ABSTRACT
This chapter discusses a dynamical system governed by a specific equation. A set of linear operators is provided in the Hilbert spaces. The usual regulator problem in infinite horizon consists in minimizing a quadratic functional of a specific form. The chapter also discusses two approaches to solve the usual regulator problem: periodic control and ergodic control. The periodic control consists in looking for periodic solutions and in minimizing the cost along a period. Instead in ergodic control, one introduces a discount factor in the cost. The chapter presents some new results about the relationship between periodic and ergodic control problems.
