Solution to the HJB Equation for LQR-Type Problems on Compact Connected Lie Groups

In this paper, we provide a solution to the HJB equation associated with LQR-type problems for fully-actuated left-invariant control systems on compact connected Lie groups. We obtain the corresponding algebraic/differential Riccati equation and in turn generalize some of the results in to a broader class of Lie groups. Closed-loop stability results are also derived.