General Lyapunov Stability and Its Application to Time-Varying Convex Optimization

In this article, a general Lyapunov stability theory of nonlinear systems is put forward and it contains asymptotic/finite-time/fast finite-time/fixed-time stability. Especially, a more accurate estimate of the settling-time function is exhibited for fixedtime stability, and it is still extraneous to the initial conditions.This can be applied to obtain less conservative convergence time of the practical systems without the information of the initial conditions. As an application, the given fixed-time stability theorem is used to resolve time-varying(TV) convex optimization problem.By the Newton's method, two classes of new dynamical systems are constructed to guarantee that the solution of the dynamic system can track to the optimal trajectory of the unconstrained and equality constrained TV convex optimization problems in fixed time, respectively. Without the exact knowledge of the time derivative of the cost function gradient, a fixed-time dynamical non-smooth system is established to overcome the issue of robust TV convex optimization. Two examples are provided to illustrate the effectiveness of the proposed TV convex optimization algorithms. Subsequently, the fixed-time stability theory is extended to the theories of predefined-time/practical predefined-time stability whose bound of convergence time can be arbitrarily given in advance, without tuning the system parameters. Under which, TV convex optimization problem is solved. The previous two examples are used to demonstrate the validity of the predefined-time TV convex optimization algorithms.

Relaxed Stability Criteria for Time-Delay Systems:A Novel Quadratic Function Convex Approximation Approach

This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.

Computation of Peak Output for Inputs Restricted in L_2 and L_∞ Norms Using Finite Difference Schemes and Convex Optimization

Control systems designed by the principle of matching gives rise to problems of evaluating the peak output. This paper proposes a practical method for computing the peak output of linear time-invariant and non-anticipative systems for a class of possible sets that are characterized with many bounding conditions on the two- and/or the infinity-norms of the inputs and their derivatives. The original infinite-dimensional convex optimization problem is approximated as a large-scale convex programme defined in a Euclidean space, which are associated with sparse matrices and thus can be solved efficiently in practice. The numerical results show that the method performs satisfactorily, and that using a possible set with many bounding conditions can help to reduce the design conservatism and thereby yield a better match.

Stabilization of linear time-varying systems with state and input constraints using convex optimization

The stabilization problem of linear time-varying systems with both state and input constraints is considered. Sufficient conditions for the existence of the solution to this problem are derived and a gain-switched（gain-scheduled） state feedback control scheme is built to stabilize the constrained timevarying system. The design problem is transformed to a series of convex feasibility problems which can be solved efficiently. A design example is given to illustrate the effect of the proposed algorithm.

Approximate Optimality Conditions for Composite Convex Optimization Problems

The purpose of this paper is to study the approximate optimality condition for composite convex optimization problems with a cone-convex system in locally convex spaces,where all functions involved are not necessarily lower semicontinuous.By using the properties of the epigraph of conjugate functions,we introduce a new regularity condition and give its equivalent characterizations.Under this new regularity condition,we derive necessary and sufficient optimality conditions ofε-optimal solutions for the composite convex optimization problem.As applications of our results,we derive approximate optimality conditions to cone-convex optimization problems.Our results extend or cover many known results in the literature.

An Overview of Sequential Approximation in Topology Optimization of Continuum Structure

This paper offers an extensive overview of the utilization of sequential approximate optimization approaches in the context of numerically simulated large-scale continuum structures.These structures,commonly encountered in engineering applications,often involve complex objective and constraint functions that cannot be readily expressed as explicit functions of the design variables.As a result,sequential approximation techniques have emerged as the preferred strategy for addressing a wide array of topology optimization challenges.Over the past several decades,topology optimization methods have been advanced remarkably and successfully applied to solve engineering problems incorporating diverse physical backgrounds.In comparison to the large-scale equation solution,sensitivity analysis,graphics post-processing,etc.,the progress of the sequential approximation functions and their corresponding optimizersmake sluggish progress.Researchers,particularly novices,pay special attention to their difficulties with a particular problem.Thus,this paper provides an overview of sequential approximation functions,related literature on topology optimization methods,and their applications.Starting from optimality criteria and sequential linear programming,the other sequential approximate optimizations are introduced by employing Taylor expansion and intervening variables.In addition,recent advancements have led to the emergence of approaches such as Augmented Lagrange,sequential approximate integer,and non-gradient approximation are also introduced.By highlighting real-world applications and case studies,the paper not only demonstrates the practical relevance of these methods but also underscores the need for continued exploration in this area.Furthermore,to provide a comprehensive overview,this paper offers several novel developments that aim to illuminate potential directions for future research.

基于改进凸内逼近法的主动配电网有功-无功协调优化

以风电、光伏为代表的分布式电源接入配电网后容易导致系统电压波动变大以及局部电压越限。以二阶锥优化为代表的松弛技术在优化时为了保证松弛后解的精确,约束条件极为严苛并且在功率的极端注入下容易导致对偶间隙增大。针对上述问题,该文提出基于改进凸内逼近法的主动配电网有功-无功优化方法。首先,基于支路潮流方程定义与支路电流、节点电压和视在功率流相关的非线性项的凸包,并与剩余线性元素结合形成凸内部近似,建立完善的数学模型;进一步提出网络容许性判据以及引入KKT条件收缩最优解的对偶间隙。最后,基于IEEE 33系统及PG&E69节点系统,利用Yalmip等平台求得电网中各有功、无功决策变量的出力区间,验证所提方法的稳定、精确与高效性。

有源RIS辅助SWIPT网络公平性资源分配算法

针对有源可重构智能表面(reconfigurable intelligent surface,RIS)辅助的同步无线信息与能量传输(simultaneous wireless information and power transfer,SWIPT)系统,提出了一种考虑公平性的能量资源采集分配算法,以解决因乘性衰落导致的公平性能量采集性能较差的问题。在有源RIS辅助的SWIPT系统采用功率切割架构实现信息与能量的同步传输,构建了以所有用户中最小的采集能量最大化为目标函数,用户信干噪比、有源RIS和基站发射功率、功率划分因子等满足需求为约束条件的联合资源分配问题。利用交替优化、半正定松弛、连续凸近似、罚函数等技术将不能直接解决的非凸问题转换成标准凸问题,提出了一种交替迭代的公平性采集能量算法。数值仿真结果表明,所提优化算法能够显著提高用户中能量资源分配最少的用户处采集到的能量值,保障通信网络中能量资源分配的公平性。

基于深度强化学习的联合通信感知系统波束优化方法

在不远的未来,ISAC系统将同时提供通信和感知服务。ISAC系统需要通过先进的波束优化算法保证所提供服务的质量,并满足形式多样的服务目标和资源约束。通常,波束算法可建模为一个优化问题。然而,基于传统优化理论设计的优化算法仅能处理带有瞬时约束的资源分配问题,而不能处理带有长时间约束的优化问题,从而降低了系统性能。一种可行的解决方案是基于RL理论设计相应算法来解决上述问题。然而,现有的工作主要致力于解决无约束RL问题,对约束强化学习问题关注较少,这限制了强化学习在波束优化问题中的应用。为了克服上述挑战,提出了一种基于CSSCA的RL方法。该方法将原有的目标函数和约束函数替换为对应的凸近似函数,通过求解一系列的凸近似问题,最终可以保证收敛到原问题的KKT点。最后,通过仿真结果展示了所提出方法的优越性。

布洛托上校博弈模型及求解方法研究进展

信息的传播扩散可以建模为在潜在传播网络上发生的随机过程。由于在实际应用场景中,潜在的传播网络拓扑结构和清晰的传播过程往往是不可见的,因此根据观测到的传播结果,如节点感染时间、状态等信息,推断传播网络拓扑结构,对于分析与理解传播过程、跟踪传播路径以及预测未来传播事件起着重要作用。近年来,传播网络推断问题吸引了众多研究者的目光。文中对近年来的信息传播网络推断工作进行系统性的介绍和总结,为传播网络推断提供一个新视角。

非凸增量前馈神经网络的收敛性分析

针对给定格式的非凸增量迭代前馈神经网络提出了一种收敛性证明,并进一步推导了相关的全局逼近性推论。同时,本文还进一步阐述了在特定非凸增量迭代下的目标函数和激活函数的关系。在此基础上,给出了随机神经元的最优选择下的收敛性证明,该结论有效地填补了随机神经元在收敛速度上的理论研究空白,也间接论证了随机神经元的全局逼近性理论的正确性。接着给出了一种随机神经元的搜索算法,该算法克服了通用的递归求导误差算法的弊病,防止神经网络陷入次优局部最优解。最后,基于几个基准回归问题进行了实验验证,实验结果支持了本文提出的理论方法的正确性和有效性。本文的研究成果不仅拓展了神经网络的理论研究领域,而且对于实际应用中神经网络的优化和改进具有一定的指导意义。

面向多任务动态场景的雷达与干扰空时协同波束联合优化方法

现代雷达对抗形势复杂多变,体系与体系的作战已成为基本特点,而体系整体性能关乎着战场的主动权乃至最终的胜负。通过优化体系中雷达与干扰波束资源可以提升整体性能,获得在空间、时间域优效的低截获探测性能,然而空时域协同波束联合优化是一个复杂多参数耦合的非凸问题。该文针对空时域多任务动态场景,建立了以雷达探测性能为优化目标,以干扰性能以及能量限制为约束条件的优化模型。为求解该模型,该文提出了基于迭代优化的空时协同波束联合设计方法,即以雷达发射、接收、多干扰机发射波束交替迭代优化。其中,针对多干扰机协同优化的不定矩阵二次约束二次规划(QCQP)问题,该文基于可行点追踪-连续凸逼近(FPP-SCA)算法,在SCA算法的基础上,通过引入松弛变量与惩罚项,保证算法在合理松弛度下的可行性,解决了矩阵不定情况下难以获得可行解的问题。仿真表明,在一定的干扰机能量约束下,该文所提方法在保证雷达高性能探测目标且不受干扰情况下,同时实现了多干扰机在空时域干扰对方每个平台以掩护我方雷达探测的效果;相比传统算法,在动态场景中基于FPP-SCA算法的协同干扰具有更优效果。

基于凸优化的有限推力远程转移轨迹优化

针对轨迹优化问题中动力学方程对凸优化方法的限制,建立了有限推力远程转移轨迹优化问题的凸优化问题模型,并提出一种迭代逼近算法,使得在每步迭代中状态矩阵保持为线性,从而实现了凸优化在远程轨迹优化中的应用,仿真分析证明了所提出的迭代逼近算法对优化问题的收敛性,所得轨迹迅速收敛至最优轨迹,并与最优控制序列所得实际轨迹保持一致。本文构建的凸优化问题模型及提出的迭代逼近算法对这类远程轨迹优化问题是可行的。

非线性梯度下降算法理论及其对Hopfield网络稳定性的分析

讨论目标函数可分解为凸函数和一个广义可微函数之差的优化问题 对于可微函数利用线性函数进行局部逼近 ,从而求得目标函数的一个凸函数逼近 然后求解凸优化问题得到最优解的一个更好近似 ;重复这个过程直到结束 利用广义梯度和凸函数的性质 ,证明得到的优化算法为全局收敛的下降算法 它所求解的优化问题可以具有光滑或非光滑的目标函数

含电力电子变压器的交直流配电网随机运行优化

间歇性可再生能源的接入,使得含电力电子变压器(power electronic transformer,PET)交直流系统的运行面临巨大挑战,因此提出基于场景分析法的优化调度模型。计及风电和光伏出力在空间上的相关性,采用多维高斯混合模型构建风电/光伏出力的联合概率分布,并基于同步回代削减法进行场景缩减,建立了含PET的交直流混合配电网随机运行优化模型,以得到满足典型场景的运行调度方案。然而随机运行优化模型属于海量高维非凸优化问题,难以求解,针对这一问题,提出基于二阶锥松弛技术和线性逼近法的逐次凸逼近规划模型,通过循环迭代实现对该问题的高效求解。仿真算例验证了所提模型方法的有效性和可行性。

固定增益与变增益最优励磁控制策略的小扰动稳定域研究

在计及励磁饱和环节条件下,利用凸优化技术和迭代搜索方法,提出以非线性系统椭球吸引域体积为指标确定小扰动稳定域边界的新算法。对比分析了其机组在固定增益和变增益线性最优励磁控制下的电力系统的小扰动稳定域,给出了采用固定增益的小扰动稳定有效范围。算例分析验证了所提算法的有效性。结果表明:当系统运行点发生变化时,固定增益控制器的控制效果会下降,偏离给定运行点越远,控制性能下降得越严重,因此,在最优励磁控制下,有必要采用变增益的控制策略,以保证系统的小扰动稳定性。

投资组合优化模型的一个序列凸近似算法

以CVaR为代表的凸优化投资组合模型近年来引起了广泛研究.为克服传统投资组合模型中凸近似的不足,提出了一个投资组合的DC规划模型.该模型用一个DC函数替代了CVaR模型中的凸近似函数,同时要求所有约束条件在概率意义下成立.进一步地,提出了一个序列凸近似(SCA)算法用于求解DC规划问题,并运用Monte-Carlo方法来实现SCA算法.初步的实验结果表明,因子收益服从"尖峰厚尾"分布时,模型的目标函数值优于采用CVaR近似的目标函数值.

Non-Orthogonal Multiple Access in Cell-Free Massive MIMO Networks

In this paper, we investigate the downlink performance of cell-free massive multi-input multi-output non-orthogonal multiple access(CF-m MIMO-NOMA) system with conjugate beamforming precoder and compare against the orthogonal multiple access(OMA) counterpart. A novel achievable closed-form spectral efficiency(SE) expression is derived, which characterizes the effects of the channel estimation error, pilot contamination, imperfect successive interference cancellation(SIC) operation, and power optimization technique. Then, motivated by the closedform result, a sum-SE maximization algorithm with the sequential convex approximation(SCA) is proposed, subject to each AP power constraint and SIC power constraint. Numerical experiments indicate that the proposed sum-SE maximization algorithms have a fast converge rate, within about five iterations. In addition, compared with the full power control(FPC) scheme, our algorithms can significantly improve the achievable sum-SE. Moreover, NOMA outperforms OMA in many respects in the presence of the proposed algorithms.

不确定凸优化问题鲁棒近似解的最优性

该文研究一类目标和约束函数均带有不确定信息的凸优化问题的鲁棒近似解.首先,在闭凸锥约束品性假设下,得到了该不确定优化问题关于近似解的最优性条件.然后,引入所研究不确定优化问题的近似鞍点的概念,并给出了近似解的鞍点刻划.