So I am new in this field (game theory, optimal control) and trying to go a step forward on a project from this equation image which is the definition of joint cost function (I am dealing with 2 players), assuming for the second equality i know all variables except Q_alpha, the state x is a rectangular matrix, for initial time t=0 would this be the right way to solve for Q_alpha in matlab and to use the equation since in reality is an integral but i am assuming I want the value at initial time t=0?
Q_alpha= pinv(x')*(J_alpha - U' * M * U)*pinv(x) %pinv or pseudoinverse since x is rectangular
(Maybe i am doing something not allowed but i am open to hear any advice, thanks a lot)
I expect the value of this matrix to be Q_alpha = [1.1,0;0,1.1]
I get Q_alpha =
-1.0399 -0.41595
-0.41595 -0.16638