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Controllability and Observability of Stochastic Singular Systems in Banach Spaces

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Journal of Systems Science & Complexity 2022年第1期35卷 194-204页

作者： ge zhaoqiang School of Mathematics and Statistics Xi’an Jiaotong UniversityXi'an 710049China.

Exact(approximate)controllability and exact(approximate)observability of stochastic singular systems in Banach spaces are ***,the condition for the existence and uniqueness of the mild solution to stochastic singular systems is given by ge-semigroup in Banach ***,the necessary and sufficient conditions for the exact(approximate)controllability and exact(approximate)observability of the systems considered are derived in terms of ge-semigroup,and the dual principle is ***,an illustrative example is given.

关键词： Banach space controllability ge-semigroup observability stochastic singular systems

Exact Controllability and Exact Observability of Descriptor Infinite Dimensional Systems

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IEEE/CAA Journal of Automatica Sinica 2021年第12期8卷 1956-1963页

作者： zhaoqiang ge School of Mathematics and Statistics Xi’an Jiaotong UniversityXi’an 710049China

Necessary and sufficient conditions for the exact controllability and exact observability of a descriptor infinite dimensional system are obtained in the sense of distributional *** general results are used to examine the exact controllability and exact observability of the Dzektser equation in the theory of seepage and the exact controllability of wave equation.

关键词： Descriptor infinite dimensional systems distribut-ional solution exact controllability exact observability

Impulse Controllability and Impulse Observability of Stochastic Singular Systems

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Journal of Systems Science & Complexity 2021年第3期34卷 899-911页

作者： ge zhaoqiang School of Mathematics and Statistics Xi'an Jiaotong UniversityXi'an 710049China

This paper discusses the impulse controllability and impulse observability of stochastic singular ***,the condition for the existence and uniqueness of the impulse solution to stochastic singular systems is given by Laplace ***,the necessary and sufficient conditions for the impulse controllability and impulse observability of systems considered are derived in terms of matrix ***,an example is given to illustrate the effectiveness of the obtained theoretical results.

关键词： Impulse controllability impulse observability stochastic singular systems

Perturbation and robust controllability of singular distributed parameter control systems in Hilbert space

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Journal of Systems Engineering and Electronics 2011年第4期22卷 647-653页

作者： zhaoqiang ge Department of Applied Mathematics Xi'an Jiaotong University Xi'an 710049 R R. China

Perturbation and robust controllability of the singular distributed parameter control system are discussed via functional analysis and the theory of ge-semigroup in Hilbert space. The perturbation principle of ge-semigroup and the sufficient condition concerning the robust controllability of the singular distributed parameter control system are obtained, in which the controllability for singular distributed parameter control system is not destroyed, if we perturb the equation by small bounded linear operator.

关键词： perturbation robust controllability singular distributedparameter system functional analysis Hilbert space.

Uniform Convergence of the Solutions of Riccati Equations for a Family of Optimal Control Problems

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Journal of Systems Science & Complexity 2020年第1期33卷 74-86页

作者： ge zhaoqiang School of Mathematics and Statistics Xi’an Jiaotong UniversityXi’an 710049China

The uniform convergence of the solutions of a parameterized family of Riccati differential equations which arise in the context of optimal control problems for systems described by a family of linear time-varying evolution equations is considered on the infinite time interval in Hilbert *** sufficient conditions and an illustrative example are given for uniform convergence of the solutions of a family of the Riccati differential *** uniform convergence of the solutions of the Riccati differential equations with respect to parameters is important for applications to problems in adaptive control of stochastic evolution systems.

关键词： Hilbert space linear quadratic control problems Riccati differential equations timevarying evolution systems uniform convergence

Impulse Observability and Impulse Controllability of Regular Degenerate Evolution Systems

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Journal of Systems Science & Complexity 2016年第4期29卷 933-945页

作者： ge zhaoqiang Department of Applied Mathematics Xi’an Jiaotong University

Impulse observability and impulse controllability of regular degenerate evolution systems are discussed by using functional analysis and operator theory in Banach space. Necessary and sufficient conditions for the impulse observability and impulse controllability of the system are obtained. This research is theoretically important for studying the design of the degenerate evolution system.

关键词： Impulse controllability impulse observability regular degenerate evolution systems.

Controllability of Singular Distributed Parameter Systems in the Sense of Mild Solution

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Journal of Systems Science & Complexity 2020年第5期33卷 1485-1496页

作者： ge zhaoqiang ge Xiaochi School of Mathematics and Statistics Xi'an Jiaotong UniversitgyXi'an 710049China Cass Business School CityUniversity of LondonLondonEC1Y 8TEUK

Necessary and sufficient conditions for the exact controllability and approximate controllability of a singular distributed parameter system are *** general results are used to examine the exact controllability and ap... 详细信息

关键词： Approximate controllability exact controllability Hilbert space mild solution singular distributed parameter systems

An exact null controllability of stochastic singular systems

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Science China(Information Sciences) 2021年第7期64卷 247-249页

作者： zhaoqiang ge Xiaochi ge School of Mathematics and Statistics Xi'an Jiaotong University Cass Business School City University of London

Dear editor,The stochastic singular system is also called the stochastic differential algebraic system, stochastic descriptor system, generalized stochastic system, and stochastic degenerate system (e.g.,[1–4]). This type of system is found in numerous fields of application, which include fluid dynamics, the modeling of multi-body mechanisms, finance, inputoutput economics and the problem of protein folding.

关键词： stochastic system impulse solution exact null controllability Ito singular system stochastic Laplace transform

ge-semigroup method for controllability of stochastic descriptor linear systems

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Science China(Information Sciences) 2023年第3期66卷 299-300页

作者： zhaoqiang ge School of Mathematics and Statistics Xi’an Jiaotong University

Dear editor, Nowadays, there are more and more researches on stochastic descriptor systems(see [1–7]). For example, Refs. [4,5] studied the exact controllability of a class of stochastic descriptor systems by a strongly continuous semigroup in Hilbert spaces. In this study, the exact controllability and approximate controllability of the following stochastic descriptor system are studied by using the ge-semigroup theory, respectively:

关键词： DEgeNERATE SOBOLEV EQUATIONS