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

## TL;DR

This paper introduces an analytical safe approximation for joint chance-constrained programming with Gaussian noises, offering a less conservative alternative to existing methods without requiring numerical sampling.

## Contribution

The paper presents a novel analytical safe approximation method for joint chance constraints with Gaussian noise, improving over previous approaches by reducing conservatism.

## Key findings

- The new approximation is less conservative than Boole's inequality-based methods.
- It is formulated as a standard nonlinear program under mild assumptions.
- The approach is validated through control of linear Gaussian-Markov models.

## Abstract

We propose a safe approximation to joint chance-constrained programming where the constraint functions are additively dependent on a normally-distributed random vector. The approximation is analytical, meaning that it requires neither numerical integrations nor sampling-based probability approximations. Under mild assumptions, the approximation is a standard nonlinear program. We compare this new safe approximation to another analytical safe approximation for joint chance-constrained programming based on Boole's inequality through two examples representing the constrained control of linear Gaussian-Markov models. It is shown that our proposed safe approximation has a lower degree of conservatism compared to the one based on Boole's inequality.