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首页> 外文会议>World Multiconference on Systemics, Cybernetics and Informatics(SCI 2002) v.6: Industrial Systems and Engineering I; 20020714-20020718; Orlando,FL; US >Singular Systems and Correctness Problem in Complex Systems Dynamics
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Singular Systems and Correctness Problem in Complex Systems Dynamics

机译：复杂系统动力学中的奇异系统和正确性问题

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摘要

The work is dedicated to the elaboration of general analysis methods in the complicated systems dynamics, which will make it possible to obtain the some important problems solving in modelling and the qualitative analysis of complex systems dynamics with control. The modelling problem in mechanics is a central problem, immediately connected with the reduction principle (A.M.Lyapunov, K.P.Persidsky,...) and comparison method (S.A.Chaplygin, V.M.Matrosov, R.Bellman,...). Besides the requirements of model adequateness with the investigated object lead to the principled tasks: to select the essential factors in systems dynamics; to construct the effective mechanical-mathematical models; to ascertain the simplified model correctness domain; to obtain the estimations. Asymptotic approach and the methods of stability theory (H.Poincare, A.M.Lyapunov, N.G.Chetayev) allow to develop the regular manners, to indicate the systematic procedures for building acceptable (legitimate) models, to obtain the theoretical substantiation of the approximate methods in rigorous analysis. Here the general approach is established via understanding the correctness problem as the singularly perturbed problem of stability. The original objects are interpreted as singularly perturbed systems, the state equations are transformed to standard form with non-regular perturbations. Such technique makes it possible to separate the state variables on the different-frequent components from first stage; to receive the hierarchical sequence of the simplified systems, and to introduce into consideration the shortened s-models (accordingly to approximate systems of s-order) as asymptotic s-models with correctness evaluation. Also the conditions of acceptability are determined by worked out method.
机译：这项工作致力于阐述复杂系统动力学中的一般分析方法，这将有可能获得一些在控制和复杂系统动力学的建模和定性分析中需要解决的重要问题。力学中的建模问题是一个中心问题，它直接与归约原理（A.M. Lyapunov，K.P。Persidsky等）和比较方法（S.A. Chaplygin，V.M。Matrosov，R.Bellman等）相关。除了模型适当性和被调查对象的需求之外，还导致了一些原则性的任务：选择系统动力学中的基本因素；建立有效的力学数学模型；确定简化的模型正确性域；获得估计。渐近方法和稳定性理论的方法（H.Poincare，AMLyapunov，NGChetayev）允许开发规则的方式，指示建立可接受（合法）模型的系统程序，以严格的方式获得近似方法的理论依据。分析。在这里，一般方法是通过将正确性问题理解为稳定性的奇异摄动问题而建立的。原始对象被解释为奇摄动系统，状态方程被转换为具有非规则摄动的标准形式。这样的技术使得有可能从第一阶段分离出不同频率组件上的状态变量。接收简化系统的分层序列，并考虑到缩短的s模型（根据s阶近似系统）渐近s模型并进行正确性评估。可接受性的条件也由制定的方法确定。

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