In the context of a masters course on constrained optimal control, we were looking to implement the classic cart-pendulum example, with a hard state constraint on the angle of the pendulum. Our implementation followed the constrained MPCaircraft model example.

During our implementation we observed that the output control sequences from the “optimal.solve_ocp” were different than from MATLAB’s “mpcActiveSetSolver” for the same model, stage cost, and prediction horizon. The following are the control sequences at time 0:
solve_ocp: 8.085e-01 1.464e-02 4.912e-01 7.621e-01 5.672e-01 5.080e-01 4.151e-01 2.398e-01 0.000e+00 0.000e+00
MATLAB: 0.8750 -0.1281 0.6964 0.7551 0.7363 0.7937 0.6934 0.6644 0.6041 0.4130

We also observed that the output from “input_output_response” simulation differed based on platform (Windows vs Linux/MacOS). On Linux/MacOS the optimiser would fail to meet the state constraints, while this behaviour does not occur on Windows.

I have included an implementation of our code in both Python and in JupyterLab, environment package lists, plots of the constrained state, and a comparison version in MATLAB:MPC_PythonControl_Analysis.zip

Are there any plans for classic MPC implementation for the cost function to directly compute the state predictions using the discrete-time linear dynamics rather than numerically computed using the trapezoid rule (line 311-322 in optimal.py)?

Are you able to provide any advice or guidance on why the numeric simulation result is different between OS versions?