针对具有不确定干扰的汽轮发电机励磁与汽阀综合控制系统,建立鲁棒综合控制模型。运用基于Sum of Squares(SOS)分解技术的鲁棒控制方法(SOSRCA),设计电力系统鲁棒综合控制方法。该方法充分考虑了综合系统中存在的不确定参数及干扰,使发...针对具有不确定干扰的汽轮发电机励磁与汽阀综合控制系统,建立鲁棒综合控制模型。运用基于Sum of Squares(SOS)分解技术的鲁棒控制方法(SOSRCA),设计电力系统鲁棒综合控制方法。该方法充分考虑了综合系统中存在的不确定参数及干扰,使发电机组具有较好的鲁棒性能。控制方法的求解过程是算法化、程序化的,避免了繁琐的递归设计和参数估计过程。最后,在三机电力系统仿真中,对基于SOSRCA所得出的鲁棒综合控制律进行仿真分析与讨论,验证其有效性及优越性。展开更多
In this paper, an efficient computational approach is proposed to solve the discrete time nonlinear stochastic optimal control problem. For this purpose, a linear quadratic regulator model, which is a linear dynamical...In this paper, an efficient computational approach is proposed to solve the discrete time nonlinear stochastic optimal control problem. For this purpose, a linear quadratic regulator model, which is a linear dynamical system with the quadratic criterion cost function, is employed. In our approach, the model-based optimal control problem is reformulated into the input-output equations. In this way, the Hankel matrix and the observability matrix are constructed. Further, the sum squares of output error is defined. In these point of views, the least squares optimization problem is introduced, so as the differences between the real output and the model output could be calculated. Applying the first-order derivative to the sum squares of output error, the necessary condition is then derived. After some algebraic manipulations, the optimal control law is produced. By substituting this control policy into the input-output equations, the model output is updated iteratively. For illustration, an example of the direct current and alternating current converter problem is studied. As a result, the model output trajectory of the least squares solution is close to the real output with the smallest sum squares of output error. In conclusion, the efficiency and the accuracy of the approach proposed are highly presented.展开更多
In this paper we present some identities for the sums of squares of Fibonacci and Lucas numbers with consecutive primes, using maximal prime gap G(x)~log2x, as indices.
Polygonal numbers and sums of squares of primes are distinct fields of number theory. Here we consider sums of squares of consecutive (of order and rank) polygonal numbers. We try to express sums of squares of polygon...Polygonal numbers and sums of squares of primes are distinct fields of number theory. Here we consider sums of squares of consecutive (of order and rank) polygonal numbers. We try to express sums of squares of polygonal numbers of consecutive orders in matrix form. We also try to find the solution of a Diophantine equation in terms of polygonal numbers.展开更多
By means of this approach, a constructive method of pandiagonal magic squares is proposed. Pandiagonalmagic squares of order mn can be generated via two ones which are orders m and n, respectively.
In this paper, we consider a general quasi-differential expressions t1,t2 Tn, each of order n with complex coefficients and their formal adjoints are t1＋,t2＋- x＋ on [0, b） respectively. We show in the direct sum s...In this paper, we consider a general quasi-differential expressions t1,t2 Tn, each of order n with complex coefficients and their formal adjoints are t1＋,t2＋- x＋ on [0, b） respectively. We show in the direct sum spaces LZ（Ip）, p = 1,2 N of functions defined on each of the separate intervals with the case of one singular end-points and under suitable conditions on the function F that all solutions of the product quasi-integro differential equations are bounded and LZw -bounded on [0,b）.展开更多
We study the eight infinite sequences of triples of natural numbers A=(F2n+1,4F2n+3,F2n+7), B=(F2n+1,4F2n+5,F2n+7), C=(F2n+1,5F2n+1,F2n+3), D=(F2n+3,4F2n+1,F2n+3) and A=(L2n+1,4L2n+3,L2n+7), B=(L2n+1,4L2n+5,L2n+7), C=...We study the eight infinite sequences of triples of natural numbers A=(F2n+1,4F2n+3,F2n+7), B=(F2n+1,4F2n+5,F2n+7), C=(F2n+1,5F2n+1,F2n+3), D=(F2n+3,4F2n+1,F2n+3) and A=(L2n+1,4L2n+3,L2n+7), B=(L2n+1,4L2n+5,L2n+7), C=(L2n+1,5L2n+1,L2n+3), D=(L2n+3,4L2n+1,L2n+3. The sequences A,B,C and D are built from the Fibonacci numbers Fn while the sequences A, B, C and D from the Lucas numbers Ln. Each triple in the sequences A,B,C and D has the property D(-4) (i. e., adding -4 to the product of any two different components of them is a square). Similarly, each triple in the sequences A, B, C and D has the property D(20). We show some interesting properties of these sequences that give various methods how to get squares from them.展开更多
目的建立超高效液相色谱法(ultra performance liquid chromatography,UPLC)快速测定蜂胶提取物中的14种化学成分,结合多元统计分析方法对不同厂家的蜂胶提取物质量进行综合评价。方法收集来自不同厂家的17批蜂胶提取物样品,采用UPLC采...目的建立超高效液相色谱法(ultra performance liquid chromatography,UPLC)快速测定蜂胶提取物中的14种化学成分,结合多元统计分析方法对不同厂家的蜂胶提取物质量进行综合评价。方法收集来自不同厂家的17批蜂胶提取物样品,采用UPLC采集色谱图,甲醇-0.2%磷酸水溶液为流动相,梯度洗脱,同时测定咖啡酸、p-香豆酸、阿魏酸、异阿魏酸、3,4-二甲氧基肉桂酸、咖啡酸苯乙酯、阿替匹林C、槲皮素、山奈素、芹菜素、异鼠李素、乔松素、白杨素、高良姜素的含量,运用统计学软件进行主成分分析(principal component analysis,PCA)、聚类分析(clustering analysis,CA)、偏最小二乘-判别分析(partial least squares-discriminant analysis,PLS-DA),筛选分析质量差异标志物。通过熵权法计算各指标权重,将结果应用于优劣解距离法(technique for order preference by similarity to ideal solution,TOPSIS)和秩和比法(rank sum ratio,RSR)构建综合评价模型,评价不同批次的蜂胶提取物质量优劣。结果14个指标成分在各自的浓度范围内线性关系良好(r≥0.9992),平均加样回收率是96.37%~102.21%,相对标准偏差小于2%。化学计量学结果表明17批样品聚为4类,同一个厂家的样品聚为一类,不同厂家的样品存在明显差异,3,4-二甲氧基肉桂酸、异阿魏酸、槲皮素、高良姜素、阿替匹林C、咖啡酸苯乙酯可能是影响厂家质量差异的潜在标志物。通过熵权-TOPSIS、熵权-RSR以及两者相结合的方式构建的综合质量评价模型,对不同批次蜂胶提取物的质量优劣排序结果较为一致。结论基于UPLC的多指标测定方法准确便捷,结合PCA、CA、PLS-DA和TOPSIS-RSR建立的评价模式能够有效分析不同厂家的差异性,为蜂胶提取物的整体质量评价提供参考。展开更多
文摘针对具有不确定干扰的汽轮发电机励磁与汽阀综合控制系统,建立鲁棒综合控制模型。运用基于Sum of Squares(SOS)分解技术的鲁棒控制方法(SOSRCA),设计电力系统鲁棒综合控制方法。该方法充分考虑了综合系统中存在的不确定参数及干扰,使发电机组具有较好的鲁棒性能。控制方法的求解过程是算法化、程序化的,避免了繁琐的递归设计和参数估计过程。最后,在三机电力系统仿真中,对基于SOSRCA所得出的鲁棒综合控制律进行仿真分析与讨论,验证其有效性及优越性。
文摘In this paper, an efficient computational approach is proposed to solve the discrete time nonlinear stochastic optimal control problem. For this purpose, a linear quadratic regulator model, which is a linear dynamical system with the quadratic criterion cost function, is employed. In our approach, the model-based optimal control problem is reformulated into the input-output equations. In this way, the Hankel matrix and the observability matrix are constructed. Further, the sum squares of output error is defined. In these point of views, the least squares optimization problem is introduced, so as the differences between the real output and the model output could be calculated. Applying the first-order derivative to the sum squares of output error, the necessary condition is then derived. After some algebraic manipulations, the optimal control law is produced. By substituting this control policy into the input-output equations, the model output is updated iteratively. For illustration, an example of the direct current and alternating current converter problem is studied. As a result, the model output trajectory of the least squares solution is close to the real output with the smallest sum squares of output error. In conclusion, the efficiency and the accuracy of the approach proposed are highly presented.
文摘In this paper we present some identities for the sums of squares of Fibonacci and Lucas numbers with consecutive primes, using maximal prime gap G(x)~log2x, as indices.
文摘Polygonal numbers and sums of squares of primes are distinct fields of number theory. Here we consider sums of squares of consecutive (of order and rank) polygonal numbers. We try to express sums of squares of polygonal numbers of consecutive orders in matrix form. We also try to find the solution of a Diophantine equation in terms of polygonal numbers.
文摘By means of this approach, a constructive method of pandiagonal magic squares is proposed. Pandiagonalmagic squares of order mn can be generated via two ones which are orders m and n, respectively.
文摘In this paper, we consider a general quasi-differential expressions t1,t2 Tn, each of order n with complex coefficients and their formal adjoints are t1＋,t2＋- x＋ on [0, b） respectively. We show in the direct sum spaces LZ（Ip）, p = 1,2 N of functions defined on each of the separate intervals with the case of one singular end-points and under suitable conditions on the function F that all solutions of the product quasi-integro differential equations are bounded and LZw -bounded on [0,b）.
文摘We study the eight infinite sequences of triples of natural numbers A=(F2n+1,4F2n+3,F2n+7), B=(F2n+1,4F2n+5,F2n+7), C=(F2n+1,5F2n+1,F2n+3), D=(F2n+3,4F2n+1,F2n+3) and A=(L2n+1,4L2n+3,L2n+7), B=(L2n+1,4L2n+5,L2n+7), C=(L2n+1,5L2n+1,L2n+3), D=(L2n+3,4L2n+1,L2n+3. The sequences A,B,C and D are built from the Fibonacci numbers Fn while the sequences A, B, C and D from the Lucas numbers Ln. Each triple in the sequences A,B,C and D has the property D(-4) (i. e., adding -4 to the product of any two different components of them is a square). Similarly, each triple in the sequences A, B, C and D has the property D(20). We show some interesting properties of these sequences that give various methods how to get squares from them.
文摘目的建立超高效液相色谱法(ultra performance liquid chromatography,UPLC)快速测定蜂胶提取物中的14种化学成分,结合多元统计分析方法对不同厂家的蜂胶提取物质量进行综合评价。方法收集来自不同厂家的17批蜂胶提取物样品,采用UPLC采集色谱图,甲醇-0.2%磷酸水溶液为流动相,梯度洗脱,同时测定咖啡酸、p-香豆酸、阿魏酸、异阿魏酸、3,4-二甲氧基肉桂酸、咖啡酸苯乙酯、阿替匹林C、槲皮素、山奈素、芹菜素、异鼠李素、乔松素、白杨素、高良姜素的含量,运用统计学软件进行主成分分析(principal component analysis,PCA)、聚类分析(clustering analysis,CA)、偏最小二乘-判别分析(partial least squares-discriminant analysis,PLS-DA),筛选分析质量差异标志物。通过熵权法计算各指标权重,将结果应用于优劣解距离法(technique for order preference by similarity to ideal solution,TOPSIS)和秩和比法(rank sum ratio,RSR)构建综合评价模型,评价不同批次的蜂胶提取物质量优劣。结果14个指标成分在各自的浓度范围内线性关系良好(r≥0.9992),平均加样回收率是96.37%~102.21%,相对标准偏差小于2%。化学计量学结果表明17批样品聚为4类,同一个厂家的样品聚为一类,不同厂家的样品存在明显差异,3,4-二甲氧基肉桂酸、异阿魏酸、槲皮素、高良姜素、阿替匹林C、咖啡酸苯乙酯可能是影响厂家质量差异的潜在标志物。通过熵权-TOPSIS、熵权-RSR以及两者相结合的方式构建的综合质量评价模型,对不同批次蜂胶提取物的质量优劣排序结果较为一致。结论基于UPLC的多指标测定方法准确便捷,结合PCA、CA、PLS-DA和TOPSIS-RSR建立的评价模式能够有效分析不同厂家的差异性,为蜂胶提取物的整体质量评价提供参考。
