Turnpike properties for partially uncontrollable systems. (March 2023)

• Record Type: Journal Article
• Authors: Gugat, Martin; Lazar, Martin
• Is Part Of: Automatica. Volume 149(2023)
• Publication Date: 2023-03
• Subjects: Turnpike phenomenon -- Optimal averaged control -- Infinite-time admissibility -- Infinite-dimensional systems -- Optimization under uncertainties; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2022.110844
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: We analyse the turnpike properties for a general, infinite dimensional, linear–quadratic (LQ) optimal control problem, in both the deterministic and the parameter dependent case. The novelty of the paper is twofold. Firstly, it obtains positive turnpike results for systems that are (partially) uncontrollable. Secondly, it provides turnpike results for optimal averaged control associated to a family of problems that depend on a random parameter, which is the first turnpike type result that extends the averaged controllability approach to optimal control problems In both cases, the results do not require assumptions on stabilizability and detectability, which are most commonly used in the study of turnpike phenomena.