Uncertainty Propagation in Stochastic Systems via Mixture Models with Error Quantification
CoRR(2024)
摘要
Uncertainty propagation in non-linear dynamical systems has become a key
problem in various fields including control theory and machine learning. In
this work we focus on discrete-time non-linear stochastic dynamical systems. We
present a novel approach to approximate the distribution of the system over a
given finite time horizon with a mixture of distributions. The key novelty of
our approach is that it not only provides tractable approximations for the
distribution of a non-linear stochastic system, but also comes with formal
guarantees of correctness. In particular, we consider the total variation (TV)
distance to quantify the distance between two distributions and derive an upper
bound on the TV between the distribution of the original system and the
approximating mixture distribution derived with our framework. We show that in
various cases of interest, including in the case of Gaussian noise, the
resulting bound can be efficiently computed in closed form. This allows us to
quantify the correctness of the approximation and to optimize the parameters of
the resulting mixture distribution to minimize such distance. The effectiveness
of our approach is illustrated on several benchmarks from the control
community.
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