No initial guess in linear MPC

[tfarger]

There currently is no initial guess implemented in LinearMPC.
In regular nonlinear MPC there is an initial guess computation using either ipopt or a constant LQR gain, that sets the initial values of the solver at the first time step, see

safe-control-gym/safe_control_gym/controllers/mpc/mpc.py

Lines 340 to 343 in 253f25c

	if self.compute_initial_guess_method is not None and self.x_prev is None and self.u_prev is None:
	x_guess, u_guess = self.compute_initial_guess(obs)
	opti.set_initial(x_var, x_guess)
	opti.set_initial(u_var, u_guess) # Initial guess for optimization problem.

This is not implemented in the LinearMPC class

I am not sure if the initial guess is needed in the linear MPC. I think the MPC solver should get the same result in the first time step without initial guess. It could be useful for solver performance or something similar.

[adamhall]

Thanks! @MingxuanChe is this intentional? or should we add the line to LinearMPC as well?

[MingxuanChe]

Thank you for pointing this out.

• The recent MPC PR MPC warm-starting and acados implementation #161, to some extent, focuses on improving the runtime. The warm-starting for linear MPC is not prioritized since it runs sufficiently fast.
• Also, I was hesitant about whether warm-starting linear MPC with a nonlinear ipopt solution makes sense because the linear MPC will satisfy only the linearized dynamics instead of the nonlinear one. But I guess it will be better than not using it.

In general, we could have the initial guess computation for completeness if you don't find any evidence against it. If you agree we should have it, please react with a thumb-up, and then I will add it.

[Federico-PizarroBejarano]

I think it is unnecessary to add warmstarting code if it is already sufficiently fast. Unless anyone disagrees, I will close this issue