  Methods based on polynomial chaos expansion allow to approximate the behavior
of systems with uncertain parameters by deterministic dynamics. These methods
are used in a wide range of applications, spanning from simulation of uncertain
systems to estimation and control. For practical purposes the exploited
spectral series expansion is typically truncated to allow for efficient
computation, which leads to approximation errors. Despite the Hilbert space
nature of polynomial chaos, there are only a few results in the literature that
explicitly discuss and quantify these approximation errors. This work derives
error bounds for polynomial chaos approximations of polynomial and
non-polynomial mappings. Sufficient conditions are established, which allow
investigating the question whether zero truncation errors can be achieved and
which series order is required to achieve this. Furthermore, convex quadratic
programs, whose argmin operator is a special case of a piecewise polynomial
mapping, are studied due to their relevance in predictive control. Several
simulation examples illustrate our findings.
