outfitting and pre-positioning theater ballistic missile
TRANSCRIPT
![Page 1: Outfitting and Pre-positioning Theater Ballistic Missile](https://reader031.vdocuments.us/reader031/viewer/2022012502/617c727bb89d9f57c20dc47f/html5/thumbnails/1.jpg)
Outfitting and Pre-positioning Theater Ballistic Missile Defense AEGIS Battle Groups to Meet an
Exigent Threat of Attack
Gerald Brown
Kevin Wood
Naval Postgraduate School
![Page 2: Outfitting and Pre-positioning Theater Ballistic Missile](https://reader031.vdocuments.us/reader031/viewer/2022012502/617c727bb89d9f57c20dc47f/html5/thumbnails/2.jpg)
The Problem
• Weapons of Mass Destruction:
• intercontinental ballistic missiles developed by rogue states
![Page 3: Outfitting and Pre-positioning Theater Ballistic Missile](https://reader031.vdocuments.us/reader031/viewer/2022012502/617c727bb89d9f57c20dc47f/html5/thumbnails/3.jpg)
The Problem
• New threats from rogue states
![Page 4: Outfitting and Pre-positioning Theater Ballistic Missile](https://reader031.vdocuments.us/reader031/viewer/2022012502/617c727bb89d9f57c20dc47f/html5/thumbnails/4.jpg)
A Solution
• Anti-Ballistic Missile Defenses
![Page 5: Outfitting and Pre-positioning Theater Ballistic Missile](https://reader031.vdocuments.us/reader031/viewer/2022012502/617c727bb89d9f57c20dc47f/html5/thumbnails/5.jpg)
A Solution
• Anti-Ballistic Missile Defenses
• Multiple-tier defense
• Air Force, Army, and Navy programs
![Page 6: Outfitting and Pre-positioning Theater Ballistic Missile](https://reader031.vdocuments.us/reader031/viewer/2022012502/617c727bb89d9f57c20dc47f/html5/thumbnails/6.jpg)
A Navy Solution
• AEGIS Ships re-fitted to carry and launch a variety of anti-missile missiles
![Page 7: Outfitting and Pre-positioning Theater Ballistic Missile](https://reader031.vdocuments.us/reader031/viewer/2022012502/617c727bb89d9f57c20dc47f/html5/thumbnails/7.jpg)
A Navy Solution
• AEGIS can be pre-positioned advantageously
North Korea
South Korea
![Page 8: Outfitting and Pre-positioning Theater Ballistic Missile](https://reader031.vdocuments.us/reader031/viewer/2022012502/617c727bb89d9f57c20dc47f/html5/thumbnails/8.jpg)
Aegis Platform
![Page 9: Outfitting and Pre-positioning Theater Ballistic Missile](https://reader031.vdocuments.us/reader031/viewer/2022012502/617c727bb89d9f57c20dc47f/html5/thumbnails/9.jpg)
Aegis Platform
•
![Page 10: Outfitting and Pre-positioning Theater Ballistic Missile](https://reader031.vdocuments.us/reader031/viewer/2022012502/617c727bb89d9f57c20dc47f/html5/thumbnails/10.jpg)
The Navy AEGIS Problem
• How do outfit and pre-position a limited number of AEGIS platforms to meet an exigent threat
![Page 11: Outfitting and Pre-positioning Theater Ballistic Missile](https://reader031.vdocuments.us/reader031/viewer/2022012502/617c727bb89d9f57c20dc47f/html5/thumbnails/11.jpg)
The Navy AEGIS Problem
• We may have multiple AEGIS defenders
North Korea
South Korea
![Page 12: Outfitting and Pre-positioning Theater Ballistic Missile](https://reader031.vdocuments.us/reader031/viewer/2022012502/617c727bb89d9f57c20dc47f/html5/thumbnails/12.jpg)
![Page 13: Outfitting and Pre-positioning Theater Ballistic Missile](https://reader031.vdocuments.us/reader031/viewer/2022012502/617c727bb89d9f57c20dc47f/html5/thumbnails/13.jpg)
The Navy AEGIS Problem
• Intercept during boost phase is best
• Intercept during ascent phase is also feasible
• After this, other layers of defense take over
![Page 14: Outfitting and Pre-positioning Theater Ballistic Missile](https://reader031.vdocuments.us/reader031/viewer/2022012502/617c727bb89d9f57c20dc47f/html5/thumbnails/14.jpg)
![Page 15: Outfitting and Pre-positioning Theater Ballistic Missile](https://reader031.vdocuments.us/reader031/viewer/2022012502/617c727bb89d9f57c20dc47f/html5/thumbnails/15.jpg)
Analysis
• Engagement cycle is very short – a minute or two
• Geographic proximity is important
• Each AEGIS will carry just a few interceptors
• More than one interceptor variant may be carried
![Page 16: Outfitting and Pre-positioning Theater Ballistic Missile](https://reader031.vdocuments.us/reader031/viewer/2022012502/617c727bb89d9f57c20dc47f/html5/thumbnails/16.jpg)
Analysis
• A rogue attack will likely be a single salvo
• The salvo will consist of just a few, or perhaps just a single ICBM
![Page 17: Outfitting and Pre-positioning Theater Ballistic Missile](https://reader031.vdocuments.us/reader031/viewer/2022012502/617c727bb89d9f57c20dc47f/html5/thumbnails/17.jpg)
Analysis
• Source of attack salvo is a small geographic area
• Physics limits boost and and ascent phase track to threatened targets
![Page 18: Outfitting and Pre-positioning Theater Ballistic Missile](https://reader031.vdocuments.us/reader031/viewer/2022012502/617c727bb89d9f57c20dc47f/html5/thumbnails/18.jpg)
Analysis
• Neither attacking ICBM’s, nor defending interceptors work perfectly
• The probability of a successful attack is a function of the attacking ICBM(s), what is attacked in the salvo, and the joint effect of interceptors launched
![Page 19: Outfitting and Pre-positioning Theater Ballistic Missile](https://reader031.vdocuments.us/reader031/viewer/2022012502/617c727bb89d9f57c20dc47f/html5/thumbnails/19.jpg)
Analysis
• The probability of an attack succeeding despite a defense interception is not an independent function of each constituent event
• A reasonable, conservative assumption is that each AEGIS platform will control its own engagement
![Page 20: Outfitting and Pre-positioning Theater Ballistic Missile](https://reader031.vdocuments.us/reader031/viewer/2022012502/617c727bb89d9f57c20dc47f/html5/thumbnails/20.jpg)
A Notional Decision Model
• The attacker wants to maximize expected target damage
• The defender wants to minimize expected target damage
![Page 21: Outfitting and Pre-positioning Theater Ballistic Missile](https://reader031.vdocuments.us/reader031/viewer/2022012502/617c727bb89d9f57c20dc47f/html5/thumbnails/21.jpg)
A Notional Model
• We seek defense actions (an intercept) that minimizes the attacker’s maximum damage
• We assume that the attacker knows what we know - where we are, and what we’ll intercept with – and that the attacker will optimize his salvo with this knowledge
![Page 22: Outfitting and Pre-positioning Theater Ballistic Missile](https://reader031.vdocuments.us/reader031/viewer/2022012502/617c727bb89d9f57c20dc47f/html5/thumbnails/22.jpg)
An Attack
• Consists of an ICBM launched at a vulnerable target with expected damage
• Multiple ICBM types allowed
• Each ICBM type limited in number
![Page 23: Outfitting and Pre-positioning Theater Ballistic Missile](https://reader031.vdocuments.us/reader031/viewer/2022012502/617c727bb89d9f57c20dc47f/html5/thumbnails/23.jpg)
A Defensive Action
• Each ICBM intercept option involves a salvo of interceptors varying in number and type
• Each AEGIS platform may be pre-positioned at some defendable ocean station
• Each AEGIS platform may be outfitted with a variety of missile type loadouts
![Page 24: Outfitting and Pre-positioning Theater Ballistic Missile](https://reader031.vdocuments.us/reader031/viewer/2022012502/617c727bb89d9f57c20dc47f/html5/thumbnails/24.jpg)
A Defensive Action
• ICBM intercept probability computed for entire salvo as a single event
• At most one option can be launched at each ICBM
• Simultaneous engagements by an AEGIS platform may be limited
![Page 25: Outfitting and Pre-positioning Theater Ballistic Missile](https://reader031.vdocuments.us/reader031/viewer/2022012502/617c727bb89d9f57c20dc47f/html5/thumbnails/25.jpg)
An Optimization Model
|
|
max 1 (1 )
. . [ ]
1 [ ]
0
a
a
a
a
a t d d aY
a d D
a m ma m m
a ta t t
a
k v X Y
s t Y s m M
Y t T
Y a A
δ
α
β
∈
=
=
− −
≤ ∀ ∈
≤ ∀ ∈ ≥ ∀ ∈
∑ ∑
∑
∑
![Page 26: Outfitting and Pre-positioning Theater Ballistic Missile](https://reader031.vdocuments.us/reader031/viewer/2022012502/617c727bb89d9f57c20dc47f/html5/thumbnails/26.jpg)
A Defensive Action
• Where to place each AEGIS defender?
• How to outfit each AEGIS defender?
• Against an ICBM salvo, which AEGIS defender(s) should engage each ICBM?
![Page 27: Outfitting and Pre-positioning Theater Ballistic Missile](https://reader031.vdocuments.us/reader031/viewer/2022012502/617c727bb89d9f57c20dc47f/html5/thumbnails/27.jpg)
An Optimizaton Model
|
|
max 1 (1 )
. . [ ]min
1 [ ]
0
a
a
a
a
a t d d aY
a d D
a m ma m mX
a ta t t
a
k v X Y
s t Y s m M
Y t T
Y a A
δ
α
β
∈
=∈Χ
=
− −
≤ ∀ ∈
≤ ∀ ∈ ≥ ∀ ∈
∑ ∑
∑
∑
![Page 28: Outfitting and Pre-positioning Theater Ballistic Missile](https://reader031.vdocuments.us/reader031/viewer/2022012502/617c727bb89d9f57c20dc47f/html5/thumbnails/28.jpg)
Restrictions on AEGIS Actions1
,
1
1
,
,
{0,1}
{0,1} ,
{0,1} ,
{0,1,2,...} ,
a
dd D
d dgg
dg gld
glg
gll
di dg igd
ig ig i
ig ig
d
gi
dg
ig
i
X a A
X R d D
R Z d D g G
Z l L
Z g G
n R F i I g G
X F SLACK fmax i I g G
F s i I
X d D
Z g G i I
R d D g G
F i I g G
fmax - f
∈
≤ ∀ ∈
≤ ∀ ∈
≤ ∀ ∈ ∈
≤ ∀ ∈
≤ ∀ ∈
≤ ∀ ∈ ∈
∈ Χ = + = ∀ ∈ ∈
≤ ∀ ∈
∈ ∀ ∈∈ ∀ ∈ ∈
∈ ∀ ∈ ∈
∈ ∀ ∈ ∈
∑
∑
∑
∑
∑
∑
0 ,i igmin SLACK i I g G
≥ ≥ ∀ ∈ ∈
![Page 29: Outfitting and Pre-positioning Theater Ballistic Missile](https://reader031.vdocuments.us/reader031/viewer/2022012502/617c727bb89d9f57c20dc47f/html5/thumbnails/29.jpg)
An Optimization Model
, ,
,
min
. .
1
0
0
{0,1}
a a a a
a
a
a
m m tX
m M t T
m t d a t d a td D
dd D
di d ia A d D
m
t
d
s
s t p k v X k v a A
X a A
n X b i I
m M
t T
X d D
α βα β
α β
αβ
∈Χ∈ ∈
∈
∈
∈ ∈
+
+ + ≥ ∀ ∈
≤ ∀ ∈
≤ ∀ ∈
≥ ∀ ∈≥ ∀ ∈
∈ ∀ ∈
∑ ∑
∑
∑
∑
![Page 30: Outfitting and Pre-positioning Theater Ballistic Missile](https://reader031.vdocuments.us/reader031/viewer/2022012502/617c727bb89d9f57c20dc47f/html5/thumbnails/30.jpg)
An Optimization Model
• We prefer Benders Decomposition– isolate the ICBM attack subproblem
– from our defensive action master problem
• This permits the defensive action to influence any feature in the attacker’s problem
![Page 31: Outfitting and Pre-positioning Theater Ballistic Missile](https://reader031.vdocuments.us/reader031/viewer/2022012502/617c727bb89d9f57c20dc47f/html5/thumbnails/31.jpg)
Instance
• 8 ICBM’s in a single salvo
• 5 Aegis platforms
• 20 Candidate Ocean Stations
• 2 Interceptor types
• 25 Interceptors available
![Page 32: Outfitting and Pre-positioning Theater Ballistic Missile](https://reader031.vdocuments.us/reader031/viewer/2022012502/617c727bb89d9f57c20dc47f/html5/thumbnails/32.jpg)
Conclusion
• Optimization offers a key tool to investigate what to develop, how to outfit, and where to deploy
• To defend from any ICBM attack scenario