UNCLASSIFIED
Faculty of Aerospace Engineering
Technion – Israel Institute of Technology, Haifa
ON DEFENSE FROM
RANDOMLY MANEUVERING
BALLISTIC MISSILES
Josef Shinar
Faculty of Aerospace Engineering,
Technion, Israel Institute of Technology, Haifa, Israel
Israel Multinational Ballistic Missile Defense Conference
May 5-6, 2010
UNCLASSIFIED
Faculty of Aerospace Engineering
Technion – Israel Institute of Technology, Haifa
OUTLINE
• INTRODUCTION
• “NATURAL” RV MANEUVERS
• INTERCEPTING MANEUVERING TARGETS
• GUIDANCE AGAINST PERIODICAL MANEUVERS
– PERIODICAL ESTIMATOR
– OPTIMAL CONTROL BASED GUIDANCE LAW
– DIFFERENTIAL GAME BASED GUIDANCE LAW
• ROBUST INTEGRATED ESTIMATOR/GUIDANCE
• CONCLUSIONS
UNCLASSIFIED
Faculty of Aerospace Engineering
Technion – Israel Institute of Technology, Haifa
INTRODUCTION
• The term “maneuvering ballistic missile” seems as an oxymoron
• Recently, the Ballistic Missile Defense community has accepted
that the last stage of a Tactical Ballistic Missile (TBM) can be
an eventually maneuvering reentry vehicle (RV)
• Research on future BMD scenarios involving maneuvering
targets have been carried out at Technion/AE since 1992
– Innovative paradigm developed for integrated design of
estimator/guidance-law
– Validation of the new design paradigm, via simulation of
generic (but realistic 3D nonlinear) MD scenarios
UNCLASSIFIED
Faculty of Aerospace Engineering
Technion – Israel Institute of Technology, Haifa
Ballistic Missile Defense
against maneuvering targets
• Existing Tactical Ballistic Missiles were not designed
to maneuver
• Due to their high reentry velocity their
maneuverability potential (below 30 km altitude) can
be used with a modest technical effort
• Two types of aerodynamic maneuvers can be
envisaged:
- spiral maneuvers due to spinning atmospheric
reentry or/and due to asymmetries
- intentionally controlled random maneuvers
UNCLASSIFIED
Faculty of Aerospace Engineering
Technion – Israel Institute of Technology, Haifa
UNINTENTIONAL RV MANEUVERING
• Unintentional (“natural”) aerodynamical maneuvering can be
obtained either during the atmospheric reentry of a spinning
(stable) RV or as a consequence of asymmetries
• Three types of asymmetries are considered:
– Mass asymmetry (center of gravity shift from the longitudinal axis)
– Aerodynamic asymmetry (existence of parasitic pitching, yawing and
rolling moments)
– Inertia asymmetry (i.e. inclination between the principle inertia axes and
the body reference axes)
• The damage due to hit of fragments on the RV body can also
create significant asymmetries of unpredictable magnitude,
including eventual loss of stability
UNCLASSIFIED
Faculty of Aerospace Engineering
Technion – Israel Institute of Technology, Haifa
INTERCEPTING MANEUVERING TARGETS
• For intercepting maneuvering targets their acceleration has to
be known
• Target acceleration cannot be measured; It has to be
estimated from available measurements
• Interception can be optimized in two different formulations:
– Optimal control needs future maneuver time history;
not suitable against random maneuvers
– Differential game formulation needs only current target
acceleration
• The main difference is in the expression of the target
contribution to the zero effort miss distance (ZEM)
UNCLASSIFIED
Faculty of Aerospace Engineering
Technion – Israel Institute of Technology, Haifa
HOMING AGAINST PERIODICAL MANEUVERS
• Uncontrolled aerodynamical maneuvers have the feature
of spiral motion motivating to use, for analysis and
simulations, a pure periodical model
• Assuming that the maneuver frequency is known, an
optimal control based guidance law was developed
• This guidance law requires the knowledge of the current
target acceleration and its derivative
• This information is obtained by a Kalman Filter type
estimator with a periodical model using the (assumed)
maneuver frequency
• Inaccurate assumption on the maneuvering frequency
leads to homing performance deterioration
UNCLASSIFIED
Faculty of Aerospace Engineering
Technion – Israel Institute of Technology, Haifa
HOMING AGAINST PERIODIC MANEUVERS/2
• The homing performance of an optimal control based (OGL/W)
and a differential game based (DGL/1) guidance law in a noise
corrupted scenario against a target, performing a pure
periodical maneuver with random phase, is compared
• Both guidance laws use the same periodical estimator “tuned”
to the same frequency wf
• The actual target maneuver frequency w is unknown
• Homing performance, as a function of wf, is compared by the
average miss distance of 500 Monte Carlo runs
• The optimal control based guidance law is very sensitive to the
frequency error |w-wf|
• DGL/1 is robust with respect to the frequency error
UNCLASSIFIED
Faculty of Aerospace Engineering
Technion – Israel Institute of Technology, Haifa
UNINTENTIONALLY MANEUVERING RV
• Thorough studies showed that the "natural" maneuver of a
spinning RV is very complex
• Neither the frequency nor the amplitude of such "natural"
maneuver is fixed
• The same is true for maneuvers created by structural
asymmetries
• Optimal control based guidance laws, requiring to know
the exact maneuver profile, cannot guarantee robust
defense against RVs performing “natural” maneuvers
UNCLASSIFIED
Faculty of Aerospace Engineering
Technion – Israel Institute of Technology, Haifa
DEFENSE AGAINST
RANDOMLY MANEUVERING TARGETS
Integrated Estimation/Guidance approach
 Differential Game based Guidance Law
 Kalman filter with a shaping filter, representing
random target maneuvers
Differential Game based Guidance Law
 Interceptor guidance modeled as a perfect
information pursuit-evasion game
 Needs to know only current target acceleration
Graph
UNCLASSIFIED
Faculty of Aerospace Engineering
Technion – Israel Institute of Technology, Haifa
DIFFERENTIAL GAME BASED GUIDANCE
• Two basic formulations
– LQDG
• The classical guidance cost function is
tf
1 2
1
J = Z (t f ) + ò [a u 2 (t ) - bv 2 (t )]dt
2
2
t0
• The LQDG formulation may not have a solution
(conjugate point).
– Linear game with bounded controls
• The solution always exists
UNCLASSIFIED
Faculty of Aerospace Engineering
Technion – Israel Institute of Technology, Haifa
DIFFERENTIAL GAME BASED GUIDANCE/2
• Linear game with bounded controls may have different models
– Ideal missile and target model, Gutman & Leitmann
(1976); DGL/I
– First-order missile vs. ideal target, Gutman (1979); DGL/0
– First-order missile and target, Shinar (1981); DGL/1
Solution structure
• Decomposition of the game space is into two regions
– In the regular region: the strategy is ”bang-bang”
• The miss distance depends on the initial conditions
– In the singular region: the strategy is arbitrary
• The miss distance is constant.
UNCLASSIFIED
Faculty of Aerospace Engineering
Technion – Israel Institute of Technology, Haifa
DIFFERENTIAL GAME BASED GUIDANCE/4
• Guidance law options in the singular region:
– “Bang-bang” strategy
• advantage: a single strategy everywhere
• disadvantage: “control chattering” for most cases
– Time varying linear strategy subject to saturation;
• advantage: a smooth strategy
• disadvantage: noisy input may drive the state out of
the singular zone creating increased miss distances
UNCLASSIFIED
Faculty of Aerospace Engineering
Technion – Israel Institute of Technology, Haifa
DIFFERENTIAL GAME BASED GUIDANCE/5
• Q: Why these guidance laws, derived 29 years ago, have not
yet been implemented?
– There was no particular need for innovation. Classical
guidance laws, with maneuverability advantage of 3 and
more, were satisfactory
– The implementation of these perfect information guidance
laws in a noisy environment requires a complex integration
scheme including estimation
– The chattering control creates implementation problems
• Conservative mind setting of the guided missile community
UNCLASSIFIED
Faculty of Aerospace Engineering
Technion – Israel Institute of Technology, Haifa
DIFFERENTIAL GAME BASED GUIDANCE
IS APPLICABLE NOW
• There is a need. The challenging task of intercepting randomly
maneuvering ballistic RVs cannot be solved otherwise
• The conceptual solution (integrated estimation/guidance) was
Graph
developed and validated at a university research level
• Only software modification is required for applying the
integrated estimation/guidance algorithm in a currently
developing interceptor
• Alleviation of chattering control problems is feasible without
deteriorating homing performance
• Conservative mind setting of the guided missile community
may (hopefully) change
UNCLASSIFIED
Faculty of Aerospace Engineering
Technion – Israel Institute of Technology, Haifa
CONCLUSIONS
The result of multi-year university research
• A robust interceptor guidance strategy against
randomly maneuvering ballistic RVs is now feasible
• The strategy consists of the following elements:
– A differential game based guidance law
– An integrated multiple model estimation/guidance
algorithm
– Alleviation of the control chattering phenomenon
• The implementation of this strategy in an interceptor
system requires only software modifications