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Numerical solutions of linear quadratic control for time-varying systems via symplectic conservative perturbation

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Applied Mathematics and Mechanics(English Edition) 2007年第3期28卷 277-287页

作者：谭述君钟万勰 state Key Laboratory of Structural Analysis for Industrial Equipment Dalian University of Technology

Optimal control system of state space is a conservative system, whose approximate method should be symplectic conservation. Based on the precise integration method, an algorithm of symplectic conservative perturbation is presented. It gives a uniform way to solve the linear quadratic control （LQ control） problems for linear timevarying systems accurately and efficiently, whose key points are solutions of differential Riccati equation （DRE） with variable coefficients and the state feedback equation. The method is symplectic conservative and has a good numerical stability and high precision. Numerical examples demonstrate the effectiveness of the proposed method.

关键词： linear time-varying systems linear quadratic control Riccati equation interval mixed energy State Transition Matrix symplectic conservativeperturbation

Multimodal process monitoring based on transition-constrained Gaussian mixture model

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Chinese Journal of Chemical Engineering 2020年第12期28卷 3070-3078页

作者： Shutian Chen Qingchao Jiang Xuefeng Yan Key Laboratory of Advanced Control and Optimization for Chemical Processes of Ministry of Education East China University of Science and TechnologyShanghai 200237China

Reliable process monitoring is important for ensuring process safety and product quality.A production process is generally characterized bymultiple operation modes,and monitoring thesemultimodal processes is challenging.Most multimodal monitoring methods rely on the assumption that the modes are independent of each other,which may not be appropriate for practical application.This study proposes a transition-constrained Gaussian mixture model method for efficient multimodal process monitoring.This technique can reduce falsely and frequently occurring mode transitions by considering the time series information in the mode identification of historical and online data.This process enables the identified modes to reflect the stability of actual working conditions,improve mode identification accuracy,and enhance monitoring reliability in cases of mode overlap.Case studies on a numerical simulation example and simulation of the penicillin fermentation process are provided to verify the effectiveness of the proposed approach inmultimodal process monitoring with mode overlap.

关键词： Multimodal process monitoring Gaussian mixture model State Transition Matrix Process control Process systems Systems engineering

THE THEOREM OF THE STABILITY OF LINEAR NONAUTONOMOUS SYSTEMS UNDER THE FREQUENTLY-ACTING PERTURBATION AND ITS APPLICATION IN THE STABILITY ANALYSIS OF ROBOT

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Applied Mathematics and Mechanics(English Edition) 1991年第11期12卷 1057-1063页

作者：张书顺 Haerbin Shipbuilding Engineering Institute Haerbin

The necessary and sufficient condition of the stability of linear nonautonomous system under the frequently-acting perturbation has been given and proved on the basis of[1] and [2], and the theorem of the equivalence on the uniform and asymptotical stability in the sense of Liapunov ami the stability under the frequently-acting perturbation of linear nonautonomous system has been given in this paper. Besides, the analysis of the dynamic stabilitv of robot has been presented by applying the theorem in this paper, which is closer to reality

关键词： stability nonautonomous system frequently-acting perturbation State Transition Matrix robot

THE THEOREM OF THE STABILITY OF NONLINEAR NONAUTONOMOUS SYSTEMS UNDER THE FREQUENTLY-ACTING PERTURBATION—LIAPUNOV’S INDIRECT METHOD

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Applied Mathematics and Mechanics(English Edition) 1991年第7期12卷 717-725页

作者：张书顺商大中 Haerbin Shipbuilding Engineering Institute Haerbin

In this paper the stability of nonlinear nonautonomous systems under the frequently-acting perturbation is studied. This study is a forward development of the study of the stability in the Liapunov sense; furthermore, it is of significance in practice since perturbations are often not single in the time domain. Malkin proved a general theorem about thesubject. To apply the theorem, however, the user has to construct a Liapunov function which satisfies specified conditions and it is difficult to find such a function for nonlinear nonautonomous systems. In the light of the principle of Liapunov's indirect method, which is an effective method to decide the stability of nonlinear systems in the Liapunov sense, the authors have achieved several important conclusions expressed in the form of theorems to determine the stability of nonlinear nonautonomous systems under the frequently-acting perturbation.

关键词： nonautonomous system frequently-acting perturbation uniformly asymptotical stability State Transition Matrix

基于STM的Verilog HDL需求一致性验证工具

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基于STM的Verilog HDL需求一致性验证工具

作者：高宏发大连理工大学

学位级别：硕士

芯片行业不断发展,IC设计规模和复杂程度进一步提高,IC验证已成为高性能芯片研发过程中的一个重要瓶颈。同样,FPGA系统的验证工作存在复杂性和全面性的问题。当前仿真验证与形式化验证技术主要针对系统实现的中后期,对于早期设计与需求... 详细信息

芯片行业不断发展,IC设计规模和复杂程度进一步提高,IC验证已成为高性能芯片研发过程中的一个重要瓶颈。同样,FPGA系统的验证工作存在复杂性和全面性的问题。当前仿真验证与形式化验证技术主要针对系统实现的中后期,对于早期设计与需求的一致性验证上未能发挥作用。而越早开始系统验证工作,发现错误后的改正成本越低。从验证的全面性角度考虑,验证工作应尽量覆盖数字系统的设计实现过程,做到问题尽早发现,提高验证效率。本文针对FPGA系统设计早期的状态转换过程,设计实现了基于STM的Verilog HDL需求一致性验证工具。本文首先分析了当前IC验证的研究现状,介绍了当前两种主要验证技术:仿真验证与形式化验证。其次对系统实现使用的相关技术进行说明。然后详细介绍了验证工具的功能需求及应用架构,并以此为设计基础进行工具实现。工具具有较为完整的设计与验证流程,主要包括:使用需求状态机语言RSML进行需求规约,为系统模块建立形式化需求模型;按照Verilog程序结构特点分为数据定义验证和基于STM的状态转换验证;以模块为单位进行Verilog HDL代码生成。其中使用状态迁移矩阵STM实现对Verilog HDL程序逻辑的状态转换显示,将不同事件下的转换与需求模型进行比较,从而实现设计与需求的一致性验证。为保证工具实现的正确性和可靠性,对工具的各部分功能进行测试。最后,以具体实例在工具上进行应用,说明工具的设计验证与代码生成能力。本文设计的基于STM的Verilog HDL需求一致性验证工具将验证工作着眼于系统设计早期,利用状态迁移矩阵实现代码编写前的需求一致性验证,并通过具体实例应用说明工具的验证能力和实用价值。本文提出的基于STM的验证方法是对当前验证技术在全面性上的一种补充,具有一定创新性。

关键词：需求验证 State Transition Matrix Verilog HDL 代码生成

Exploration Opportunity Search for Near Earth Small Body

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Exploration Opportunity Search for Near Earth Small Body