Can anyone please tell me how can I use inbuilt Matlab function "Integral" or "quadl" for calculating the scalar quadratic cost function. J(x,t)=integral(x'(t)Qx(t))dt.
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the cost function is J(x,t)=integral(x'(t)[Q+KRK]x(t))dt. tau=0 to 0.6
Following code says better what exactly I am trying to figure out.
I dont know how to bring in the dependent term x(t) while using function integral or quadl.
%%%%code
syms x
Q=eye(4);
K_new=[ 0.5 1 0.5 0.5];
R=1;
f = @(t,K) x(t)'.*(Q+K'.*R.*K).*x(t)
QQ = integral(@(x)f(t,K_new),0,0.6)
I know that representing x(t), considers x as a indexed variable which is not what I mean. x(t) is a dependent variable with respect to t (x is a time varying variable). Please see that J(x,t) is a common quadratic cost function associated with LQR problems. Please tell me whether I can use Matlab inbuilt function to solve or to get an approximate solution for the cost function.
Many many thanks for your valuable time in advance
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