Safety assessment for stochastic linear systems using enclosing hulls of probability density functions

This contribution addresses the problem of computing the probability that a linear system with uncertain inputs reaches an unsafe region in the state space. The probability of reaching unsafe states is bounded by an upper limit, by intersecting enclosing hulls of the probability density function for time intervals with the specified unsafe regions. Disturbances are modeled as white Gaussian noise, whose mean is modeled as uncertain within specified sets. This allows to consider white non-Gaussian noise in an over-approximative manner. The presented approach is efficient in the sense that high-dimensional systems can be handled.