Averaging and Deterministic Optimal Control

François Chaplais (1)

1 CAS - Centre Automatique et Systèmes

Averaging is often used in ordinary differential equations when dealing with fast periodic phenomena. It is shown here that it can be used efficiently in optimal control. As the period tends to zero, a limit or "averaged" problem is defined. The open loop optimal control of the limit problem induces a cost which is optimal up to the second order when evaluated through the original dynamics. The definition of the averaged problem is then generalized to the nonperiodic case. It is shown that the Bellman function of the original "fast" problem tends uniformly on any compact set to that of the averaged problem.

Domaines: Automatique / Robotique

François Chaplais. Averaging and Deterministic Optimal Control. SIAM Journal on Control and Optimization, 1986, 25 (3), pp.767-780. ⟨10.1137/0325044⟩. ⟨hal-00654159⟩