S. Zamorano (2024)Almost periodic turnpike phenomenon for time-dependent systems
Abstract. This paper explores the turnpike behavior of a controlled system with almost periodic inputs and a cost functional based on almost periodic tracking term and periodic observation. Roughly speaking, we establish that the optimal state-control pair for the controlled system is exponentially close to the optimal pair of an almost periodic problem for a significant portion of the time during which the control system evolves. Our approach heavily relies on the thorough investigation of both differential Riccati equations, periodic differential Riccati equations and almost periodic functions.