Mean square stability of a second-order parametric linear system excited by a colored Gaussian noise

Floris, Claudio

doi:10.1016/j.jsv.2014.09.023

Cited by 14 publications

(3 citation statements)

References 57 publications

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“…Substitution of linear kinematic theory conducts the relationship as below in Eqs. (12)(13)(14). Also, Fig.…”

Section: Satellite Systemmentioning

confidence: 86%

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Adaptive Control of Satellite System using Kalman Estimates in the presence of Disturbance

Dube¹,

Patel²

2019

International Conference of Control, Dynamic Systems, and Robotics

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There has always been an increasing interest in the space related activities. The research on aerospace vehicles have become popular due to the problems and complexity of the systems involved. The main challenge lies in keeping a balance when in motion and hence tracking plays a key role here. The satellite system discussed in this paper is described for the problem arising due to presence of disturbances (colored and white noise). This model is evinced by the augmentation of discrete Kalman filter, a powerful tool for controlling the noisy estimates. Whereas, the regulation of the state dynamics (Euler angles and velocity) is achieved with the adaptive law which focuses on guaranteeing stability of adaptive control scheme using a good choice of Lyapunov argument. The presence of Gaussian White noise is also mentioned where a comparison resembles stability for almost, mean square, third moment and mean value between the satellite and oscillator system. A clear discussion of the system in the presence of colored and white noise with perfect estimates derived from kalman filter and an adaptation law governing the evolution of system around equilibrium is done.

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“…Substitution of linear kinematic theory conducts the relationship as below in Eqs. (12)(13)(14). Also, Fig.…”

Section: Satellite Systemmentioning

confidence: 86%

“…The stability criteria for white noise excitation. From top to bottom: almost sure stability, stability in mean, mean square and third moment stability for oscillator system[13].…”

mentioning

confidence: 99%

Adaptive Control of Satellite System using Kalman Estimates in the presence of Disturbance

Dube¹,

Patel²

2019

International Conference of Control, Dynamic Systems, and Robotics

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“…Nevertheless, most of the literatures took white Gaussian noise for grant, although noise correlation is common in cortical firing activities, only a few (Averbeck et al 2006;Guo 2011;Sakai et al1999) paid attention to the "color" of noise but far from enough. Therefore, in this paper we investigate the effect of (Orenstein-Ulunbeck type) Gaussian colored noise (Floris 2015;Wang and Wu 2016) of nonzero correlation time on the aperiodic stochastic resonance. As a starting point, we will generalize the existing perturbation results (Freidlin and Wentzell 2012) of nonlinear dynamical systems from Gaussian white noise to Gaussian colored noise.…”

Section: Introductionmentioning

confidence: 99%

Aperiodic stochastic resonance in neural information processing with Gaussian colored noise

2020

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The aim of this paper is to explore the phenomenon of aperiodic stochastic resonance in neural systems with colored noise. For nonlinear dynamical systems driven by Gaussian colored noise, we prove that the stochastic sample trajectory can converge to the corresponding deterministic trajectory as noise intensity tends to zero in mean square, under global and local Lipschitz conditions, respectively. Then, following forbidden interval theorem we predict the phenomenon of aperiodic stochastic resonance in bistable and excitable neural systems. Two neuron models are further used to verify the theoretical prediction.Moreover, we disclose the phenomenon of aperiodic stochastic resonance induced by correlation time and this finding suggests that adjusting noise correlation might be a biologically more plausible mechanism in neural signal processing.

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A microbial growth kinetics model driven by hybrid stochastic colored noises in the water environment

Dong

et al. 2016

Stoch Environ Res Risk Assess

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Mean square stability of a second-order parametric linear system excited by a colored Gaussian noise

Cited by 14 publications

References 57 publications

Adaptive Control of Satellite System using Kalman Estimates in the presence of Disturbance

Adaptive Control of Satellite System using Kalman Estimates in the presence of Disturbance

Aperiodic stochastic resonance in neural information processing with Gaussian colored noise

A microbial growth kinetics model driven by hybrid stochastic colored noises in the water environment

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