Sparse and Switching Infinite Horizon Optimal Control with Mixed-Norm Penalizations
For researchers in optimal control, this work provides a theoretical framework for incorporating sparsity and switching into infinite horizon problems, though it is incremental as it extends known mixed-norm techniques to a new setting.
This paper addresses infinite horizon optimal control problems with mixed-norm cost functionals to promote sparsity and switching in controls. It proves existence and structural properties of optimal controls via first-order conditions and uses dynamic programming for numerical realization.
A class of infinite horizon optimal control problems involving mixed quasi-norms of $L^p$-type cost functionals for the controls is discussed. These functionals enhance sparsity and switching properties of the optimal controls. The existence of optimal controls and their structural properties are analyzed on the basis of first order optimality conditions. A dynamic programming approach is used for numerical realization.