Steepest Ascent Method to find maximum
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I am looking for a problem in my implementation for steepest ascent method. My answer is in a long equation form with h in it. But I am calculating h in the loop still ther is no value of it for the answer. The solution is at the end of the function
function STPAscent(x,theta,TC)
x0 =1500;
theta0=pi/6;
i=0;
i_max=100;
ea=5;
es=1;
while (es<double(subs(ea)) && i<i_max)
fx = tan(theta0)/(2*100^2*(cos(theta0))^2) + (2*9.81*x0)/(2*100^2*(cos(theta0))^2); % derivative wrt "x"
ftheta= x0*(sin(theta0)*(100*sin(theta0)+981*x0*cos(theta0))+50)/(1000000*(cos(theta0))^4); % derivative wrt "theta"
syms h
x=x0+fx*h;
theta=theta0+ftheta*h;
f= 1000 + (x*tan(theta))/(2*100^2*(cos(theta))^2) + (9.81*x^2)/(2*100^2*(cos(theta))^2);
c=diff(f,h);
assume(h,'clear')
h=solve(c==0,h,'PrincipalValue',true);
x_new=x+fx*h;
theta_new=theta0+ftheta*h;
ea=abs((x_new-x0)/x_new)*100;
x0=x_new;
theta0=theta_new;
i=i+1;
end
fxtheta = 1000 + (x0*tan(theta0))/(2*100^2*(cos(theta0))^2) + (9.81*x0^2)/(2*100^2*(cos(theta0))^2)
simplify(fxtheta)
end
Command Window
Warning: Unable to solve symbolically. Returning a numeric
solution using vpasolve.
> In sym/solve (line 304)
In STPAscent (line 18)
fxtheta =
(981*((8836235812531391*h)/4503599627370496 + 1499.9993954193889930311396801317)^2)/(2000000*cos(pi/6 - 0.52363352427033321420523588398365)^2) + (tan(pi/6 - 0.52363352427033321420523588398365)*((8836235812531391*h)/4503599627370496 + 1499.9993954193889930311396801317))/(20000*cos(pi/6 - 0.52363352427033321420523588398365)^2) + 1000
ans =
0.0018882263675909642813601409431637*h^2 + 2.8871384744661982638760370739896*h + 2103.6241090862540686603690416302
댓글 수: 3
Torsten
2022년 12월 13일
You can define a function dependent on an unknown h for which you want to find the root and use "fzero" or "fsolve" to solve for h.
That's exactly what "solve" will do in your case because it doesn't find an analytical solution for h.
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