基于积分因子方法研究Chaplygin非完整系统的守恒律

提出并研究了构建Chaplygin非完整系统守恒律的积分因子方法.基于正则形式的Chaplygin方程,定义了积分因子,给出了系统存在守恒量的必要条件,建立了Chaplygin非完整系统的守恒定理及其逆定理.研究表明:对应于必要条件的每一组非奇异函数解,系统存在一个守恒量;反之,对于一个已知守恒量,可找到相应的积分因子,且解是不唯一的.文末以匀质圆球在粗糙水平面上纯滚动为例,讨论了该方法的应用.     

Mechanical verification of strategies

This paper presents a method of representing planning domains in the Boyer-Moore logic so that we can prove mechanically whether a strategy solves a problem. Current approaches require explicit frame axioms and state constraints to be included as part of a domain specification and use a programming language for expressing strategies. These make it difficult to specify domains and verify plans efficiently. Our method avoids explicit frame axioms, since domains are specified by programming an interpreter for sequences of actions in the Boyer-Moore logic. Strategies are represented as planners, Lisp programs that take an initial state and other arguments as input and return a sequence of actions that, when executed in the given initial state, will bring about a goal state. Mechanical verification of a strategy is accomplished by proving that the corresponding planner solves all instances of the given problem. We illustrate our approach by verifying strategies in some variations of the blocks world.The work described here was supported in part by NSF Grant MIP-9017499.     

Design Of Robust Pid Controllers

In this paper, a new method is proposed to design the robust PID controllers for uncertain linear time‐invariant systems. We describe a simple and programming procedure for designing PID controllers by applying Kharitonov's theorem and LMI method. Such a controller enables the resulting control system to achieve robust stability as well as asymptotic tracking.     

Convergence and comparison theorems for double splittings of matrices

In this paper, some convergence theorems for the double splitting of a monotone matrix or a Hermitian positive definite matrix are presented. Two comparison theorems for two double splittings of a monotone matrix are obtained. Meanwhile, we establish a new sufficient condition for convergence of the Gauss-Seidel double SOR method for an H-matrix.     

鞅超收敛定理与遗忘因子最小二乘算法的收敛法分析

本文扩展了用于分析时不变系统辨识算法收敛性的鞅收敛定理，建立了鞅超收敛定理。它可以作为工具来分析时变系统的各种辨识算法的收敛性，为地变系统收敛性和稳定性分析这一困难课题提供了新方法，开辟了新路。     

An Improvement of Herbrands Theorem and Its Application to Model Generation Theorem Proving

This paper presents an improvement of Herbrand's theorem.We propose a method for specifying a sub- universe of the Herbrand universe of a clause set S for each argument of predicate symbols and function symbols in S. We prove that a clause set S is unsatisfiable if and only if there is a finite unsatisfiable set of ground instances of clauses of S that are derived by only instantiating each variable,which appears as an argument of predicate symbols or function symbols,in S over its corresponding argument's sub-universe of the Herbrand universe of S.Because such sub-universes are usually smaller(sometimes considerably)than the Herbrand universe of S,the number of ground instances may decrease considerably in many cases.We present an algorithm for automatically deriving the sub-universes for arguments in a given clause set,and show the correctness of our improvement.Moreover,we introduce an application of our approach to model generation theorem proving for non-range-restricted problems,show the range-restriction transformation algorithm based on our improvement and provide examples on benchmark problems to demonstrate the power of our approach.     

微内核操作系统互斥量模块功能正确性的形式化验证

操作系统在许多安全攸关领域为软件系统提供关键性底层支撑，操作系统中一个微小的错误或漏洞都可能引起整个软件系统的重大故障，造成巨大经济损失或危及人身安全.为了减少此类安全事故的发生，对操作系统正确性进行验证十分必要.传统测试手段无法穷尽系统中的所有潜在错误，因而操作系统验证有必要使用具有严格数学理论基础的形式化方法.在操作系统中，互斥量可协调多任务对资源的访问，是一种常用的任务同步方式，其功能正确性对于保障多任务应用的正确性十分关键.本文基于定理证明方法，在交互式定理证明器Coq中对某抢占式微内核操作系统的互斥量模块进行代码级形式化建模，给出其接口函数的形式化规范，并实现这些接口函数的功能正确性验证.     

Computer-aided proofs of Arrow's and other impossibility theorems

Arrow's impossibility theorem is one of the landmark results in social choice theory. Over the years since the theorem was proved in 1950, quite a few alternative proofs have been put forward. In this paper, we propose yet another alternative proof of the theorem. The basic idea is to use induction to reduce the theorem to the base case with 3 alternatives and 2 agents and then use computers to verify the base case. This turns out to be an effective approach for proving other impossibility theorems such as Muller-Satterthwaite and Sen's theorems as well. Motivated by the insights of the proof, we discover a new theorem with the help of computer programs. We believe this new proof opens an exciting prospect of using computers to discover similar impossibility or even possibility results.     

半参数预报方法在水位预报中的应用

本文用ARMA序列的半参数预报方法对湘江水位进行预报,结果表明,这一方法具有好的应用价值。     

Decidability by Resolution for Propositional Modal Logics

The paper shows that satisfiability in a range of popular propositional modal systems can be decided by ordinary resolution procedures. This follows from a general result that resolution combined with condensing, and possibly some additional form of normalization, is a decision procedure for the satisfiability problem in certain so-called path logics. Path logics arise from normal propositional modal logics by the optimized functional translation method. The decision result provides an alternative method of proving decidability for modal logics, as well as closely related systems of artificial intelligence. This alone is not interesting. A more far-reaching consequence of the result has practical value, namely, many standard first-order theorem provers that are based on resolution are suitable for facilitating modal reasoning.     

Web应用中数据库交互行为验证

采用定理证明和逆向工程的方法,对Web应用中的数据库交互行为进行验证。使用Z规格说明描述需求模型,根据数据库交互的源代码和转换规则得到实现模型。从实现模型中获取Web应用的相关性质,通过Z/EVES定理证明器验证这些性质是否在需求模型的 Z规格说明中得到满足。在此基础上,设计该方法的验证框架,并开发相应的原型系统。通过图书馆数据库管理系统实例证明该方法的有 效性。     

控制系统的Bayes可靠性评估算法

针对特定试验条件下小子样控制系统可靠性评定的特点,提出了利用验前信息来弥补现场试验信息不足的改进双重Bayes MC方法。在对单元可靠性分析的基础上,给出单元的可信验前信息,依据特定的可靠性框图,结合有限的系统试验数据,推导出试验用控制系统可靠性评估步骤和计算公式,并对系统可靠度进行了数值仿真计算,计算结果令人满意。     

可由用户持续发展的几何自动推理平台的推理算法

目前的几何定理证明器都不具有可持续性。提出一种结构具有一般性的知识表示和能够统一处理所有规则的推理算法，初步实现了可由用户持续发展的几何自动推理平台。该推理平台允许用户添加几何知识，如几何对象、谓词和规则，并可以综合使用多种推理算法，如前推搜索法和一部分面积法，它将更适合用于几何教学。     

An effective stationary iterative method via double splittings of matrices

In this paper, a new stationary iterative method based on two double splittings of coefficient matrix is proposed to solve linear system $Ax=b$. Some convergence results and comparison theorems of the new method are provided. Theoretical analysis shows that this method is superior to some existing ones under certain conditions. Numerical examples are given to illustrate the theoretical results and examine the effectiveness of the proposed method.     

基于单位分解的一类非线性系统的变结构控制设计

采用单位分解概念和技术,结合交结构控制方法和LMI方法,讨论一类非线性系统的控制设计问题．首先利用单位分解在紧致域上能够以任意给定精度逼近连续函数的性质,将一类非线性系统表示为带有误差的近似模形式;然后在误差满足某些条件的情况下,利用交结构控制设计了渐近稳定控制器;最后以仿真实例说明了该方法的有效性。     

命题时态逻辑定理证明新方法

本文通过对近１０年命题时态逻辑定理证明方法的研究，提出了一种新的证明方法，前人的工作基于对公式的现时部分和后时部分的分解，本文的工作是基于语义反驳树构造。这种新方法为计算机自动证明命题时态逻辑定理，提供了比较好的理论框架．最后还证明了该方法的可靠性和完全性．     

New robust stability criterion and robust controller synthesis

In this paper, a new robust stability criterion for linear systems is proposed by combining the passivity and small gain theorems in different frequency bands. A controller synthesis method based on the new criterion is also developed. The controller can achieve both good performance and robustness in the same frequency band, if the uncertainty in that frequency band is passive or near passive. For processes with near passive lumped uncertainties with large gain in the frequency region in which good performance is required, the proposed controller can have better performance than that of H_∞ control for the same robustness specification. © 1998 John Wiley & Sons, Ltd.     

.NET平台下故障树分析技术的实现及应用

故障树分析是一种自上而下的方法,通过对可能造成系统故障的硬件、软件、环境、人为因素进行分析,分析得出故障原因的各种可能组合方式,由总体至部分,按树状结构,逐层细化的一种分析方法.开发了故障树分析工具,提供了对规范化故障树定性的割集计算、简化等功能,提出了基于容斥定理的定量化顶事件概率简化计算方法,可满足企业对部件级元件进行故障详细分析的需求.还给出了所开发的系统实现界面,系统已在某企业中得到了具体的应用.