Safe and Efficient Switching Mechanism Design for Uncertified Linear Controller

Abstract: 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.