Final Presentation Online-implementable robust optimal guidance law

1. Final PresentationOnline-implementable robust optimal guidance law Raghunathan T., Ph.D. student (On behalf of Late Dr. S Pradeep, Associate Professor, Aerospace Engineering Department) Final presentation - DRDO IISc Prgm on Adv. Res. in Math. Engg

2. Two dimensional missile-target engagement model Final presentation - DRDO IISc Prgm on Adv. Res. in Math. Engg

3. Background and motivation: Miss distances for the linear model Final presentation - DRDO IISc Prgm on Adv. Res. in Math. Engg

4. Background and motivation • Optimal guidance law (OGL) • Assumptions a) linear model of missile-target engagement : b) unbounded control : infinite lateral acceleration c) tgo known accurately d) constant target maneuver Yields an analytical/closed form solution that is implementable online Final presentation - DRDO IISc Prgm on Adv. Res. in Math. Engg

5. Reality : how valid are the assumptions? a) Missile-target engagement kinematics is highly nonlinear b) Lateral acceleration is limited by saturation c) tgo cannot be known accurately d) Constant target maneuver? Final presentation - DRDO IISc Prgm on Adv. Res. in Math. Engg

6. Result of applying OGL to the nonlinear kinematic modelMiss distances for the plant Final presentation - DRDO IISc Prgm on Adv. Res. in Math. Engg

7. Objective An improved, robust guidance law i) that nullifies or at least mitigates the effect of assumptions made ii) implementable in real-time Final presentation - DRDO IISc Prgm on Adv. Res. in Math. Engg

8. Solution Methodology (i) Make use of the solution (i.e. OGL) that we know, as a starting point (ii) Explore the solution space around this starting point for the best solution Final presentation - DRDO IISc Prgm on Adv. Res. in Math. Engg

9. The starting point: optimal guidance law (OGL) Minimise subject to Final presentation - DRDO IISc Prgm on Adv. Res. in Math. Engg

10. Linear model Final presentation - DRDO IISc Prgm on Adv. Res. in Math. Engg

11. The starting point: OGL (cont’d) The solution/control input/lateral acceleration/OGL: Cancellation of system dynamics Final presentation - DRDO IISc Prgm on Adv. Res. in Math. Engg

12. Own problem formulation Minimize subject to free and free Control input/guidance law : Final presentation - DRDO IISc Prgm on Adv. Res. in Math. Engg

13. Nonlinear kinematic model Final presentation - DRDO IISc Prgm on Adv. Res. in Math. Engg

14. Challenges 1) lack of optimal control methods to deal with inequality constraints 2) real-time implementation Final presentation - DRDO IISc Prgm on Adv. Res. in Math. Engg

15. Our approach: The Differential Evolution Tuned Optimal Guidance Law (DE-OGL): Control input/guidance law : (Differential Evolution is one of the evolutionary computation (EC) methods) Final presentation - DRDO IISc Prgm on Adv. Res. in Math. Engg

16. Differential Evolution (DE) parameters used: • Crossover constant, CR = 0.9 • Weighting factor, F = 0.8 • Population size, NP = 12 • Stopping criterion: max. no. of generations = 4 or solution < tolerance limit Final presentation - DRDO IISc Prgm on Adv. Res. in Math. Engg

17. Real-time implementation:The Optimal Control Problem and evolutionary computation(EC) In general, EC is computationally intensive! Which leads to the second set of challenges : • System dynamics slow enough • A ‘good enough’ (suboptimal) solution • Massively parallel implementation Final presentation - DRDO IISc Prgm on Adv. Res. in Math. Engg

18. EC for the Missile Guidance Problem • Fast dynamics • Acceptable: almost the best solution • Limited onboard computation power • Must be available in real-time ! Final presentation - DRDO IISc Prgm on Adv. Res. in Math. Engg

19. OGL + plant/ guidance system actuator + OGL DE- OGL DE OGL model plant model Online Implementation Final presentation - DRDO IISc Prgm on Adv. Res. in Math. Engg

20. Acceleration signatures Final presentation - DRDO IISc Prgm on Adv. Res. in Math. Engg

21. Comparison of total acceleration Final presentation - DRDO IISc Prgm on Adv. Res. in Math. Engg

22. Miss distances for all guidance laws Final presentation - DRDO IISc Prgm on Adv. Res. in Math. Engg

23. N’ for OGL and DE-OGL Final presentation - DRDO IISc Prgm on Adv. Res. in Math. Engg

24. Convergence of the solution Final presentation - DRDO IISc Prgm on Adv. Res. in Math. Engg

25. Future work • For more practical maneuvers of target • More complex model? • Applicability to a larger range of initial conditions? 29 Oct 2007

26. Publications Papers: • (a) Raghunathan T. and S. Pradeep, “A Differential Evolution Tuned Optimal Guidance Law,” in The 15th Mediterranean Conference on Control and Automation - MED’07 held at Athens, Greece during June 27-29, 2007. • (b) Raghunathan T. and S. Pradeep, “An online Implementable Differential Evolution Tuned Optimal Guidance Law,” in Genetic and Evolutionary Computation Conference - GECCO 2007, held at London, United Kingdom, during July 7-11, 2007. Technical Report: • Raghunathan T. and S. Pradeep, “Online-implementable Robust Optimal Guidance Law,” Technical Report No. TR-PME-2007-12 dated 20 December 2007, under DRDO-IISc Programme on Advanced Research in Mathematical Engineering. The financial support provided for the above by DRDO-IISc Program on Advanced Research in Mathematical Engineering is gratefully acknowledged Final presentation - DRDO IISc Prgm on Adv. Res. in Math. Engg

27. The End Final presentation - DRDO IISc Prgm on Adv. Res. in Math. Engg