How can the lqr function in matlab be modified so that the 2*x'Nu term in the cost function J be replaced with a scalar value?

Hi,

I am trying to replicate a research paper which uses a scalar value for the term 2*x'Nu term in the cost function J(u). The paper states it also uses Matlab. I'm not sure how to pass a scalar value into the in-built lqr function in Matlab that only accepts matrices. Thanks in advance

Answer 1

[Torsten]

I wonder why the integral should be finite if you replace 2*x'*N*u by a fixed scalar value. This scalar value must definitely be 0.

Thus set N to the zero matrix.

[Alice Grant]

Thank you for your help, and sorry for my bad explaination at the problem. The paper replaces the 2*x'*N*u term by a scalar value (the scalar value term updates each iteration and is a function of x). Setting N to zero removes the 2*x'*N*u term, but I am not sure how to include the scalar value term into the cost function using the lqr function.

[Torsten]

And what is the form of this "scalar value as a function of x" ?

If the scalar value only depends on x and not on u, you better change Q and set N to 0.

[Alice Grant]

The expression for the scalar value (OBS) is defined here, and the J function with the scalar value is here. The authors use OBS as a obstacle avoidance term in the cost function. Thank you for your help again!

[Torsten]

I think you have to use a nonlinear model:

https://de.mathworks.com/help/mpc/ug/nonlinear-mpc.html