LQR problem with controllable system

Good morning to everybody;

I need to design an LQR based control system for a 4 indipendent WaterJet boat.

The state vector is the following

where u is the longitudinal velocity, v is the lateral velocity and omega is the yaw rate.

I linearized the system starting from this function, in which I rotated the velocities and the forces in the fixed reference frame

f1, f2, f3, f4 are the thrust from the WaterJet

And after this i used the Jacobian function in order to create the A and B matrices.

But when i run the LQR this error appear:

Cannot compute the stabilizing Riccati solution S for the LQR design. This could be because:

* R is singular,

* [Q N;N' R] needs to be positive definite,

* The E matrix in the state equation is singular.

So i checked the controllability of the model by imposing zero velocities and all the Thrust = 10.

The rank of the controllability matrix was equal to 6, so my system is controllable.

I cannot understand where is the problem.

Thank you in advance.

Answer 1

[Dongming]

For high dimensional problem, try to use icare to solve Riccati equation