Sparsity of Linear Discrete-Time Optimal Control Problems with $l-1$ Objectives

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This paper explores optimal control problems with l1 objectives involving linear discrete-time systems. These problems can be efficiently solved as linear programs. They also have previously been shown to yield sparse solutions, including idle or deadbeat solutions where the input or output is respectively zero along the entire control horizon. The main contribution of this paper is to derive conditions on the problem parameters that specify when idle or deadbeat solutions occur. These results, based on analyzing the dual problem, demonstrate how different types of sparse solutions result from the choice of the problem parameters and, as a consequence, may guide the design of controllers employing l1 objectives.

Original languageEnglish (US)
Article number7993042
Pages (from-to)513-517
Number of pages5
JournalIEEE Transactions on Automatic Control
Issue number2
StatePublished - Feb 2018


  • Duality
  • l objectives
  • linear programming
  • optimal control
  • sparsity

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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