Infinite horizon sparse optimal control

A class of infinite horizon optimal control problems involving Lp-type cost functionals with 0<p≤ 1 is discussed. The existence of optimal controls is studied for both the convex case with p=1 and the nonconvex case with 0<p<1, and the sparsity structure of the optimal controls promoted by the Lp-type penalties is analyzed. A dynamic programming approach is proposed to numerically approximate the corresponding sparse optimal controllers.