Almost periodic turnpike phenomenon for time-dependent systems

Abstract

This paper examines the turnpike behavior of a controlled system with almost periodic inputs and a cost functional that includes an almost periodic tracking term and periodic observations. Roughly speaking, we establish that the optimal state–control pair for the controlled system remains exponentially close to the optimal pair of an almost periodic problem for a substantial portion of the time during which the control system evolves. Our approach heavily relies on a thorough investigation of differential Riccati equations, periodic differential Riccati equations, and almost periodic functions.