论文标题
未经认证的线性控制器的安全有效的开关机制设计
Safe and Efficient Switching Mechanism Design for Uncertified Linear Controller
论文作者
论文摘要
持续的研究工作已致力于学习具有未知参数的线性随机动力学系统的最佳控制器，但是由于噪声的损坏，学到的控制器通常未经认证，因为它们可能会破坏该系统的稳定。为了解决这种潜在的不稳定，我们向未认证的控制器提出了“插件”修改，当未认证的和倒下后的控制输入之间的差异范围超过一定阈值时，该修改将落回已知的稳定控制器。我们表明，从某种意义上说，开关策略既安全有效，又是有效的：1）即使原始未经认证的控制器不稳定，系统的线性季节成本也总是有限的； 2）如果未经认证的控制器正在稳定，则高斯噪声的切换造成的性能损失将超级指数收敛至$ 0 $，而对于一般的重尾噪声而言，多发融合。最后，我们通过田纳西伊士曼进程的数值模拟来证明拟议的切换策略的有效性。
Sustained research efforts have been devoted to learning optimal controllers for linear stochastic dynamical systems with unknown parameters, but due to the corruption of noise, learned controllers are usually uncertified in the sense that they may destabilize the system. To address this potential instability, we propose a "plug-and-play" modification to the uncertified controller which falls back to a known stabilizing controller when the norm of the difference between the uncertified and the fall-back control input exceeds a certain threshold. We show that the switching strategy is both safe and efficient, in the sense that: 1) the linear-quadratic cost of the system is always bounded even if original uncertified controller is destabilizing; 2) in case the uncertified controller is stabilizing, the performance loss caused by switching converges super-exponentially to $0$ for Gaussian noise, while the converging polynomially for general heavy-tailed noise. Finally, we demonstrate the effectiveness of the proposed switching strategy via numerical simulation on the Tennessee Eastman Process.
