Research Papers

Stability of Nonlinear Stochastic Distributed Parameter Systems and Its Applications

[+] Author and Article Information
K. D. Do

Department of Mechanical Engineering,
Curtin University,
Bentley, WA 6102, Australia
e-mail: duc@curtin.edu.au

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received July 6, 2015; final manuscript received June 8, 2016; published online July 21, 2016. Assoc. Editor: Davide Spinello.

J. Dyn. Sys., Meas., Control 138(10), 101010 (Jul 21, 2016) (12 pages) Paper No: DS-15-1304; doi: 10.1115/1.4033946 History: Received July 06, 2015; Revised June 08, 2016

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.

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Grahic Jump Location
Fig. 1

An elastic string coordinate system

Grahic Jump Location
Fig. 2

Simulation results without a boundary control

Grahic Jump Location
Fig. 3

Simulation results with the proposed boundary control



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