# Nonlinear Uncertainty Control with Iterative Covariance Steering

## TL;DR

This paper introduces an iterative covariance steering (iCS) method for controlling nonlinear stochastic systems to reach a desired state distribution while satisfying probabilistic constraints, demonstrated on a noisy double integrator.

## Contribution

The paper presents a novel iterative approach for nonlinear uncertainty control that linearizes the problem and solves it as a convex program, enabling effective distribution steering.

## Key findings

- Successfully controls a nonlinear system with probabilistic constraints.
- Demonstrates effectiveness on a double integrator with quadratic drag.
- Provides a practical iterative algorithm for nonlinear stochastic control.

## Abstract

This paper considers the problem of steering the state distribution of a nonlinear stochastic system from an initial Gaussian to a terminal distribution with a specified mean and covariance, subject to probabilistic path constraints. An algorithm is developed to solve this problem by iteratively solving an approximate linearized problem as a convex program. This method, which we call iterative covariance steering (iCS), is numerically demonstrated by controlling a double integrator with quadratic drag force subject to additive Brownian noise while satisfying probabilistic path constraints.