A penalty function-based random search algorithm for optimal control of switched systems with stochastic constraints and its application in automobile test-driving with gear shifts

Practical industrial process is usually a dynamic process including uncertainty. Stochastic constraints can be used for industrial process modeling, when system sate and/or control input constraints cannot be strictly satisfied. Thus, optimal control of switched systems with stochastic constraints can be available to address practical industrial process problems with different modes. In general, obtaining an analytical solution of the optimal control problem is usually very difficult due to the discrete nature of the switching law and the complexity of stochastic constraints. To obtain a numerical solution, this problem is formulated as a constrained nonlinear parameter selection problem (CNPSP) based on a relaxation transformation (RT) technique, an adaptive sample approximation (ASA) method, a smooth approximation (SA) technique, and a control parameterization (CP) method. Following that, a penalty function-based random search (PFRS) algorithm is designed for solving the CNPSP based on a novel search rule-based penalty function (NSRPF) method and a novel random search (NRS) algorithm. The convergence results show that the proposed method is globally convergent. Finally, an optimal control problem in automobile test-driving with gear shifts (ATGS) is further extended to illustrate the effectiveness of the proposed method by taking into account some stochastic constraints. Numerical results show that compared with other typical methods, the proposed method is less conservative and can obtain a stable and robust performance when considering the small perturbations in initial system state. In addition, to balance the computation amount and the numerical solution accuracy, a tolerance setting method is also provided by the numerical analysis technique.     

Generalized sentinels defined via least squares

We address the problem of monitoring a linear functional (c, x)_Eof an unknown vectorx of a Hilbert spaceE, the available data being the observationz, in a Hilbert spaceF, of a vectorAx depending linearly onx through some known operatorA(E; F). WhenE=E ₁×E ₂,c=(c ₁ 0), andA is injective and defined through the solution of a partial differential equation, Lions ([6]–[8]) introduced sentinelssF such that (s, Ax)_Fis sensitive to x₁ E ₁ but insensitive to x₂ E₂. In this paper we prove the existence, in the general case, of (i) a generalized sentinel (s, ) ×E, where F withF dense in 80, such that for anya priori guess x₀ ofx, we have s, Ax + (, x₀)_E=(c, x)_E, where x is the least-squares estimate ofx closest tox ₀, and (ii) a family of regularized sentinels (s _n , _n ) F×E which converge to (s, ). Generalized sentinels unify the least-squares approach (by construction !) and the sentinel approach (whenA is injective), and provide a general framework for the construction of sentinels with special sensitivity in the sense of Lions [8]).     

硫代磷酸酯类化合物的^31P化学位移加和规则

对近８０年种自行合成的硫逐及硫超磷酸酯类化合物进行了＾３１Ｐ ＮＭＲ谱的测定，提出了一个经验方程、一套化学位移参数的立体电子效应参数，比较准确地计算了它们的＾１Ｐ化学位移，其计算值与测定值的平均误差为±０．０９６，标准偏差为±０．１３。同时，就取代基的电负性，键角和立体电子效应等对＾３１Ｐ化学位移的影响作了理论上的探讨。     

Three-dimensional quantum dynamics study of vibrational predissociation of HeI2 van der Waals molecule for low vibrational excitation using the time-dependent wave packet method

Three-dimensional quantum mechanical calculations for vibrational predissociation of He1₂(B) van der Waals molecules are presented using the time-dependent wave packet technique within the golden rule approximation. The total and partial decay widths, lifetimes, rates and their dependence on initial vibrational states were obtained for HeI₂ at low initial vibrational excited levels. Our calculations show that the calculated total decay widths, lifetimes and rates agree well with those extrapolated from experimental data available. The predicted total decay widths as a function of initial vibrational states exhibit highly nonlinear behavior. The very short propagation time (less than 1 ps) required in the golden rule wave packet calculation is determined by the duration time of the final state interaction between the fragments on the vibrationally deexcited adiabatic potential surface. The final state interaction between the fragments is shown to play an important role in determining the final rotational distribution. This interpretation clearly explains the dynamical effect that the final rotational distribution shifts to the lower rotational energy levels as the initial vibrational quantum numberu increases.     

The correlations of the enthalpy of vaporization and the surface tension of molecular liquids

Correlation relations based on Stefan's rule, which defined dependence between the enthalpy of vaporization, the surface tension, the molar volume and the molar mass of a substance, were obtained. For development of the correlation equations two computational procedures were used: a method of the least squares and a method of artificial neural networks. The method of artificial neural networks was shown to give somewhat better results than the linear least-squares procedure. The average deviation of the calculated values from the experimental ones did not exceed 6% for training set of substances and 10% for control set (the method of the least squares). For the method of artificial neural networks it is 3% and 8%, respectively.     

Parameter-dependent renewal theorems with applications

Let ₁, ₂, ... be a sequence of i.i.d. random variables with positive mean and finite variance and letr(b), b0, be real numbers tending to 0 asb . Definings _n=₁+...+_n andS _n=S_n(b)=s_n+r(b)n, the stopping time =(b)=inf {n>/1:S_n >b} whereb=b(b) , will be considered with special regard to the excess over the boundaryR _b=s+r(b)–b. It turns out that the limiting distribution ofR _b is the same as in the caser(b)0 for allb. Proving this, Blackwell's renewal theorem and its integral version have to be established first in the above stated situation. Finally, an expansion ofE to vanishing terms asb will be provided and applied to some examples arising in economics.

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Zusammenfassung Seien ₁, ₂, ... unabhängige identisch verteilte Zufallsgrößen mit positivem Erwartungswert und endlicher Varianz sowier(b), b0, reelle Zahlen mitr(b)0 für b. Sei ferners ₁, s₂, ... der zugehörige Summenprozeß,S _n= S_n(b)=s_n+r(b)n fürn1 und =(b)=inf {n1: S_n>b, wobeib=b(b) fürb . Es wird gezeigt, daß die asymptotische Verteilung des ExzessesR _b=s +r(b) –b mit der im Fallr(·)0 übereinstimmt. Dazu werden sowohl das Blackwellsche Erneuerungstheorem als auch seine Integralversion in der vorher beschriebenen parameterabhängigen Situation geeignet formuliert und bewiesen. Als Folgerung ergibt sich dann eine asymptotische Entwicklung vonE(b) fürb bis zu Termen o(1). Anh- and einiger Beispiele aus dem ökonomischen Bereich wird schließlich noch aufgezeigt, wo Approximationen fürE(b) von Interesse sein können.

     

双组分冷模射流流化床气化炉内流体动力学特性模拟

针对实际工业生产中经常遇到的多组分体系，本文选取了具有代表性意义的非等密度/直径的双组分体系(树脂和砂子)为研究对象，以Goossens等提出的平均物性法则计算了固体混合物的平均粒径和平均密度，采用欧拉－欧拉计算流体动力学模型(CFD)模拟了二维冷模射流床气化炉内，诸如气、固相流场的时空分布、时均空隙率分布、射流穿透深度等流体动力学的时空特征，所得结果与文献报道相吻合。     

八面体配合物分子的旋光性和构型

在极化度多级圆球不对称模型(该模型运用于含一个或二个不对称碳的有机化合物)和对称性规则的基础上,我们提出了某些规则和八面体配合物的八区律。利用这些规则和规律,八面体配合物的分子构型可以方便的与它们的旋光方向联系起来。