fusee - a set of Scilab macro for a landing rocket problem

Description

FUSEE [xdot]=fusee(t,x) gives the dynamical motion equation for the rocket

FINIT finit() Initialises the following parameters for rocket landing.

k : The acceleration of the rocket engines

gamma : The moon gravity acceleration.

umax : the gaz ejection flow out.

mcap : the mass of the space capsule.

cpen : penalisation in the cost function of the final state.

FUSEEGRAD [ukp1]=fuseegrad(niter,ukp1,pasg) Iterate a gradient method and returns the computed control.

niter : number of gradient iteration steps.

ukp1 : initial control value ( vector of sie 135 )

pasg : the gradient step value.

FUSEEP [pdot]=fuseep(t,p) adjoint equation for the landing rocket problem.

POUSSE [ut]=pousse(t) return the value of a piece wise constant control build on the discrete control uk

UBANG [uk]=ubang(tf,tcom) returns a bang-bang control, 0 form time 0 to tcom and 1 form tcom to tf.

FCOUT [c,xk,pk,ukp1]=fcout(tf,uk,pasg) optimise the following cost function by gradient iterations. c = -m(tf) + C*( h(tf)**2 + v(tf)**2)

SFUSEE []=sfusee(tau,h0,v0,m0,Tf) computes the rocket trajectory when a bang-bang control is used tau is the commutation time.

h0 : The initial position (high)

v0 : The initial speed ( negative if the rocket is landing )

m0 : The total initial mass ( capsule and fuel).

Tf : Time horizon.

EQUAD [xk,pk]=equad(tf,uk) Computes the state and adjoint state of the rocket system for a given control ur .

TRAJ [xt]=traj(t) returns a piece wise value of the mass evolution.