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Study of Certain Stochastic Predator-Prey Models 某些随机捕食者-猎物模型的研究
Pub Date : 1900-01-01 DOI: 10.1137/1.9781611974072.56
N. Du, N. H. Dang, G. Yin
In this paper, we provide sufficient conditions for the permanence and ergodicity of a stochastic predator-prey model with Beddington-DeAngelis functional response. These sufficient conditions are sharp and close to the necessary conditions as well. In addition to the nondegenerate diffusion, degenerate cases are also treated. In the degenerate case, our results characterize the support of the associated unique invariant probability measure. Convergence in total variation of the transition probability to the invariant measures is given. We also consider a stochastic model with regime-switching. Our results are demonstrated by several examples.
本文给出了具有Beddington-DeAngelis函数响应的随机捕食-食饵模型的持久性和遍历性的充分条件。这些充分条件是尖锐的,也接近于必要条件。除非退化扩散外,还治疗退化病例。在退化情况下,我们的结果表征了相关唯一不变概率测度的支持度。给出了转移概率的总变分对不变测度的收敛性。我们还考虑了一个具有状态切换的随机模型。通过几个例子证明了我们的结果。
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引用次数: 0
Optimal Control of Crop Irrigation based on the Hamilton-Jacobi-Bellman Equation 基于Hamilton-Jacobi-Bellman方程的作物灌溉最优控制
Pub Date : 1900-01-01 DOI: 10.1137/1.9781611973273.4
J. Ramanathan, Yuting Chen, P. Cournède
Water management in agriculture is a key issue due to the increasing problem of water scarcity worldwide. Based on the recent progress in the dynamic modeling of plant growth in interaction with the water resource, our objective is to study the optimal control problem of crop irrigation. For this purpose, we first describe the LNAS model for sugar beet growth, driving the dynamics of both plant biomass and soil water reserve. We then introduce the utility function corresponding to the farmer’s profit and derive the value function from the Hamilton-Jacobi-Bellman (HJB) equation. Then a backward finite-difference scheme is implemented to solve the HJB equation. It is proved to converge under a proper Courant-Friedrichs-Lewy condition for the discretization step. A few numerical simulations are provided to illustrate the resolution.
由于全球水资源短缺问题日益严重,农业用水管理是一个关键问题。基于植物生长与水资源相互作用的动态模型的最新进展,我们的目标是研究作物灌溉的最优控制问题。为此,我们首先描述了甜菜生长的LNAS模型,该模型驱动了植物生物量和土壤水分储备的动态。然后引入与农民利润相对应的效用函数,并由哈密顿-雅可比-贝尔曼(HJB)方程推导出价值函数。然后采用逆向有限差分格式求解HJB方程。在适当的Courant-Friedrichs-Lewy条件下证明了离散化步骤是收敛的。给出了一些数值模拟来说明这种解析度。
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引用次数: 1
Optimal Bidding Strategies for Wind Power Producers with Meteorological Forecasts 有气象预报的风力发电商最优投标策略
Pub Date : 1900-01-01 DOI: 10.1137/1.9781611973273.3
Antonio Giannitrapani, S. Paoletti, A. Vicino, Donato Zarrilli
In recent years, the interest in clean renewable energy resources, such as wind and photovoltaic, has grown rapidly. It is well known that the inherent variability in wind power generation and the related difficulty in predicting future generation profiles, raise major challenges to wind power integration into the electricity grid. In this work we study the problem of optimizing energy bids for an independent Wind Power Producer (WPP) taking part into a competitive electricity market. It is assumed that the WPP is subject to financial penalties for generation shortfall and surplus. This means that, if the energy delivered over a given time slot is different from that subscribed in the bid, the WPP will be penalized, the monetary entity of the penalty depending on the wholesale market behavior, the day of the year and the time slot involved. An optimization procedure is devised to minimize this risk and maximize the expected profit of the seller. Specifically, each energy bid is computed by exploiting the forecast energy price for the day ahead market, the historical wind statistics at the plant site and the day-ahead wind speed forecasts provided by a meteorological service. We also examine and quantify the strategic role of an energy storage device in increasing reliability of bids and mitigating the financial risks of the WPP.
近年来,人们对风能和光伏等清洁可再生能源的兴趣迅速增长。众所周知,风力发电的内在可变性以及预测未来发电状况的相关困难,对风力发电并入电网提出了重大挑战。本文研究了独立风力发电商(WPP)参与竞争性电力市场时的能源报价优化问题。假设WPP会因发电不足和盈余而受到经济处罚。这意味着,如果在给定时间段内交付的能源与投标中订购的能源不同,WPP将受到处罚,处罚的货币实体取决于批发市场行为,一年中的哪一天以及所涉及的时间段。设计了一个优化程序,使这种风险最小化,并使卖方的预期利润最大化。具体来说,每个能源报价是通过利用前一天市场的预测能源价格、工厂现场的历史风力统计数据和气象机构提供的前一天风速预报来计算的。我们还研究并量化了储能设备在提高投标可靠性和减轻WPP财务风险方面的战略作用。
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引用次数: 5
Computing the structured distance to instability 计算不稳定的结构距离
Pub Date : 1900-01-01 DOI: 10.1137/1.9781611974072.58
P. Apkarian, D. Noll, Laleh Ravanbod
We analyze robust stability and performance of dynamical systems with real uncertain parameters. We compute criteria like the distance to instability, the worst-case spectral abscissa, or the worst-case H∞-norm, which quantify the degree of robustness of such a system when parameters vary in a given set ∆. As computing these indices is NP-hard, we present a heuristic which finds good lower bounds fast and reliably. Posterior certification is then obtained by an intelligent global strategy. A test bench of 87 systems with up to 70 states 39 uncertain parameters with up to 11 repetitions demonstrates the potential of our approach. 1 Problem Specification. Robustness specifications limit the loss of performance and stability in a system where differences between the mathematical model and reality crop up. Robustness against real parametric uncertainties is among the most challenging calls in this regard. Already deciding whether a given system with uncertain real parameters δ is robustly stable over a given parameter range δ ∈ ∆ is NP-hard, and this is aggravated when it comes to deciding whether a given level of H2or H∞-performance is guaranteed over that range. In this work we address this type of uncertainty by computing three key criteria, which quantify the degree of parametric robustness of a system. These are (a) the worst-case H∞-norm, and (b) the worst-case spectral abscissa over a given parameter range, and (c) the distance to instability, or stability margin, of a system with uncertain parameters. Consider a Linear Fractional Transform [23] with real parametric uncertainties as in Figure 1, where P (s) :    ẋ = Ax + Bpp + Bww q = Cqx + Dqpp + Dqww z = Czx + Dzpp + Dzww (1.1) and x ∈ R is the state, w ∈ R1 a vector of exogenous inputs, and z ∈ R1 a vector of regulated outputs. The uncertainty channel is defined as p = ∆q, where the time-invariant uncertain matrix ∆ has the blockdiagonal form ∆ = diag [δ1Ir1 , . . . , δmIrm ] , (1.2) ONERA, Control System Department, Toulouse, France Universite de Toulouse, Institut de Mathematiques with δ1, . . . , δm representing real uncertain parameters, and ri giving the number of repetitions of δi. Here we assume without loss that δ = 0 ∈ ∆ represents the nominal parameter value, and we consider δ ∈ ∆ in one-to-one correspondence with the matrix ∆ in (1.2). For practical applications it is generally sufficient to consider the case ∆ = [−1, 1]. To analyze the performance of (1.1) in the presence of the uncertain δ ∈ R we compute the worst-case H∞-performance h = max{‖Twz(δ)‖∞ : δ ∈ ∆}, (1.3) where ‖·‖∞ is the H∞-norm, and where Twz(s, δ) is the transfer function z(s) = Fu(P (s), ∆)w(s), obtained by closing the loop between (1.1) and p = ∆q with (1.2) in Figure 1. The solution δ ∈ ∆ of (1.3) represents a worst possible choice of the parameters δ ∈ ∆, which may be an important element in analyzing performance and robustness of the system, see e.g. [1]. Our second criterion is similar in nature, as it
本文分析了具有真实不确定参数的动力系统的鲁棒稳定性和性能。我们计算诸如到不稳定的距离、最坏情况谱横坐标或最坏情况H∞范数等标准,这些标准量化了当参数在给定集∆变化时这样一个系统的鲁棒性程度。由于这些指标的计算是np困难的,我们提出了一种快速可靠地找到良好下界的启发式方法。然后通过智能全局策略获得后验认证。一个包含多达70个状态、39个不确定参数、多达11次重复的87个系统的试验台证明了我们的方法的潜力。1问题说明。鲁棒性规范限制了出现数学模型与现实之间差异的系统中性能和稳定性的损失。对实际参数不确定性的鲁棒性是这方面最具挑战性的要求之一。在给定的参数范围δ∈∆内,确定具有不确定实参数δ的给定系统是否鲁棒稳定已经是NP-hard了,当决定在该范围内是否保证给定水平的H2or H∞性能时,这一点就变得更加严重了。在这项工作中,我们通过计算三个关键标准来解决这种类型的不确定性,这些标准量化了系统的参数鲁棒性程度。它们是(a)最坏情况H∞范数,(b)给定参数范围内的最坏情况谱横坐标,以及(c)具有不确定参数的系统到不稳定或稳定裕度的距离。考虑如图1所示的具有实参数不确定性的线性分数阶变换[23],其中P (s): = Ax + Bpp + Bww q = Cqx + Dqpp + Dqww z = Czx + Dzpp + Dzww (1.1), x∈R为状态,w∈R1为外源输入向量,z∈R1为调节输出向量。不确定通道定义为p =∆q,其中定常不确定矩阵∆具有块对角线形式∆= diag [δ1Ir1,…]。, δmIrm], (1.2) ONERA,控制系统系,法国图卢兹大学,δ1数学研究所,. ., δm表示实际不确定参数,ri表示δi的重复次数。这里我们不损失地假设δ = 0∈∆表示标称参数值,我们认为δ∈∆与矩阵∆in(1.2)一一对应。对于实际应用,通常考虑∆=[−1,1]的情况就足够了。为了分析不确定δ∈R存在时(1.1)的性能,我们计算最坏情况H∞-性能H = max{‖Twz(δ)‖∞:δ∈∆},(1.3)其中‖·‖∞是H∞范数,其中Twz(s, δ)是传递函数z(s) = Fu(P (s),∆)w(s),通过将图1中的(1.1)和P =∆q之间的回路闭合得到。(1.3)的解δ∈∆表示参数δ∈∆的最坏可能选择,这可能是分析系统性能和鲁棒性的重要元素,例如[1]。我们的第二个准则在性质上是相似的,因为它允许验证不确定系统(1.1)是否在给定参数范围∆上是鲁棒稳定的。这可以通过在参数范围α = max{α(A(δ)): δ∈∆},(1.4)上最大化系统A-矩阵的谱横坐标来检验,其中A(δ) = A + Bp∆(I - Dpq∆)Cq,其中方阵A的谱横坐标定义为α(A) = max{Reλ: A的λ特征值}。由于当且仅当α(A) < 0时A是稳定的,因此当α < 0时证明(1.1)在∆上的鲁棒稳定性,而当α≥0时发现不稳定的δ∈∆。但是请注意,只有在计算了∆的全局最大值后,基于α < 0的有利于稳健稳定的决定才有效。这使得(1.4)成为一个困难的问题,事实上,在全局范围内解决(1.4)是np困难的。1996年,Poljak和Rohn已经证明,对于给定的矩阵集A0,…, Ak,决定A0 + r1A1 +…+ rkAk对于所有ri∈[0,1]都是稳定的,并且Braatz et al.[6]已经证明,确定具有真实(或混合或复杂)不确定性的系统在∆=[- 1,1]范围内是否鲁棒稳定比全局解决非凸二次规划问题更难,因此是np困难的。423版权所有©SIAM。未经授权,禁止转载本文。
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引用次数: 11
Convexity + curvature: Tools for the global stabilization of nonlinear systems with control inputs subject to magnitude and rate bounds 凸性+曲率:控制输入服从幅度和速率界的非线性系统的全局稳定工具
Pub Date : 1900-01-01 DOI: 10.1137/1.9781611974072.19
J. Solís-Daun
The aim of this paper is to address the global asymptotic stabilization (gas) of affine systems with control inputs subject to magnitude and rate bounds, in the framework of ArtsteinSontag’s control Lyapunov function (clf) approach. These bounds are defined by compact (convex) control value sets (cvs) U with 0 ∈ intU . Convex Analysis together with Differential Geometry allow us to reveal the intrinsic geometry involved in the clf stabilization problem, and to solve it, if an optimal control ω(x) exists. The existence and uniqueness of ω(x) depends on convexity properties of cvs U ; whereas its regularity and boundedness of its differential is achieved in terms of the curvature of U . However, in view that control ω(x) is singular, we redesign it to derive an explicit formula for regular damping feedback controls fulfilling magnitude and rate bounds that render gas a class of affine systems.
本文的目的是在ArtsteinSontag的控制Lyapunov函数(clf)方法的框架下,研究控制输入受幅度和速率界约束的仿射系统的全局渐近镇定(气体)问题。这些边界由紧(凸)控制值集(cvs) U定义,其中0∈intU。如果存在最优控制ω(x),凸分析和微分几何使我们能够揭示clf稳定问题所涉及的内在几何,并解决它。ω(x)的存在唯一性取决于cv U的凸性;而它的正则性和微分的有界性是用U的曲率来表示的。然而,考虑到控制ω(x)是奇异的,我们重新设计了它,以推导出一个显式公式,用于规则阻尼反馈控制,满足使气体成为一类仿射系统的幅度和速率界限。
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引用次数: 1
Periodic Control System Stabilization on Time Scales 时间尺度上的周期控制系统镇定
Pub Date : 1900-01-01 DOI: 10.1137/1.9781611973273.14
Francisco Miranda
The stabilization of periodic control systems using time scales is studied. Time scale is a model of time. The language of time scales seems to be an ideal tool to unify the continuous-time and the discrete-time theories. In this work we suggest an alternative way to solve stabilization problems. This method is based on a combination of the Lyapunov functions method with local controllability conditions. In many situations this method admits a rigorous mathematical justification and leads to effective numerical methods. Applications to mechanical problems are provided here.
研究了含时间尺度的周期控制系统的镇定问题。时标是时间的模型。时间尺度语言似乎是统一连续时间理论和离散时间理论的理想工具。在这项工作中,我们提出了一种解决稳定问题的替代方法。该方法是将李雅普诺夫函数方法与局部可控条件相结合的方法。在许多情况下,这种方法有严格的数学证明,并导致有效的数值方法。这里提供了机械问题的应用。
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引用次数: 1
New Results On Stochastic Consensus Networks 关于随机共识网络的新结果
Pub Date : 1900-01-01 DOI: 10.1137/1.9781611974072.17
C. Somarakis, J. Baras
We revisit the general linear consensus problem and provide new conditions for asymptotic consensus on two types of stochastic versions of the algorithm, in discrete and continuous time. We show that our method unifies a number of proposed models in the literature as well as it extends and generalizes existing results.
我们重新研究了一般线性一致性问题,并给出了在离散时间和连续时间下两种随机版本算法的渐近一致性的新条件。我们表明,我们的方法统一了文献中提出的一些模型,并扩展和推广了现有的结果。
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引用次数: 3
Adaptive Polynomial Identification and Optimal Tracking Control for Nonlinear Systems 非线性系统的自适应多项式辨识与最优跟踪控制
Pub Date : 1900-01-01 DOI: 10.1137/1.9781611974072.36
Fernando Ornelas, A. Villafuerte
The paper proposes an adaptive polynomial identifier and a robust nonlinear optimal tracking control scheme for polynomial systems. The identifier approximates an uncertain nonlinear system, where its parameters are on-line adapted using a Kalman-Bucy filter. Then, based on the identifier an optimal tracking controller is synthesized, including an integral term to provide it robustness. The identification and control scheme is illustrated via simulations for the control of the blood glucose level in diabetic patients.
针对多项式系统,提出了一种自适应多项式辨识器和鲁棒非线性最优跟踪控制方案。该辨识器近似于一个不确定非线性系统,该系统的参数采用卡尔曼-布西滤波器在线自适应。然后,基于辨识器合成了一个最优跟踪控制器,并引入了一个积分项以保证其鲁棒性。通过对糖尿病患者血糖水平控制的仿真,说明了该识别和控制方案。
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引用次数: 2
Modeling and Analysis of Adaptive-Conversion-Ratio-Based Bidirectional Switched-Capacitor Converter 基于自适应转换比的双向开关电容变换器建模与分析
Pub Date : 1900-01-01 DOI: 10.1137/1.9781611973273.21
Yuen-Haw Chang, Kun-Wei Wu
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引用次数: 0
A max-plus fundamental solution semigroup for a class of lossless wave equations 一类无损波动方程的极大+基本解半群
Pub Date : 1900-01-01 DOI: 10.1137/1.9781611974072.55
P. Dower, W. McEneaney
A new max-plus fundamental solution semigroup is presented for a class of lossless wave equations. This new semigroup is developed by employing the action principle to encapsulate the propagation of all possible solutions of a given wave equation in the evolution of the value function of an associated optimal control problem. The max-plus fundamental solution semigroup for this optimal control problem is then constructed via dynamic programming, and used to formulate the fundamental solution semigroup for the original wave equation. An application of this semigroup to solving twopoint boundary value problems is discussed via an example.
给出了一类无损波动方程的一个新的极大+基本解半群。这个新的半群是利用作用原理来封装一个给定的波动方程的所有可能解的传播在一个相关的最优控制问题的值函数的演化。然后通过动态规划构造了该最优控制问题的极大+基本解半群,并用于构造原波动方程的基本解半群。应用程序解决两点边值问题的半群的讨论通过一个例子。
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引用次数: 6
期刊
SIAM Conf. on Control and its Applications
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