Inferring System and Optimal Control Parameters of Closed-Loop Systems from Partial Observations

TL;DR

This paper develops probabilistic inference methods to identify system and control parameters in partially observed stochastic LQ systems, addressing non-identifiability issues and improving recovery with additional measurements or finite horizons.

Contribution

It introduces novel inference techniques for joint system identification and inverse control in partially observed stochastic LQ systems, highlighting non-identifiability and solutions.

Findings

Non-identifiability in infinite-horizon settings from closed-loop data.

Enhanced parameter recovery using partial control signal measurements.

Finite-horizon setting improves identifiability and estimation accuracy.

Abstract

We consider the joint problem of system identification and inverse optimal control for discrete-time stochastic Linear Quadratic Regulators. We analyze finite and infinite time horizons in a partially observed setting, where the state is observed noisily. To recover closed-loop system parameters, we develop inference methods based on probabilistic state-space model (SSM) techniques. First, we show that the system parameters exhibit non-identifiability in the infinite-horizon from closed-loop measurements, and we provide exact and numerical methods to disentangle the parameters. Second, to improve parameter identifiability, we show that we can further enhance recovery by either (1) incorporating additional partial measurements of the control signals or (2) moving to the finite-horizon setting. We further illustrate the performance of our methodology through numerical examples.