Linear Differential Game With Two Pursuers and One Evader

11000
10000
9000
8000
7000
Distance [m]
6000
5000
4000
3000
2000
1000
0
0 2 4 6 8 10 12
τ go
[s]
Figure 5 : NEZ extension in 2x1 game
Figure 6 characterizes the saturations that apply in the evader optimal controls. Outside the 2x1
capture zone (always still considering E between the two pursuers) three different end games can
happen:
If z
1 f
= 0 and z
2 f
= 0 then the initial conditions belong to the 2x1 no-escape-zone.
If z
if
≠ 0 and z1 f
= z2
f
then the initial conditions belong to the 2x1 non-saturate zone (area in red in
Figure 6).
If z
if
≠ 0 and z1 f
≠ z2
f
then the initial conditions belong to the 2x1 saturate zone (case
corresponding to the “trade off” evader controls overcoming the control bounds).
12000
10000
8000
ZEM [m]
6000
4000
2000
0
0 1 2 3 4 5 6 7 8 9 10
τ go
[s]
Figure 6 : Evader control saturation
*
This new limit, as well as the zone of v
2x1
saturation, have been investigated in linear and non-linear
simulations in order to confirm the computation of τ
2x1. Up to now, the 2x1 game trajectories (Figure
3, Figure 5, Figure 6) have been plotted on a single ( ZEM , τ
go
) representation. Figure 7 represents
ZEM , τ go
, ΔP1P2
. On the left side delimited by the
the barrier of the 2x1 game in the state space ( )
red surface P2 intercepts E. On the right part (delimited by the blue surface) E is captured by P1. The
capture zone extension due to the presence of two pursuers is depicted by green and purple lines.
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