Finite element method for optimal guidance of an advanced launch vehicle

Hodges, Dewey H.; Bless, Robert R.; Calise, Anthony J.; Leung, M. S.

doi:10.2514/3.20889

Cited by 25 publications

(7 citation statements)

References 2 publications

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“…h + ha \h . , n\ + --]rl2 =ga (1) (2) (3) (4) where h a = I s (u s + co i) = angular momentum of (R about e\ h\ = /icoi +/ 5 co 5 = angular momentum of (P + (R about e\ hi = 7, co/ = angular momentum of (P + (R about e f (/ = 1,2,3) // = moment of inertia of (P + (R about e { (i = 1,2,3) I s = moment of inertia of (R about e\ IP = 11 -I s = moment of inertia of (P about e\ co/ = angular velocity of (P about e t (i = 1,2,3) co 5 = angular velocity of (R about e\ relative to (P g a = torque applied by (P on (R about e\ e { = principal axes of (P + (R (/•= 1,2,3) It is evident from Eqs. (1-3) that the magnitude of I p relative to 12 and 7 3 plays an important role.…”

Section: Equations Of Motionmentioning

confidence: 99%

“…This Note is intended to fill in some of the details omitted in Ref. 2 concerning the solution of problems with state-control inequality constraints. Herein it is shown that the formulation does not require element quadrature, and it produces a sparse system of nonlinear algebraic equations.…”

Section: Introductionmentioning

confidence: 99%

“…The extension of the weak formulation is already outlined in Ref. 2 where the methodology is applied to a two-stage rocket trajectory optimization problem. This Note is intended to fill in some of the details omitted in Ref.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Finite element solution of optimal control problems with state-control inequality constraints

Bless

Hodges

1992

Journal of Guidance, Control, and Dynamics

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Section: Equations Of Motionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Finite element solution of optimal control problems with state-control inequality constraints

Bless

Hodges

1992

Journal of Guidance, Control, and Dynamics

Self Cite

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“…The number N of control segments between the sample point and the final point is held constant. This work was motivated by the finite element approach, 8 which uses low-order integration but exact equations of motion.…”

Section: Approximate Optimal Control Problemmentioning

confidence: 99%

Guidance law for hypersonic gliders based on piecewise constant control

Hull

Seguin

1994

Journal of Guidance, Control, and Dynamics

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A midcourse guidance law is developed for the descent of a hypersonic glider, initially in level flight, to a fixed target on the ground. It is based on an optimal piecewise constant control (N intervals) obtained from an approximate physical model (flat Earth, exponential atmosphere, parabolic drag polar, etc). The resulting optimal control equations can be integrated either analytically or by quadrature, and the guidance algorithm requires the solution of 2N + \ nonlinear algebraic equations. The guidance law is implemented in a realistic glider simulation, the intercept is achieved, and final velocities within 14% of the true values are obtained for the downrange and crossranges considered. Nomenclatureof gravity at sea level, ft/s 2 h = altitude, ft K = coefficient of parabolic drag polar M -Mach number m = mass, slugs N = number of intervals R = planet radius, ft S r = aerodynamic reference area, ft 2 T g = guidance period, s V = velocity, ft/s v = dimensionless velocity, -ln(V/V 0 ) X = downrange, ft Y = crossrange, ft a = angle of attack, rad ft = sideslip angle, rad fi e = density scale height, ft y = flight path angle, rad i/r = heading angle, rad p -atmospheric density, slugs/ft 3 p e = density at sea level, slugs/ft 3

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“…Hodges and Bless 13 developed a weak Hamiltonian nite element method, and Hodges et al 14 applied it to solve an atmospheric ight trajectory optimization problem.…”

mentioning

confidence: 99%