Pontryagin maximum principle for the deterministic mean field type optimal control problem via the Lagrangian approach

• DOI: 10.48550/arxiv.2207.01892
• Publication Date: 2022-01-01
• Authors: Yurii Averboukh; Dmitry Khlopin
• Keywords: Maximum principle; Pontryagin's minimum principle; Hamiltonian (control theory)

We study the necessary optimality conditions for general deterministic mean field type free-endpoint optimal control problem. Our relies on Lagrangian approach that treats system as a crowd of infinitely many agents who are labeled by elements some probability space. Within framework approach, we derive Pontryagin maximum principle. In particular, it implies costate variables also Furthermore, consider Kantorovich and Eulerian formalizations those describe via distribution set trajectories nonlocal continuity equation respectively. prove each local minimizer in or formulation corresponds to within approach. Using this, deduce principle forms. To illustrate theory, examine model linear quadratic regulator. For this system, show strategy is determined feedback.