Robust MPC using YALMIP

[OnTheLeftHalfPlane]

Hello Prof. Lofberg,

In the tutorial for solving robust min-max MPC in YALMIP, the plants are all linear. In case I have a nonlinear plant and want to solve min-max MPC will it be possible? 

For example my system is: 

x1_dot = x_2 

x2_dot = u - 0.6 x2 - x1 - x1^3 + w

and I have hard constraints on u, x, and w: |u| <= u_0, |x| \le x_0, |w| \le w_0 

It is possible to solve this problem in YALMIP? 

Thanks

[Johan Löfberg]

not with yalmip ( and you won't find any tool that does it for you, this is basically a problem without any nice solution. already the case without uncertainty is hard)

[OnTheLeftHalfPlane]

So I can't use YALMIP to solve any min-max problem with non-linear dynamics?

[Johan Löfberg]

Sure if you can derive the robust counterpart to begin with (sounds horribly hard), and then use some suitable nonlinear nonconvex solver to solve it, it is up to you. You will not be able to use the built-in robust framework though

[OnTheLeftHalfPlane]

Thanks. Sorry for the silly question: I have not gone through the inner code of the robust solver in YALMIP, how to derive robust counterpart? where can I find that? 

[Johan Löfberg]

there is no general way. it is a theoretical field on its own and only tractable in some limited cases, i.e. basically those yalmip does

[OnTheLeftHalfPlane]

Thanks, any paper that you recommend? For example is there any article that charts out the derivation of robust counter part in YALMIP? 

[Johan Löfberg]

https://yalmip.github.io/tutorial/robustoptimization/