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We propose a safe approximation to joint chance-constrained programming wherethe constraint functions are additively dependent on a normally-distributedrandom vector. The approximation is analytical, meaning that it requiresneither numerical integrations nor sampling-based probability approximations.Under mild assumptions, the approximation is a standard nonlinear program. Wecompare this new safe approximation to another analytical safe approximationfor joint chance-constrained programming based on Boole's inequality throughtwo examples representing the constrained control of linear Gaussian-Markovmodels. It is shown that our proposed safe approximation has a lower degree ofconservatism compared to the one based on Boole's inequality.

An analytical safe approximation to joint chance-constrained programming with additive Gaussian noises