Application of polynomial chaos in stability and control

DOI10.1016/j.automatica.2006.01.010zbMath1110.93052OpenAlexW2169982942MaRDI QIDQ875980

Michael S. Triantafyllou, Franz S. Hover

Publication date: 16 April 2007

Published in: Automatica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.automatica.2006.01.010

zbMATH Keywords

polynomial chaoscontrol applications

Mathematics Subject Classification ID

Related Items (19)

The stochastic linear quadratic optimal control problem in Hilbert spaces: a polynomial chaos approach ⋮ A novel model predictive controller for uncertain constrained systems ⋮ Optimal Control of Uncertain Systems Using Sample Average Approximations ⋮ Adaptive weighted least-squares polynomial chaos expansion with basis adaptivity and sequential adaptive sampling ⋮ Polynomial chaos-based \(\mathcal{H}_2\) output-feedback control of systems with probabilistic parametric uncertainties ⋮ A polynomial chaos approach to the robust analysis of the dynamic behaviour of friction systems ⋮ Design of linear parameter varying quadratic regulator in polynomial chaos framework ⋮ Model order reduction of random parameter-dependent linear systems ⋮ Spectral representation of stochastic field data using sparse polynomial chaos expansions ⋮ Region of attraction analysis of nonlinear stochastic systems using polynomial chaos expansion ⋮ A note on polynomial chaos expansions for designing a linear feedback control for nonlinear systems ⋮ Gradient dynamic optimization with Legendre chaos ⋮ Stochastic finite element technique for stochastic one-dimensional time-dependent differential equations with random coefficients ⋮ Consistent numerical methods for state and control constrained trajectory optimisation with parameter dependency ⋮ Linear quadratic regulation of systems with stochastic parameter uncertainties ⋮ Convergence Analysis and Adaptive Order Selection for the Polynomial Chaos Approach to Direct Optimal Control under Uncertainties ⋮ A new non-intrusive polynomial chaos using higher order sensitivities ⋮ Numerical Trajectory Optimization for Stochastic Mechanical Systems ⋮ Generalised polynomial chaos expansion approaches to approximate stochastic model predictive control^†

Cites Work

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• The orthogonal development of non-linear functionals in series of Fourier-Hermite functionals
• Generalized polynomial chaos and random oscillators
• The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations

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