Trajectory-Shape-Varying Missile Guidance for Interception of Ballistic Missiles during the Boost Phase

The paper presents a near-optimal guidance law that has been developed using the direct method of calculus of variations. By the direct access to controlling the shape of the trajectory, this guidance law seeks to maximize the kinetic energy transfer upon interception from a surface launched medium range interceptor missile to a ballistic missile target during the boost phase of flight. Mathematical models of a two-stage liquid-fueled medium-range ballistic missile and a velocity-limited endoatmospheric interceptor missile with onboard active radar guidance are used to demonstrate the guidance law’s performance. This law will utilize the interceptor's onboard computer and active radar sensors to independently predict an intercept point, solve the two-point boundary-value problem, and determine the best feasible flight path to that point. While determining a truly optimal flight path would require significant computing power and therefore cannot be realized online, the proposed nearoptimal flight path can be calculated onboard the interceptor in fractions of a second and updated in multiple times during the intercept without significant technological advancements in the interceptor’s onboard hardware. That near-optimal guidance path is then converted into a set of command functions and fed back into the control system of the interceptor. By modifying just a few parameters affecting the higher-order derivatives at the intercept point, the optimization algorithm varies the shape of a three-dimensional trajectory over a wide range without compromising the constraints on controls or jeopardizing satisfaction of the final conditions. An example features the guidance solution for probably the most difficult scenario of maximizing kinetic energy upon impact by forcing it to occur at a right angle.

[1]  Joseph Z. Ben-Asher,et al.  Optimal Guidance with Reduced Sensitivity to Time-to-Go Estimation Errors , 1997 .

[2]  George M Siouris,et al.  Missile Guidance and Control Systems , 2004 .

[3]  Ernest J. Ohlmeyer,et al.  Control of terminal engagement geometry using generalized vector explicit guidance , 2003, Proceedings of the 2003 American Control Conference, 2003..

[4]  Antonios Tsourdos,et al.  Differential Geometric Guidance Based on the Involute of the Target's Trajectory , 2005 .

[5]  John H. Blakelock,et al.  Automatic control of aircraft and missiles , 1965 .

[6]  Andrey V. Savkin,et al.  Circular Navigation Missile Guidance with Incomplete Information and Uncertain Autopilot Model , 2003 .

[7]  Eugene L. Fleeman.  Tactical Missile Design , 2001 .

[8]  N. A. Shneydor,et al.  Missile guidance and pursuit , 1998 .

[9]  Arthur Gelb,et al.  Applied Optimal Estimation , 1974 .

[10]  Leo C. George.  Missile Guidance and Control System Design Trends , 1974 .

[11]  Andrey V. Savkin,et al.  Circular navigation guidance law for precision missile/target engagements , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[12]  Peter H. Zipfel,et al.  Modeling and Simulation of Aerospace Vehicle Dynamics , 2001 .

[13]  Taek Lyul Song,et al.  Impact angle control for planar engagements , 1999 .

[14]  Ching-Fang Lin,et al.  Linearized kappa guidance , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[15]  Antonios Tsourdos,et al.  Direct Intercept Guidance using Differential Geometry Concepts , 2005 .

[16]  Chen-Yuan Kuo,et al.  Geometric analysis of missile guidance command , 2000 .

[17]  A. Carter,et al.  Ballistic Missile Defense , 1984 .

[18]  Joseph Z. Ben-Asher,et al.  Advances in Missile Guidance Theory , 1998 .

[19]  Chen-Yuan Kuo,et al.  GEOMETRIC APPROACH TO THREE-DIMENSIONAL MISSILE GUIDANCE PROBLEM , 1998 .

[20]  C. Lin,et al.  Analytical solution of optimal trajectory-shaping guidance , 1987 .

[21]  Ching-Fang Lin,et al.  Modern Navigation, Guidance, And Control Processing , 1991 .

[22]  Paul Zarchan,et al.  Ballistic missile defense guidance and control issues , 1999 .

[23]  Arthur E. Bryson,et al.  Applied Optimal Control , 1969 .

[24]  Naira Hovakimyan,et al.  Coordinated Path Following for Time-Critical Missions of Multiple UAVs via L1 Adaptive Output Feedback Controllers , 2007 .

[25]  Ching-Fang Lin,et al.  Linearized kappa guidance , 1995 .

[26]  Oleg A. Yakimenko.  Direct method for real-time prototyping of optimal control , 2006 .

[27]  O. Yakimenko.  Direct Method for Rapid Prototyping of Near-Optimal Aircraft Trajectories , 2000 .

[28]  I. Yaesh,et al.  Optimum guidance with a single uncertain time lag , 1995 .

[29]  Ching-Fang Lin,et al.  Three dimensional mid-course guidance state equations , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[30]  Vincent C. Lam.  Acceleration-Compensated Zero-Effort-Miss Guidance Law , 2006 .

[31]  Vincent Lam.  Time-to-Go Estimate for Missile Guidance , 2005 .

[32]  Didik Soetanto,et al.  Geometric analysis of flight control command for tactical missile guidance , 2001, IEEE Trans. Control. Syst. Technol..

[33]  San Jose,et al.  Theatre Ballistic Missile Defense-Multisensor Fusion, Targeting and Tracking Techniques , 1998 .

[34]  Robert M. Soofer.  Ballistic Missile Defense from the Sea , 1994 .

[35]  Andrey V. Savkin,et al.  The problem of precision missile guidance: LQR and H ∞ control frameworks , 2001 .

[36]  Oleg A. Yakimenko,et al.  Trajectory-Shaping Guidance for Interception of Ballistic Missiles During the Boost Phase , 2008 .

[37]  Michael J. Hemsch.  Tactical missile aerodynamics : general topics , 1992 .

[38]  Ernest J. Ohlmeyer,et al.  Generalized Vector Explicit Guidance , 2006 .

[39]  Jang Gyu Lee,et al.  Biased PNG law for impact with angular constraint , 1998 .

[40]  William L. Brogan.  Applied Optimal Estimation (Arthur Gels, ed.) , 1977 .

[41]  Florios Bardanis.  Kill Vehicle Effectiveness for Boost Phase Interception of Ballistic Missiles , 2004 .

[42]  Taek Lyul Song,et al.  Time-optimal impact angle control for vertical plane engagements , 1999 .

[43]  G. Cherry,et al.  A general, explicit, optimizing guidance law for rocket-propelled spaceflight , 1964 .

[44]  M. Kim,et al.  Terminal Guidance for Impact Attitude Angle Constrained Flight Trajectories , 1973, IEEE Transactions on Aerospace and Electronic Systems.

[45]  Joseph Z. Ben-Asher,et al.  TRAJECTORY SHAPING AND TERMINAL GUIDANCE USING LINEAR QUADRATIC DIFFERENTIAL GAMES , 2002 .