Missile Guidance


This course presents both fundamental concepts and practical implementation of parallel navigation. It dedicated to missile guidance. The guidance law design is considered from the point of view of control theory, i.e., as design of controls guiding missiles to hit targets. Guidance laws design is considered as design of controls. The design procedure is presented in the time-domain and in the frequency-domain. The different approaches, in the time and frequency domain, generate different guidance laws that supplement each other. The proportional navigation is considered also as a control problem.

A wider class of guidance laws is obtained based on Lyapunov approach. The analytical expressions of the guidance law are given for the generalized planar and three-dimensional engagement models for missiles with and without axial controlled acceleration. The Lyapunov-Bellman approach is used to justify the choice of some guidance law parameters.

The problem of the integrated design of guidance and control laws is discussed. The problem of modification of the existing autopilots is presented as a problem of new guidance laws design. Computational aspects of missile guidance are considered. As an example, the application of the theory to design of the boost-phase interceptors is considered.

The course is based on a book Modern Missile Guidance (Taylor & Francis, London, New York, 2007) by R. Yanushevsky A complete set of lecture notes will be prepared.

What you will learn:

  • About various types of missiles and related problems
  • Where the most promising international research is being performed.
  • Guidance laws design as a control problem.
  • Theoretical aspects and computational algorithms.
  • Example of guidance laws for the new generation of interceptors.

Course Outline:

  1. Introduction Various types of missiles. Current research efforts
  2. Basics of Missile Guidance. Parallel NavigationRepresentation of Motion. Guidance Process. Parallel Navigation. Proportional Navigation. Augmented Proportional Navigation. Planar engagement. Three-dimensional engagement.
  3. Analysis of PN Guided Missile Systems in Time and Frequency DomainsFrequency-Domain Analysis. Steady-state Miss Analysis. Weave Maneuver Analysis. Frequency Analysis and Miss Step Response. BIBO Stability. Frequency Response of the Generalized Missile Guidance Model.
  4. Design of Guidance Laws Implementing Parallel Navigation. Time-Domain ApproachGuidance as a Control Problem. Lyapunov Approach to Control Law Design. Modified Linear Planar Model of Engagement. General Planar Case. Three-Dimensional Engagement Model. Generalized Guidance Laws. Optimal Guidance Laws.
  5. Design of Guidance Laws Implementing Parallel Navigation. Frequency-Domain ApproachNeo-classical Missile Guidance. Pseudo-classical Missile Guidance.
  6. Guidance Law Performance Analysis Under Stochastic InputsRandom Target Maneuvers. Analysis of Influence of Noises on Miss Distance. Effect of Random Target Maneuvers on Miss Distance. Filtering
  7. Integrated DesignIntegrated guidance and control model. Synthesis of control laws. Integration and decomposition.
  8. Computational aspects. ExamplesSoftware for Frequency-Domain Approach.Software for Time-Domain Methods. An example of the boost-phase interceptors design.
  9. Concluding RemarksThe future trend in developing the new generation of missiles and related problems


REGISTRATION:  There is no obligation or payment required to enter the Registration for an actively scheduled course.   We understand that you may need approvals but please register as early as possible or contact us so we know of your interest in this course offering.

SCHEDULING:  If this course is not on the current schedule of open enrollment courses and you are interested in attending this or another course as an open enrollment, please contact us at (410)956-8805 or ati@aticourses.com. Please indicate the course name, number of students who wish to participate. and a preferred time frame. ATI typically schedules open enrollment courses with a 3-5 month lead-time.   To express your interest in an open enrollment course not on our current schedule, please email us at ati@aticourses.com.

For on-site pricing, you can use the request an on-site quote form, call us at (410)956-8805, or email us at ati@aticourses.com.


  • Dr. Rafael Yanushevsky received the M.S. in mathematics, M.S. degree in electro-mechanical engineering, and the PhD degree in optimization of multivariable systems from the Institute of Control Sciences of the USSR Academy of Sciences, Moscow, Russia. His research interests were in optimal control theory and its applications (especially in aerospace), optimal control of differential-difference systems, signal processing, game theory and operations research. He started teaching in 1987 at the University of Maryland and at the University of the District of Columbia. Since 1999 he has been involved in projects related to the aerospace industry. He participated in development of engagement model as a part of Battle-Space Engineering Assessment Tool, WCS software, developed new guidance laws. He wrote sections of Modeling and Simulation Handbook related to the weapon control system and fire control system of SM-3 missiles. In 2002 he received Letter of Appreciation from the Department of the Navy, the Navy Area Theater Ballistic Missile Program. He has published over 80 papers, 4 books including Modern Missile Guidance (2007) and Unmanned Aerial Vehicle Guidance & Control, ( 2011). Dr Yanushevsky also teaches for ATI the course Unmanned Aerial Vehicles Guidance & Control He is included in “Who’s Who in America,” “Who’s Who in Science and Engineering,” and “Who’s Who in American Education.”

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