Controllability and observability of stochastic implicit systems and stochastic GE-evolution operator

Zhaoqiang Ge

doi:10.3934/naco.2021009

Article Contents

2022, Volume 12, Issue 2: 339-351. Doi: 10.3934/naco.2021009

This issue Previous Article Applying particle swarm optimization based on Padé approximant to solve ordinary differential equation Next Article Second order discrete time-varying and time-invariant linear continuous systems and Kalman type conditions

Controllability and observability of stochastic implicit systems and stochastic GE-evolution operator

Zhaoqiang Ge^,

School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China

^* Corresponding author: gezqjd@mail.xjtu.edu.cn
^* Corresponding author: gezqjd@mail.xjtu.edu.cn

Received: October 2020

Revised: February 2021

Early access: March 2021

Published: June 2022

The author is supported by National Natural Science Foundation of China grant Nos. 11926402 and 61973338

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Abstract

This paper discusses exact (approximate) controllability and exact (approximate) observability of stochastic implicit systems in Banach spaces. Firstly, we introduce the stochastic GE-evolution operator in Banach space and discuss existence and uniqueness of the mild solution to stochastic implicit systems by stochastic GE-evolution operator in Banach space. Secondly, we discuss conditions for exact (approximate) controllability and exact (approximate) observability of the systems considered in terms of stochastic GE-evolution operator and the dual principle. Finally, an illustrative example is given.

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Mathematics Subject Classification: Primary: 93B05, 93B07.

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