Question

Explain the Simplex Search Method and demonstrate for minimization of $f(x) = 2x_1^2+5x_2^2-9$ starting at $(x^0)^T = [4, 3]$ in the direction $s^0=[-1 -3]^T$ Perform 2 iterations.

Answer 1

For a Given system $\dot{x}_1 = x_1^2+x_2-2, \dot{x}_2=x_1+x_2$ Explain clearly Input - Output linearization and Input state linearization.