Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Complete Differential Game of Active Target Defense   In the Target-Attacker-Defender (TAD) differential game, an Attacker missile
strives to capture a Target aircraft. The Target tries to escape the Attacker
and is aided by a Defender missile which aims at intercepting the Attacker
before the latter manages to close in on the Target. The conflict between these
intelligent adversaries has been suitably modeled as a zero-sum differential
game. Optimal strategies have been synthesized covering the region of the state
space where the Target/Defender team is able to win the game. However, the Game
of Degree in the Attacker's region of win has not been fully addressed.
Preliminary attempts at designing the players' strategies have not been proven
to be optimal in the differential game sense. The main results of the paper
present the optimal strategies of the Game of Degree in the Attacker's winning
region of the state space. It is proven that the obtained strategies provide
the saddle-point solution of the game; the Value function is obtained and it is
shown to be continuous and continuously differentiable. It is also demonstrated
that it is the solution of the Hamilton-Jacobi-Isaacs (HJI) equation. Finally,
the obtained strategies are compared to recent results addressing the TAD
differential game in [22]. It is shown by counterexample that the strategies
proposed in [22] are not optimal. The unique regular solution of this
differential game that actually provides a semipermeable Barrier surface is
synthesized and verified in this paper.

23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph