Averaged observations and turnpike phenomenon for parameter-dependent systems

TL;DR

This paper proves the turnpike property for parameter-dependent systems with averaged observations, showing that optimal controls and states converge to stationary solutions and are exponentially close over time.

Contribution

It establishes the integral and exponential turnpike property for systems with averaged observations, extending previous results to parameter-dependent dynamics.

Findings

Optimal control and state converge in average to stationary solutions.

Over large time intervals, solutions are exponentially close.

Turnpike property holds under suitable matrix assumptions.

Abstract

Our main contribution in this article is the achievement of the turnpike property in its integral and exponential forms for parameter-dependent systems with averaged observations in the cost functional. Namely, under suitable assumptions with respect to the matrices that defined the dynamics and the cost functional, we prove that the optimal control and state for the evolutionary problem converge in average to the optimal pair of an associated stationary problem. Moreover, we characterize the closeness between these two optimal solutions, proving that over a large time interval, they are exponentially close.