Optimal periodic control: The π test revisited

The paper examines second-order conditions for both steady-state and dynamic optimality in a periodic control problem. It centers on the π condition of Bittanti, Fronza, and Guardabassi [2] and has three main objectives: 1) to form a π "test" for a somewhat more general problem than considered in [2]; 2) to point out that certain auxiliary conditions must be added if the results of [2] are to be valid; and 3) to explore more fully the relationships between second-order conditions for steady-state optimality and second-order conditions for optimality in the dynamic problem.