  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.
