Sparse and switching infinite horizon optimal controls with mixed-norm penalizations

¹ School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2QL, UK.
² Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstraße 36, 8010 Graz, Austria.
³ Radon Institute of Computational and Applied Mathematics, Austrian Academy of Sciences, A-4040 Linz, Austria.
⁴ School of Mathematics and Statistics, and Hubei Key Laboratory of Computational Sciences, Wuhan University, Wuhan 430072, Hubei, PR China.

^* Corresponding author: dante.kalise@nottingham.ac.uk

Received: 31 August 2018
Accepted: 5 June 2019

Abstract

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.