Objective function with summation

I want to solve an MPC problem in matlab using fmincon function.

Im having hard time in figuring it out the way to write the objective function . Minimization is only wrt u ( x(t+1) = Ax(t)+Bu(t) )

Could someone please help else guide me to relevant sources

[Torsten]

What are the dimensions of A and B ? How large do you want to choose N ?

I assume x(0) is given ?

[Walter Roberson]

I do not understand the notation. x subscript k+t is normally a scalar, butit does not make sense to transpose a scalar.

[SANDEEP SURAVARAPU]

@Torsten A is 2x2 matrix and B 2x1 matrix

@Walter Roberson or simply x(k+t|t) means at time t we have the observation/value x(t) and the summation is k=0 to N hence it would be x(t+1),....,x(t+N) . x is a scalar if A and B are assumed scalars (1x1 matrices) else they would be a vector

[Torsten]

B is (2x1) - so u is a scalar for each t ?

How big is N ? x0 is a given 2x1 vector ?

[SANDEEP SURAVARAPU]

@Torsten yes u is scalar for each t.

let me re-write the problem in clearer way :

Answer 1

[Torsten]

Choose u_0,...,u_N as unknowns.

In the objective function, calculate x_1,...x_(N+1) from A and u_0,...u_N.

Return u_0^2 + ... + u_N^2 + x_1.'*x_1 + ... + x_(N+1).'*x_(N+1)

That's all.

No constraints are necessary.

[SANDEEP SURAVARAPU]

Thanks, this helps