Stable Online Control of Linear Time-Varying Systems
This work addresses a central challenge in control theory for real-world dynamical systems, offering a practical solution for applications like power systems, though it appears incremental as it builds on existing LQ control frameworks.
The paper tackles the problem of ensuring stability for linear time-varying systems in online control settings, where existing methods often lead to high control costs, and proposes the COCO-LQ algorithm that guarantees input-to-state stability while minimizing control cost, with empirical validation in synthetic and power system experiments.
Linear time-varying (LTV) systems are widely used for modeling real-world dynamical systems due to their generality and simplicity. Providing stability guarantees for LTV systems is one of the central problems in control theory. However, existing approaches that guarantee stability typically lead to significantly sub-optimal cumulative control cost in online settings where only current or short-term system information is available. In this work, we propose an efficient online control algorithm, COvariance Constrained Online Linear Quadratic (COCO-LQ) control, that guarantees input-to-state stability for a large class of LTV systems while also minimizing the control cost. The proposed method incorporates a state covariance constraint into the semi-definite programming (SDP) formulation of the LQ optimal controller. We empirically demonstrate the performance of COCO-LQ in both synthetic experiments and a power system frequency control example.