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.

我们在确定性和参数相关情况下分析了一般无限维线性二次 (LQ) 最优控制问题的收费公路属性。这篇论文的新颖性是双重的。首先，对于（部分）不可控的系统，它获得了积极的收费公路结果。其次，它提供了与取决于随机参数的一系列问题相关的最优平均控制的收费公路结果，这是第一个将平均可控性方法扩展到最优控制问题的收费公路类型结果。在这两种情况下，结果都不需要假设关于稳定性和可检测性，它们最常用于收费公路现象的研究。