死锁预防：基于监视器的ξ资源S3PR强化控制器设计

研究论文
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"基于ξ资源的S3PR基于监视器的生命增强监控器的综合" 这篇研究论文专注于解决在灵活制造系统（FMSs）中的死锁问题，死锁是这类系统中一个非常不希望出现的现象。作者Dan You、Shouguang Wang（IEEE资深会员）和Mengchu Zhou（IEEE院士）提出了一种通过添加监视器来实现死锁预防的策略，该策略适用于一类名为α-S3PR（State-Successor State Place/Transition Petri Net with Resources）并带有ξ资源的系统。 首先，他们介绍了一种算法，用于通过ξ资源来简化S3PR。ξ资源在α-S3PR中被划分为两种类型：A-ξ资源和B-ξ资源。对于只有B-ξ资源的α-S3PR，论文证明了一个最大允许的、能确保活力（liveness）的监督器可以通过控制所有已清空的严格最小输油管（siphons）来设计。如果α-S3PR包含A-ξ资源，那么可以迭代地通过A-ξ资源减少网络，并添加相应的监视器来设计一个活力增强的监督器。 最后，论文提出了一个针对α-S3PR的死锁预防算法。为了进一步验证提出的理论，文中给出了两个FMS实例进行分析和应用。这些实例有助于直观展示如何应用所提方法来避免系统的死锁状态，从而提高系统的稳定性和效率。 通过引入监视器，该研究不仅解决了死锁问题，还增强了系统的监控能力，使得系统管理者可以实时了解系统状态并及时采取预防措施。这在实际的制造环境中具有重要的应用价值，因为死锁可能导致生产流程停滞，造成资源浪费和效率降低。通过这种方法，可以提高系统的灵活性和可靠性，确保制造过程的连续性和高效性。

基于灰色综合评价模型的矿井通风系统可靠性评价_刘通海1

2022-08-03 上传
《基于灰色综合评价模型的矿井通风系统可靠性评价》这篇文章主要探讨了如何运用灰色综合评价模型来评估矿井通风系统的可靠性。矿井通风系统对于确保矿山的安全生产至关重要，它可以有效控制井下的粉尘和有毒有害气体...

比较标准模型的Rξ规和单一规：一个示例

2020-04-07 上传
此处给出一个示例，其中对于标准模型中的物理过程，使用两个不同量规（Rξ量规和单一量规）计算出的矩阵元素被明确验证为不同。 这是通过从另一个矩阵元素减去一个矩阵元素来实现的。 这个非零的差异原来有一个微妙...

设f(x)是[0,1]上二阶可导的正值函数，f(0)=2，f(1)=1且f(0)'＝-2，证明存在ξ∈(0,1),使得f(ξ)f(ξ)'+f(ξ)''=0

2023-07-15 上传
h'(ξ) = f'(ξ)g(ξ) + f(ξ)g'(ξ) = f'(ξ)[f(ξ)]² + f(ξ)f'(ξ) = 2f(ξ)f'(ξ) + [f(ξ)]²f''(ξ) 因此，我们得到 2f(ξ)f'(ξ) + [f(ξ)]²f''(ξ) = 0。即，存在一个点 ξ ∈ (0, 1)，使得 f(ξ)f(ξ)' ...

证明:设f(x)在[a,b]上连续,在(a,b)内可导,则(a,b)内存在n个互不相同的ξ1,ξ2,...,ξn,使得f'(ξ1)*f'(ξ2)*...*f'(ξn)=[(f(b)-f(a))/(b-a)]^n

2023-06-01 上传
假设当n=k时结论成立，即存在k个互不相同的ξ1,ξ2,...,ξk，使得f'(ξ1)*f'(ξ2)*...*f'(ξk)=[(f(b)-f(a))/(b-a)]^k。 考虑当n=k+1时，由拉格朗日中值定理可知，存在η∈(a,b)，使得 (f(η)-f(a))/(η-a)=f'(\xi...

用python 实现 从Z文件 和ξ 文件中读取矩，然后求α=1、2、3时，等式左边Z的三个值 对于每个i，Z是3*3矩阵，ξ是3*2矩阵（但是只取第一列） Z: α是行，γ是列； ξ： γ是行

2023-03-07 上传
我可以回答这个问题。可以使用Python中的NumPy...然后，使用NumPy的dot函数计算等式左边Z的三个值对于每个i，即Z.dot(ξ[:,])，Z.dot(ξ[:,1])和Z.dot(ξ[:,2])，其中ξ[:,]表示ξ的第一列。最后，将结果打印出来即可。

Algorithm 1: The online LyDROO algorithm for solving (P1). input : Parameters V , {γi, ci}Ni=1, K, training interval δT , Mt update interval δM ; output: Control actions 􏰕xt,yt􏰖Kt=1; 1 Initialize the DNN with random parameters θ1 and empty replay memory, M1 ← 2N; 2 Empty initial data queue Qi(1) = 0 and energy queue Yi(1) = 0, for i = 1,··· ,N; 3 fort=1,2,...,Kdo 4 Observe the input ξt = 􏰕ht, Qi(t), Yi(t)􏰖Ni=1 and update Mt using (8) if mod (t, δM ) = 0; 5 Generate a relaxed offloading action xˆt = Πθt 􏰅ξt􏰆 with the DNN; 6 Quantize xˆt into Mt binary actions 􏰕xti|i = 1, · · · , Mt􏰖 using the NOP method; 7 Compute G􏰅xti,ξt􏰆 by optimizing resource allocation yit in (P2) for each xti; 8 Select the best solution xt = arg max G 􏰅xti , ξt 􏰆 and execute the joint action 􏰅xt , yt 􏰆; { x ti } 9 Update the replay memory by adding (ξt,xt); 10 if mod (t, δT ) = 0 then 11 Uniformly sample a batch of data set {(ξτ , xτ ) | τ ∈ St } from the memory; 12 Train the DNN with {(ξτ , xτ ) | τ ∈ St} and update θt using the Adam algorithm; 13 end 14 t ← t + 1; 15 Update {Qi(t),Yi(t)}N based on 􏰅xt−1,yt−1􏰆 and data arrival observation 􏰙At−1􏰚N using (5) and (7). i=1 i i=1 16 end With the above actor-critic-update loop, the DNN consistently learns from the best and most recent state-action pairs, leading to a better policy πθt that gradually approximates the optimal mapping to solve (P3). We summarize the pseudo-code of LyDROO in Algorithm 1, where the major computational complexity is in line 7 that computes G􏰅xti,ξt􏰆 by solving the optimal resource allocation problems. This in fact indicates that the proposed LyDROO algorithm can be extended to solve (P1) when considering a general non-decreasing concave utility U (rit) in the objective, because the per-frame resource allocation problem to compute G􏰅xti,ξt􏰆 is a convex problem that can be efficiently solved, where the detailed analysis is omitted. In the next subsection, we propose a low-complexity algorithm to obtain G 􏰅xti, ξt􏰆. B. Low-complexity Algorithm for Optimal Resource Allocation Given the value of xt in (P2), we denote the index set of users with xti = 1 as Mt1, and the complementary user set as Mt0. For simplicity of exposition, we drop the superscript t and express the optimal resource allocation problem that computes G 􏰅xt, ξt􏰆 as following (P4) : maximize 􏰀j∈M0 􏰕ajfj/φ − Yj(t)κfj3􏰖 + 􏰀i∈M1 {airi,O − Yi(t)ei,O} (28a) τ,f,eO,rO 17 ，基于模型的DRL算法和无优化的DRL算法和DNN深度学习都各体现在哪

2023-05-12 上传
基于模型的DRL算法和无优化的DRL算法是两种不同的算法类型，它们在处理问题时的思路和方法不同。 基于模型的DRL算法，如LyDROO算法，会建立一个模型来预测未来的状态和奖励，然后基于该模型进行决策。这种算法需要...

input : Parameters V , {γi, ci}Ni=1, K, training interval δT , Mt update interval δM ; output: Control actions 􏰕xt,yt􏰖Kt=1; 1 Initialize the DNN with random parameters θ1 and empty replay memory, M1 ← 2N; 2 Empty initial data queue Qi(1) = 0 and energy queue Yi(1) = 0, for i = 1,··· ,N; 3 fort=1,2,...,Kdo 4 Observe the input ξt = 􏰕ht, Qi(t), Yi(t)􏰖Ni=1 and update Mt using (8) if mod (t, δM ) = 0; 5 Generate a relaxed offloading action xˆt = Πθt 􏰅ξt􏰆 with the DNN; 6 Quantize xˆt into Mt binary actions 􏰕xti|i = 1, · · · , Mt􏰖 using the NOP method; 7 Compute G􏰅xti,ξt􏰆 by optimizing resource allocation yit in (P2) for each xti; 8 Select the best solution xt = arg max G 􏰅xti , ξt 􏰆 and execute the joint action 􏰅xt , yt 􏰆; { x ti } 9 Update the replay memory by adding (ξt,xt); 10 if mod (t, δT ) = 0 then 11 Uniformly sample a batch of data set {(ξτ , xτ ) | τ ∈ St } from the memory; 12 Train the DNN with {(ξτ , xτ ) | τ ∈ St} and update θt using the Adam algorithm; 13 end 14 t ← t + 1; 15 Update {Qi(t),Yi(t)}N based on 􏰅xt−1,yt−1􏰆 and data arrival observation 􏰙At−1􏰚N using (5) and (7). i=1 i i=1 16 end这个算法中的基于模型的优化和无优化DRL和DNN深度学习怎么体现

2023-05-12 上传
在这个算法中，第7步是基于模型的优化，即对于每个二进制决策向量 $x_{ti}$，都通过解决问题（P2）来计算全局效用函数 $G(x_{ti},\xi_t)$。这个优化问题需要求解资源分配向量 $y_{it}$，使得总能耗最小。这是一个...

出一个基于quertus的VHDL实验中遇到的主要问题和解决方法，例如综合时的报错和修改、仿真发现的问题及解决等内容

2023-07-08 上传
在基于Quartus的VHDL实验中，常见的问题和解决方法包括： 1. 综合时的报错和修改： - 问题：综合时可能会出现语法错误、信号冲突等报错信息。 - 解决方法：首先，仔细检查代码中的语法错误，确保所有的语法都正确...

Algorithm 1: The online LyDROO algorithm for solving (P1). input : Parameters V , {γi, ci}Ni=1, K, training interval δT , Mt update interval δM ; output: Control actions 􏰕xt,yt􏰖Kt=1; 1 Initialize the DNN with random parameters θ1 and empty replay memory, M1 ← 2N; 2 Empty initial data queue Qi(1) = 0 and energy queue Yi(1) = 0, for i = 1,··· ,N; 3 fort=1,2,...,Kdo 4 Observe the input ξt = 􏰕ht, Qi(t), Yi(t)􏰖Ni=1 and update Mt using (8) if mod (t, δM ) = 0; 5 Generate a relaxed offloading action xˆt = Πθt 􏰅ξt􏰆 with the DNN; 6 Quantize xˆt into Mt binary actions 􏰕xti|i = 1, · · · , Mt􏰖 using the NOP method; 7 Compute G􏰅xti,ξt􏰆 by optimizing resource allocation yit in (P2) for each xti; 8 Select the best solution xt = arg max G 􏰅xti , ξt 􏰆 and execute the joint action 􏰅xt , yt 􏰆; { x ti } 9 Update the replay memory by adding (ξt,xt); 10 if mod (t, δT ) = 0 then 11 Uniformly sample a batch of data set {(ξτ , xτ ) | τ ∈ St } from the memory; 12 Train the DNN with {(ξτ , xτ ) | τ ∈ St} and update θt using the Adam algorithm; 13 end 14 t ← t + 1; 15 Update {Qi(t),Yi(t)}N based on 􏰅xt−1,yt−1􏰆 and data arrival observation 􏰙At−1􏰚N using (5) and (7). i=1 i i=1 16 end With the above actor-critic-update loop, the DNN consistently learns from the best and most recent state-action pairs, leading to a better policy πθt that gradually approximates the optimal mapping to solve (P3). We summarize the pseudo-code of LyDROO in Algorithm 1, where the major computational complexity is in line 7 that computes G􏰅xti,ξt􏰆 by solving the optimal resource allocation problems. This in fact indicates that the proposed LyDROO algorithm can be extended to solve (P1) when considering a general non-decreasing concave utility U (rit) in the objective, because the per-frame resource allocation problem to compute G􏰅xti,ξt􏰆 is a convex problem that can be efficiently solved, where the detailed analysis is omitted. In the next subsection, we propose a low-complexity algorithm to obtain G 􏰅xti, ξt􏰆. B. Low-complexity Algorithm for Optimal Resource Allocation Given the value of xt in (P2), we denote the index set of users with xti = 1 as Mt1, and the complementary user set as Mt0. For simplicity of exposition, we drop the superscript t and express the optimal resource allocation problem that computes G 􏰅xt, ξt􏰆 as following (P4) : maximize 􏰀j∈M0 􏰕ajfj/φ − Yj(t)κfj3􏰖 + 􏰀i∈M1 {airi,O − Yi(t)ei,O} (28a) τ,f,eO,rO 17 ，这个算法中基于模型的DRL算法和无优化的DRL算法和DNN深度学习都各体现在哪

2023-05-12 上传
这个算法中基于模型的DRL算法和无优化的DRL算法体现在如何生成离散的决策xt。具体来说，在第5行，算法使用一个基于深度神经网络的Actor模型来生成一个连续的决策xˆt。然后在第6行，算法使用了一个无优化的离散化...

、二阶系统对数频率特性在交接频率处，其幅值与ξ有什么关系？

2023-06-03 上传
|H(jω)| = K/[(1-ω^2/ωn^2)^2 + 4ξ^2ω^2/ωn^2] 其中，K为系统增益，ω为频率，ωn为系统的自然频率，ξ为系统的阻尼比。在交接频率处，即ω=ωn时，上式变为： |H(jωn)| = K/4ξ 因此，二阶系统对数频率...
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