Stability of Nonlinear Stochastic Distributed Parameter Systems and Its Applications
MetadataShow full item record
This paper derives several well-posedness (existence and uniqueness) and stability results for nonlinear stochastic distributed parameter systems (SDPSs) governed by nonlinear partial differential equations (PDEs) subject to both state-dependent and additive stochastic disturbances. These systems do not need to satisfy global Lipschitz and linear growth conditions. First, the nonlinear SDPSs are transformed to stochastic evolution systems (SESs), which are governed by stochastic ordinary differential equations (SODEs) in appropriate Hilbert spaces, using functional analysis. Second, Lyapunov sufficient conditions are derived to ensure well-posedness and almost sure (a.s.) asymptotic and practical stability of strong solutions. Third, the above results are applied to study well-posedness and stability of the solutions of two exemplary SDPSs.
Showing items related by title, author, creator and subject.
Do, Khac Duc (2018)© 2018 Elsevier Ltd A constructive design of boundary controllers is proposed to stabilize transverse motion of flexible marine risers under stochastic loads induced by restoring membrane and fluid/air velocity. For ...
On-Line dynamic security assessment of wind farm connected power systems using a class of intelligent algorithmsTiako, Remy (2012)Recently large-scale wind farms are integrated quite commonly into power systems. The stochastic operation of wind plants due to intermittency and intra-interval effects of the wind is a problematic issue to determine the ...
Do, Khac Duc (2015)Optimality has not been addressed in existing works on control of (stochastic) nonholonomic systems.This paper presents a design of optimal controllers with respect to a meaningful cost function to globally asymptotically ...