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

Description

Iterate a gradient method and returns the computed control.

adjoint equation for the landing rocket problem.

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.

[xk,pk]=equad(tf,uk)
   

Computes the state and adjoint state of the rocket system for a given control ur.

FUSEE

[xdot]=fusee(t,x)
   

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)
   

• niter : number of gradient iteration steps.
• ukp1 : initial control value ( vector of sie 135 )
• pasg : the gradient step value.

FUSEEP

[pdot]=fuseep(t,p)
   

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)
   

DESCRITION

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)
   

EQUAD

TRAJ

[xt]=traj(t)
   

returns a piece wise value of the mass evolution.