Can anyone help me with dynamic programming of this linear quadratic regulator (LQR) system in order to find optimal control and optimal trajectory in MATLAB m. file? I should discritize it with Ts=0.1 and I should also do interpolations and extrapolation.
To use dynamic programming for LQR problems, you start with the Hamilton-Jacobi equation and seek a quadratic solution of the form: V = x' Z(t) x + 2 x' \xi(t) + c(t). Substituting this solution into the HJ equation and equate the coefficients of the quadratic, linear, and constant terms to zero. Then, you obtain the equations for Z, \xi, and c (ODEs). The Z equation is the Riccati differential equation.
Based on your past questions, I think that you need to enter a degree program to formally study the topic. It will be a lot of wasted effort if you go it on your own.
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