Behavioral Feedback for Optimal LQG Control

TL;DR

This paper presents a behavioral reformulation of the LQG control problem, deriving a static feedback solution that simplifies computation and enhances data-driven control from demonstrations.

Contribution

It introduces a behavioral perspective to LQG control, deriving a static feedback form and demonstrating its advantages for data-driven learning.

Findings

Optimal LQG controller can be expressed as a static behavioral-feedback gain.

The static form allows for gradient descent-based computation.

The approach benefits learning from expert demonstrations.

Abstract

In this work, we revisit the Linear Quadratic Gaussian (LQG) optimal control problem from a behavioral perspective. Motivated by the suitability of behavioral models for data-driven control, we begin with a reformulation of the LQG problem in the space of input-output behaviors and obtain a complete characterization of the optimal solutions. In particular, we show that the optimal LQG controller can be expressed as a static behavioral-feedback gain, thereby eliminating the need for dynamic state estimation characteristic of state space methods. The static form of the optimal LQG gain also makes it amenable to its computation by gradient descent, which we investigate via numerical experiments. Furthermore, we highlight the advantage of this approach in the data-driven control setting of learning the optimal LQG controller from expert demonstrations.