Sparse and Switching Infinite Horizon Optimal Control with Mixed-Norm Penalizations

TL;DR

This paper studies infinite horizon optimal control problems with mixed quasi-norm costs that promote sparse and switching controls, analyzing their properties and providing a numerical solution approach.

Contribution

It introduces a novel class of control problems with mixed quasi-norm costs, analyzing their optimality conditions and developing a dynamic programming method for solutions.

Findings

Optimal controls exhibit sparsity and switching behavior.

Existence and structural properties of optimal controls are established.

A dynamic programming approach enables numerical realization.

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.