why the number of states is +1 the number of inputs in optimal control or in optimization??

Question

clc; clear;
T = 5
dt = 0.2
N = T/dt
n_x = 2 % number of states (x1,x2)
n_u = 2 % number of inputs (u1,u2)
N_x = (N+1)*n_x
N_u = N*n_u
n = 2 + N_u % number of decision variables

Answer 1

Hi