Risk-Aware Linear-Quadratic Regulation with Temporally Coupled States

TL;DR

This paper introduces a risk-aware finite-horizon LQR framework that penalizes both temporal and stochastic variability of the state trajectory, allowing for explicit risk sensitivity and improved control performance.

Contribution

It extends predictive variance to temporally coupled states in LQR, enabling explicit risk-aware regulation balancing state regulation and variability reduction.

Findings

Penalizing temporal variability can reduce stochastic variability.

Explicit risk sensitivity influences control strategies.

Temporal coupling impacts risk-aware control outcomes.

Abstract

We formulate and solve a discrete-time linear-quadratic regulation (LQR) problem in a finite horizon that penalizes temporal variability and stochastic variability of the state trajectory. Our approach enables the user to strike a balance between regulating the state and reducing temporal variability, with explicit sensitivity to risk. We achieve this by extending a risk measure called predictive variance to a setting with temporally coupled states. Numerical examples demonstrate the effect of temporal coupling in both risk-aware and risk-neutral control settings. Particularly, we observe that explicitly penalizing temporal variability alone can also reduce stochastic variability.