Almost Surely √T Regret for Adaptive LQR

• 成果类型: Article
• 署名作者: Lu, Yiwen; Mo, Yilin
• 署名单位: Tsinghua University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3535997
• 发表日期: 2025
• 页码: 5145-5159
• 关键词: convergence; switches; noise; COSTS; Closed loop systems; Upper bound; vectors; Symmetric matrices; stability analysis; safety; Adaptive control; almost sure convergence; linear quadratic regulator; Switched systems; Regret Analysis

摘要

The linear-quadratic regulation (LQR) problem with unknown system parameters has been widely studied, but it has remained unclear whether O-similar to(root T) regret, which is the best known dependence on time, can be achieved almost surely. In this article, we propose an adaptive LQR controller with almost surely O-similar to(root T) regret upper bound. The controller features a circuit-breaking mechanism, which falls back to a known stabilizing controller when the input signal or control gain is large, thereby circumventing potential safety breach and ensuring the convergence of the system parameter estimate. Meanwhile, the circuit-breaking is shown to be triggered only finitely often, and hence has a negligible effect on the asymptotic performance of the controller. The proposed controller is also validated via simulation on Tennessee Eastman process (TEP), a commonly used industrial process example.