Ergodic Optimal Quadratic Control for an Affine Equation with Stochastic and Stationary Coefficients

TL;DR

This paper investigates ergodic quadratic optimal control for affine stochastic systems with stationary coefficients, providing a full characterization of the optimal cost and control under stationarity assumptions.

Contribution

It offers a comprehensive analysis of ergodic control for affine stochastic systems with stationary coefficients, linking ergodic and stationary control problems.

Findings

Optimal cost coincides with stationary control problem cost

Full characterization of ergodic optimal cost and control

Stationarity assumption is crucial for analysis

Abstract

We study ergodic quadratic optimal stochastic control problems for an affine state equation with state and control dependent noise and with stochastic coefficients. We assume stationarity of the coefficients and a finite cost condition. We first treat the stationary case and we show that the optimal cost corresponding to this ergodic control problem coincides with the one corresponding to a suitable stationary control problem and we provide a full characterization of the ergodic optimal cost and control.