On the Convergence of the Iterative Linear Exponential Quadratic Gaussian Algorithm to Stationary Points

TL;DR

This paper analyzes the convergence properties of the iterative linear exponential quadratic Gaussian algorithm used in risk-sensitive nonlinear control, revealing the objective it minimizes and how proximal terms ensure convergence to stationary points.

Contribution

It provides the first convergence analysis of the algorithm from an optimization perspective, identifying the objective and the role of proximal terms.

Findings

The algorithm minimizes a specific objective function.

Adding a proximal term guarantees convergence to stationary points.

The analysis offers insights into the algorithm's stability and convergence behavior.

Abstract

A classical method for risk-sensitive nonlinear control is the iterative linear exponential quadratic Gaussian algorithm. We present its convergence analysis from a first-order optimization viewpoint. We identify the objective that the algorithm actually minimizes and we show how the addition of a proximal term guarantees convergence to a stationary point.