Closure to “Discussions of ‘On the Almost Sure Stability of Linear Dynamic Systems With Stochastic Coefficients’” (1966, ASME J. Appl. Mech., 33, pp. 234–236)

1966 ◽  
Vol 33 (1) ◽  
pp. 236-236
Author(s):  
T. K. Caughey ◽  
A. H. Gray
Keyword(s):  
Dynamic Systems ◽  
Almost Sure Stability ◽  
Linear Dynamic Systems ◽  
Linear Dynamic

On the Almost Sure Stability of Linear Dynamic Systems With Stochastic Coefficients

1965 ◽  
Vol 32 (2) ◽  
pp. 365-372 ◽  
Author(s):  
T. K. Caughey ◽  
A. H. Gray
Keyword(s):  
Nonlinear System ◽  
Dynamic Systems ◽  
Sufficient Conditions ◽  
Forced Oscillations ◽  
Almost Sure Stability ◽  
Linear Dynamic Systems ◽  
Linear Dynamic

In this paper a Lyapunov type of approach is used to obtain sufficient conditions guaranteeing the almost sure stability of linear dynamic systems with stochastic coefficients. The results are generalized to include a certain class of nonlinear system and also to guarantee the almost sure boundedness of the forced oscillations of linear dynamic systems with stochastic coefficients.

scholarly journals On the Uncertainty Identification for Linear Dynamic Systems Using Stochastic Embedding Approach with Gaussian Mixture Models

Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3837
Author(s):  
Rafael Orellana ◽  
Rodrigo Carvajal ◽  
Pedro Escárate ◽  
Juan C. Agüero
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Dynamic Systems ◽  
Gaussian Mixture ◽  
Error Model ◽  
Fault Detection And Diagnosis ◽  
Deterministic Models ◽  
Linear Dynamic Systems ◽  
Linear Dynamic

In control and monitoring of manufacturing processes, it is key to understand model uncertainty in order to achieve the required levels of consistency, quality, and economy, among others. In aerospace applications, models need to be very precise and able to describe the entire dynamics of an aircraft. In addition, the complexity of modern real systems has turned deterministic models impractical, since they cannot adequately represent the behavior of disturbances in sensors and actuators, and tool and machine wear, to name a few. Thus, it is necessary to deal with model uncertainties in the dynamics of the plant by incorporating a stochastic behavior. These uncertainties could also affect the effectiveness of fault diagnosis methodologies used to increment the safety and reliability in real-world systems. Determining suitable dynamic system models of real processes is essential to obtain effective process control strategies and accurate fault detection and diagnosis methodologies that deliver good performance. In this paper, a maximum likelihood estimation algorithm for the uncertainty modeling in linear dynamic systems is developed utilizing a stochastic embedding approach. In this approach, system uncertainties are accounted for as a stochastic error term in a transfer function. In this paper, we model the error-model probability density function as a finite Gaussian mixture model. For the estimation of the nominal model and the probability density function of the parameters of the error-model, we develop an iterative algorithm based on the Expectation-Maximization algorithm using the data from independent experiments. The benefits of our proposal are illustrated via numerical simulations.

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