A class of infinite horizon optimal control problems involving nonsmooth cost functionals is discussed. The existence of optimal controls is studied for both the convex case and the nonconvex case, and the sparsity structure of the optimal controls promoted by the nonsmooth penalties is analyzed. A dynamic programming approach is proposed to numerically approximate the corresponding sparse optimal controllers.
['Dante Kalise', 'Karl Kunisch', 'Zhiping Rao']
Infinite Horizon Sparse Optimal Control