# A probabilistic framework for the control of systems with discrete states and stochastic excitation

## TL;DR

This paper introduces a probabilistic framework for optimizing control strategies in systems with discrete states and stochastic inputs, enabling flexible control rules and broad applicability to stochastic systems.

## Contribution

It presents a novel probabilistic approach replacing state trajectories with probability distributions for control optimization, applicable to mixed-variable stochastic systems.

## Key findings

- Framework effectively handles hysteresis and mixed variables.
- Applicable to atmospheric balloon control and other stochastic systems.
- Enables new classes of control rules.

## Abstract

A probabilistic framework is proposed for the optimization of efficient switched control strategies for physical systems dominated by stochastic excitation. In this framework, the equation for the state trajectory is replaced with an equivalent equation for its probability distribution function in the constrained optimization setting. This allows for a large class of control rules to be considered, including hysteresis and a mix of continuous and discrete random variables. The problem of steering atmospheric balloons within a stratified flowfield is a motivating application; the same approach can be extended to a variety of mixed-variable stochastic systems and to new classes of control rules.