Guaranteed cost structured control in infinite-horizon linear-quadratic cooperative differential games
arXiv:2605.13103
The paper studies infinite‑horizon linear‑quadratic cooperative differential games with output‑feedback, introducing feedback guaranteed‑cost structured control (GCSC) to ensure the team cost stays below a set threshold while respecting structural constraints.
Abstract
In this paper, we consider the infinite-horizon linear-quadratic cooperative differential games with output feedback information structure. We first show that computing Pareto optimal controls under output feedback is difficult even for low-dimensional games. To address this, we introduce the concept of feedback guaranteed cost structured control (GCSC). At a feedback GCSC, the total weighted team cost remains below a prescribed threshold while satisfying the structural constraint. We derive monotonicity properties of the feedback GCSC set and the admissible weight set, respectively. Further, we show that Pareto optimal controls (if they exist) belong to the class of feedback GCSCs. We provide performance measures of the Pareto optimal controls and the proposed GCSC relative to the output feedback optimal control. We also establish verification and synthesis conditions for a feedback GCSC using linear matrix inequalities, where the synthesis formulation is convex and requires no semi-definite programming relaxation. Finally, we illustrate the effectiveness of the proposed approach through numerical examples, including a microgrid tracking synchronization case study.
This extended version was accepted for the 65th IEEE Conference on Decision and Control (CDC 2026)