncertain parameters. With the duality theory of convex optimization, the authors derive a robust counterpart of the robust resource allocation problem. Based on the robust counterpart, the authors propose a novel distributed continuous-time algorithm, in which each agent only knows its local objective function, local uncertainty parameter, local constraint set, and its neighbors’ information. Using the stability theory of differential inclusions, the authors show that the algorithm is able to find the optimal solution under some mild conditions. Finally, the authors give an example to illustrate the efficacy of the proposed algorithm.     

多任务微小卫星姿态仿真研究

为了实现在整星制约条件下,以经济而可靠的手段满足三轴稳定多任务微小卫星(MTMS)姿态控制系统的功能和性能要求,分析了MTMS的运行任务,提出了基于多任务要求的工作模式划分,并对多任务过程的姿态确定和姿态控制系统进行综合分析和设计,建立数学模型。通过仿真验证,可实现多任务微小卫星的复杂任务设计要求。     

APPROXIMATE SUBDIFFERENTIALS AND NONSMOOTH ANALYSIS FINITE DIMENSIONS

Ioffe's approximate subdifferentials are reviewed and some of his resultsare generalized.An extension of the calculus of the approximate subdifferentials forthe sums to any finite number of functions is provided along with a generalizationof the Dubovitzkii-Milyutin theorem.The presentation also indicates some of thelimitations of nonsmooth analysis and optimization.Restriction to the class offunction which is suitable for most of the purposes in nonsmooth optimization issuggested.