Approximation of Cumulative Distribution Functions Based on L_∞and L₁ Norms for Stochastic Systems Control

Abstract

This paper studies approximation of probabilistic distributions behind discrete-time linear systems with stochastic dynamics for advances in control of the systems. We discuss two approximation methods leading to optimal discrete distributions whose errors from the probabilistic distribution behind the system are minimal in the sense of the L_∞ and L₁ norms of the differences between associated cumulative distribution functions. The effectiveness of those approximation methods is demonstrated with numerical examples, in which the methods are compared with another simple method of constructing discrete distributions based on random sampling.