Is there any Python code for MPC examples on discrete-time models?

zhanghd · August 13, 2025, 2:21am

Hi

Thanks for your distinguish work on Acados！

I have to use discrete model obtained by Koopman operator in my research, but I have only found various examples for continuous time systems. Could you please point me to Python code for MPC examples using discrete time systems？

Thanks

kaethe · August 13, 2025, 4:41am

Hi

In order to use a discrete time model, you need to provide disc_dyn_expr as is done here:

github.com/acados/acados

examples/acados_python/pendulum_on_cart/common/pendulum_model.py

3fb63b106


      
              val = ca.substitute(ca.substitute(model.f_expl_expr, model.x, xbar), model.u, ubar)
              jac_x = ca.substitute(ca.substitute(ca.jacobian(model.f_expl_expr, model.x), model.x, xbar), model.u, ubar)
              jac_u = ca.substitute(ca.substitute(ca.jacobian(model.f_expl_expr, model.u), model.x, xbar), model.u, ubar)
          
              model.f_expl_expr = val + jac_x @ (model.x-xbar) + jac_u @ (model.u-ubar)
              model.f_impl_expr = model.f_expl_expr - model.xdot
              model.name += '_linearized'
              return model
          
          
          def export_pendulum_ode_model_with_discrete_rk4(dT):
          
              model = export_pendulum_ode_model()
          
              x = model.x
              u = model.u
          
              ode = Function('ode', [x, u], [model.f_expl_expr])
              # set up RK4
              k1 = ode(x,       u)
              k2 = ode(x+dT/2*k1,u)

Best, Katrin

josipkh · August 13, 2025, 8:40am

Hello,
I just wanted to add that, in case you’re formulating a linear MPC with the Koopman operator-based model, this example might be useful as well.
It’s in MATLAB, but the commands should be very similar in Python.
Kind regards,
Josip

zhanghd · August 13, 2025, 9:03am

Thanks! It’s useful. Besides that, I have another question. If a continuous-time model is input, will Acados convert the continuous-time system into a discrete-time system through a discretization method (such as RK4)?

zhanghd · August 13, 2025, 9:09am

Thank you! It’s very useful. For a dynamic system, does the time interval ts when using a discrete-time model need to be equal to the simulation time tf / N_nodes when using a continuous-time model?

josipkh · August 13, 2025, 10:07am

Glad to hear that
Yes, that should be the case.

FreyJo · August 13, 2025, 2:37pm

acados deploys an integrator corresponding to the options integrator_type, and sim_method_*.
Nonuniform time grids are supported by the acados integrators.
If you want to use discrete dynamics with nonuniform grids, you need to introduced a parameter for the time steps.

Alex · September 18, 2025, 9:37am

Have I understood you correctly that the sample time of the discrete model cannot be set by acados like it does for the RK integrators and must be either fed into the model at code generation time or updated as a runtime parameter by the user?
Will the integrator option “num_steps” have an effect on discrete “integrator” type as well or is it necessary to create more shooting nodes to get a finer sample time resolution of my discrete model?