UNCLASSIFIED Faculty of Aerospace Engineering Technion Israel

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 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 3 D 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 ü Differential Game based Guidance Law ü Kalman filter with a shaping filter, representing random target maneuvers Differential Game based Guidance Law ü Interceptor guidance modeled as a perfect information pursuit-evasion game ü 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 • 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 Engineering Technion – Israel Institute of Technology, Haifa Aerospace 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