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Final Presentation Online-implementable robust optimal guidance law. Raghunathan T., Ph.D. student (On behalf of Late Dr. S Pradeep, Associate Professor, Aerospace Engineering Department). Two dimensional missile-target engagement model.

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final presentation online implementable robust optimal guidance law

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

two dimensional missile target engagement model
Two dimensional missile-target engagement model

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

background and motivation miss distances for the linear model
Background and motivation: Miss distances for the linear model

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

background and motivation
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

reality how valid are the assumptions
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

result of applying ogl to the nonlinear kinematic model miss distances for the plant
Result of applying OGL to the nonlinear kinematic modelMiss distances for the plant

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

objective
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

solution methodology
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

the starting point optimal guidance law ogl
The starting point: optimal guidance law (OGL)

Minimise

subject to

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

linear model
Linear model

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

the starting point ogl cont d
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

own problem formulation
Own problem formulation

Minimize

subject to

free and free

Control input/guidance law :

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

nonlinear kinematic model
Nonlinear kinematic model

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

challenges
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

our approach
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

differential evolution de parameters used
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

real time implementation the optimal control problem and evolutionary computation ec
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

ec for the missile guidance problem
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

online implementation

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

acceleration signatures
Acceleration signatures

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

comparison of total acceleration
Comparison of total acceleration

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

miss distances for all guidance laws
Miss distances for all guidance laws

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

n for ogl and de ogl
N’ for OGL and DE-OGL

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

convergence of the solution
Convergence of the solution

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

future work
Future work
  • For more practical maneuvers of target
  • More complex model?
  • Applicability to a larger range of initial conditions?

29 Oct 2007

publications
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

slide27
The End

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