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.
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