A characteristic function framework for chance constraint programming in stochastic model predictive control

TL;DR

This paper introduces a novel computational framework using characteristic functions to efficiently compute chance constraints in stochastic model predictive control with non-Gaussian disturbances.

Contribution

It presents a numerical inversion method leveraging characteristic functions, enabling direct probability and gradient computation for arbitrary non-Gaussian disturbances within an optimization framework.

Findings

Framework successfully computes chance constraints for non-Gaussian disturbances.

Implementation within YALMIP facilitates easy specification of disturbance distributions.

Numerical example demonstrates the method's effectiveness in stochastic control applications.

Abstract

The computation of chance constraints in stochastic model predictive control is often numerically challenging due to the non-Gaussian nature of the disturbances. To overcome this problem, we propose an optimization computational framework applicable to non-Gaussian disturbances. This framework employs a numerical inversion method, utilizing the characteristic function of the disturbance distribution to compute the probability in the chance constraint as well as its gradient. To improve efficiency, it vectorizes integral points and reuses intermediate computations in Gauss-Kronrod quadrature. The framework is implemented within the YALMIP toolbox to perform chance constraint calculations for arbitrary non-Gaussian disturbances, applicable to both single-component distributions and mixture models. It allows the user to simply specify a distribution type and its parameters for the disturbance and directly compute the probability and its gradient to solve the optimization problem. The method is validated through a numerical example of a stochastic model predictive control application.