A Variable Structural Control for a Hybrid Hyperbolic Dynamic System

Xuezhang Hou

doi:10.24297/jam.v20i.8978

Authors

Xuezhang Hou Towson University

DOI:

https://doi.org/10.24297/jam.v20i.8978

Keywords:

Partial differential equations, Hyperbolic dynamic system, Variable structural control, Semigroup of linear operators

Abstract

Abstract: 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.

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