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Stability analysis of stochastic systems using polynomial chaos

James Robert Fisher · Raktim Bhattacharya

50 citations0/0 files storedProceedings of the ... American Control Conference/Proceedings of the American Control Conference

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Probabilistic and Robust Engineering Design Stability and Control of Uncertain Systems Control Systems and Identification

Abstract

A novel framework for stability analysis of linear and polynomial stochastic systems is presented. The framework is built on generalized polynomial chaos theory, which enables analysis of dynamical systems with probabilistic uncertainty on system parameters with various distributions. The theory allows for the transformation of stochastic problems into a higher dimensional deterministic problem, that is able to accurately approximate the evolution of uncertainty in the state trajectories due to stochastic system parameters. The developed theory is applied to analyze a linear flight control design for an F-16 aircraft model. The problem of generating stability certificates for stochastic polynomial systems is also considered.

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References

1991Stochastic Finite Elements: A Spectral Approach 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations 2003Modeling uncertainty in flow simulations via generalized polynomial chaos 1999Ingredients for a general purpose stochastic finite elements implementation 2006Wiener Chaos expansions and numerical solutions of randomly forced equations of fluid mechanics 1999Propagation of probabilistic uncertainty in complex physical systems using a stochastic finite element approach 2006Application of polynomial chaos in stability and control

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2013Stochastic study of a non-linear self-excited system with friction 2012Non-intrusive generalized polynomial chaos for the robust stability analysis of uncertain nonlinear dynamic friction systems 2011A polynomial chaos approach to the robust analysis of the dynamic behaviour of friction systems 2013Wiener's Polynomial Chaos for the Analysis and Control of Nonlinear Dynamical Systems with Probabilistic Uncertainties 2010Distributional uncertainty analysis using polynomial chaos expansions 2012

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