Open AccessA Variable Structural Control for a Hybrid Hyperbolic Dynamic System
Author(s) -
Xihuan Hou
Publication year - 2021
Publication title -
journal of advances in mathematics
Language(s) - English
Resource type - Journals
ISSN - 2347-1921
DOI - 10.24297/jam.v20i.8978
Subject(s) - mathematics , semigroup , hilbert space , variable (mathematics) , operator (biology) , partial differential equation , hyperbolic partial differential equation , boundary (topology) , state space , variable structure system , analytic semigroup , control system , distributed parameter system , state variable , control theory (sociology) , mathematical analysis , control (management) , variable structure control , sliding mode control , computer science , nonlinear system , repressor , artificial intelligence , chemistry , engineering , biochemistry , quantum mechanics , transcription factor , statistics , physics , electrical engineering , gene , thermodynamics
In this paper, we are concerned with a hybrid hyperbolic dynamic system formulated by partial differential equations with initial and boundary conditions. First, the system is transformed to an abstract evolution system in an appropriate Hilbert space, and spectral analysis and semigroup generation of the system operator is discussed. Subsequently, a variable structural control problem is proposed and investigated, and an equivalent control method is introduced and applied to the system. Finally, a significant result that the state of the system can be approximated by the ideal variable structural mode under control in any accuracy is derived and examined.