Open AccessControllability and observability of stochastic implicit systems and stochastic GE-evolution operator
Author(s) -
Zhaoqiang Ge
Publication year - 2022
Publication title -
numerical algebra, control and optimization
Language(s) - English
Resource type - Journals
eISSN - 2155-3289
pISSN - 2155-3297
DOI - 10.3934/naco.2021009
Subject(s) - controllability , observability , banach space , mathematics , operator (biology) , uniqueness , commutative property , hilbert space , pure mathematics , mathematical analysis , biochemistry , chemistry , repressor , transcription factor , gene
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.