The Linear-Quadratic Regulation (LQR) problem with unknown system parameters has been widely studied, but it has remained unclear whether $\tilde{ \mathcal{O}}(\sqrt{T})$ regret, which is the best known dependence on time, can be achieved almost surely. In this paper, we propose an adaptive LQR controller with almost surely $\tilde{ \mathcal{O}}(\sqrt{T})$ regret upper bound. The controller features a circuit-breaking mechanism, which circumvents potential safety breach and guarantees the convergence of the system parameter estimate, but is shown to be triggered only finitely often and hence has 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.

翻译：具有未知系统参数的线性二次型调节(LQR)问题已被广泛研究，但能否几乎必然实现时间依赖最优的$\tilde{ \mathcal{O}}(\sqrt{T})$遗憾界尚不明确。本文提出一种自适应LQR控制器，其遗憾上界几乎必然为$\tilde{ \mathcal{O}}(\sqrt{T})$。该控制器采用断路机制，既能规避潜在的安全风险、保证系统参数估计的收敛性，又经证明该机制仅被有限次触发，因此对控制器的渐近性能影响可忽略。通过工业过程常用示例——田纳西-伊斯曼过程(TEP)的仿真实验验证了所提控制器的有效性。