Symbolic Controller Synthesis for Discrete and Timed Systems
Hybrid Systems II
Symbolic Model Checking of Biochemical Networks
CMSB '03 Proceedings of the First International Workshop on Computational Methods in Systems Biology
Modeling uncertainty in flow simulations via generalized polynomial chaos
Journal of Computational Physics
Hybrid Systems: Computation and Control: 7th International Workshop, Hscc 2004, Philadelphia, Pa, Usa, March 2004: Proceedings (Lecture Notes in Computer Science, 2993)
An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
Journal of Computational Physics
Beyond Wiener---Askey Expansions: Handling Arbitrary PDFs
Journal of Scientific Computing
Journal of Computational Physics
Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems
Journal of Computational Physics
Polynomial stochastic hybrid systems
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Orthogonal functionals of the Poisson process
IEEE Transactions on Information Theory
Uncertainty quantification in kinematic-wave models
Journal of Computational Physics
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Uncertainty quantification (UQ) techniques are frequently used to ascertain output variability in systems with parametric uncertainty. Traditional algorithms for UQ are either system-agnostic and slow (such as Monte Carlo) or fast with stringent assumptions on smoothness (such as polynomial chaos and Quasi-Monte Carlo). In this work, we develop a fast UQ approach for hybrid dynamical systems by extending the polynomial chaos methodology to these systems. To capture discontinuities, we use a wavelet-based Wiener-Haar expansion. We develop a boundary layer approach to propagate uncertainty through separable reset conditions. We also introduce a transport theory based approach for propagating uncertainty through hybrid dynamical systems. Here the expansion yields a set of hyperbolic equations that are solved by integrating along characteristics. The solution of the partial differential equation along the characteristics allows one to quantify uncertainty in hybrid or switching dynamical systems. The above methods are demonstrated on example problems.