hello sir;

following equation needed to be solved in closed form solution and its graph taking first  3 terms.

u=-R^-1*g^t [T0+T1+T2+..... ]*[x1 x2 x3 x4 ]^t

where u=control input;

R=positive definite constant matrix

g= (4x2) matrix

T0=positive definite constant matrix(4x4)

T1=constatnt matrix

T2=constant matrix

waiting for your reply.

thank u.

nsd

hello,

thanks for giving  earlier solution.

next question again i m posting for its solution  .u are requested to crack it.

question1;

following first order diffrential equation's are given.

x=[x1, x2 ,x3, x4]^t =[r, rdot, lamda,r8lamdadot]^t  ----------------these are  four state variables

x1=r=relative range; x2=rdot=closing velocity; x3=lamda=line of site angle; x4=r*lamdadot=normal velocity.

 first order s.s equations are---------

dx1/dt=x2=rdot ;--------------(1)

dx2/dt=r*lamdadot^2 -acceleration ; ( along line of site direction) ------------(2)

dx3/dt=x4/x1;--------------------------(3)

dx4/dt= - x2*x4/x1- aceeleration ;  (in normal to  the line of site direction) --------------------(4)

these can be  in the form of ------ [xdot=f(x)*x+gu];  where f(x) is state  matrix  of (4x4) and g is  input control matrix of (4x2);

initial condition u can assume accordingly.each state(total four no.) and input control(two no.) to be plotted with time.

waiting for your reply.

question2: how kronecker product can be solved in maple? if matrices are given(A,B)

hi,

can u explain me how to  write code for new theta-d method in  nonlinear optimal control (i.e closed form solution)?

and how to plot it in maple?