Theory and Modern Applications
Table 5 Summary of the items regarding control
From: Mean-field optimal control in a multi-agent interaction model for prevention of maritime crime
Item | Meaning | Comment |
|---|---|---|
\(\mathcal{U}\subset \mathbb{R}^{2 {\times }L}\) | set of admissible controls | compact |
\(H^{\mathrm{d}}\) | kernel for dangerous contacts in cost functional | bounded and Lipschitz continuous |
\(\mathcal{J}_{N,M}\) | cost functional associated to (3.2), for fixed N,M | defined in (3.3) |
\(\mathcal{J}_{N}\) | cost functional defined in (7.16), for fixed N | obtained as the Γ-limit of \(\mathcal{J}_{N,M}\) as M→ + ∞ in Theorem 7.3 |
\(\mathcal{J}\) | cost functional defined in (8.58) | obtained as the Γ-limit of \(\mathcal{J}_{N}\) as N→ + ∞ in Theorem 8.6 |