Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
Brief paper: Gradient dynamic optimization with Legendre chaos
Automatica (Journal of IFAC)
Linear quadratic regulation of systems with stochastic parameter uncertainties
Automatica (Journal of IFAC)
Uncertainty propagation using polynomial chaos and centre manifold theories
ISPRA'10 Proceedings of the 9th WSEAS international conference on Signal processing, robotics and automation
WSEAS TRANSACTIONS on SYSTEMS
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The polynomial chaos of Wiener provides a framework for the statistical analysis of dynamical systems, with computational cost far superior to Monte Carlo simulations. It is a useful tool for control systems analysis because it allows probabilistic description of the effects of uncertainty, especially in systems having nonlinearities and where other techniques, such as Lyapunov's method, may fail. We show that stability of a system can be inferred from the evolution of modal amplitudes, covering nearly the full support of the uncertain parameters with a finite series. By casting uncertain parameters as unknown gains, we show that the separation of stochastic from deterministic elements in the response points to fast iterative design methods for nonlinear control.