6,791 research outputs found
Controller Synthesis for Discrete-Time Polynomial Systems via Occupation Measures
In this paper, we design nonlinear state feedback controllers for
discrete-time polynomial dynamical systems via the occupation measure approach.
We propose the discrete-time controlled Liouville equation, and use it to
formulate the controller synthesis problem as an infinite-dimensional linear
programming problem on measures, which is then relaxed as finite-dimensional
semidefinite programming problems on moments of measures and their duals on
sums-of-squares polynomials. Nonlinear controllers can be extracted from the
solutions to the relaxed problems. The advantage of the occupation measure
approach is that we solve convex problems instead of generally non-convex
problems, and the computational complexity is polynomial in the state and input
dimensions, and hence the approach is more scalable. In addition, we show that
the approach can be applied to over-approximating the backward reachable set of
discrete-time autonomous polynomial systems and the controllable set of
discrete-time polynomial systems under known state feedback control laws. We
illustrate our approach on several dynamical systems
Determination of Bootstrap confidence intervals on sensitivity indices obtained by polynomial chaos expansion
Lâanalyse de sensibilitĂ© a pour but dâĂ©valuer lâinfluence de la variabilitĂ© dâun ou plusieurs paramĂštres dâentrĂ©e dâun modĂšle sur la variabilitĂ© dâune ou plusieurs rĂ©ponses. Parmi toutes les mĂ©thodes dâapproximations, le dĂ©veloppement sur une base de chaos polynĂŽmial est une des plus efficace pour le calcul des indices de sensibilitĂ©, car ils sont obtenus analytiquement grĂące aux coefficients de la dĂ©composition (Sudret (2008)). Les indices sont donc approximĂ©s et il est difficile dâĂ©valuer lâerreur due Ă cette approximation. Afin dâĂ©valuer la confiance que lâon peut leur accorder nous proposons de construire des intervalles de confiance par rĂ©-Ă©chantillonnage Bootstrap (Efron, Tibshirani (1993)) sur le plan dâexpĂ©rience utilisĂ© pour construire lâapproximation par chaos polynĂŽmial. Lâutilisation de ces intervalles de confiance permet de trouver un plan dâexpĂ©rience optimal garantissant le calcul des indices de sensibilitĂ© avec une prĂ©cision donnĂ©e
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