About the data.npz file (resources)

Jonas-Nicodemus / PINNs-based-MPC

We discuss nonlinear model predictive control (NMPC) for multi-body dynamics via physics-informed machine learning methods. Physics-informed neural networks (PINNs) are a promising tool to approximate (partial) differential equations. PINNs are not suited for control tasks in their original form since they are not designed to handle variable control actions or variable initial values. We thus present the idea of enhancing PINNs by adding control actions and initial conditions as additional network inputs. The high-dimensional input space is subsequently reduced via a sampling strategy and a zero-hold assumption. This strategy enables the controller design based on a PINN as an approximation of the underlying system dynamics. The additional benefit is that the sensitivities are easily computed via automatic differentiation, thus leading to efficient gradient-based algorithms. Finally, we present our results using our PINN-based MPC to solve a tracking problem for a complex mechanical system, a multi-link manipulator.

MIT License

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Your code is really well written!! At the same time, I would like to ask about how the X and Y parameters (i.e. X_star and Y_star) in the data.npz file are generated? data.npz: ['X ','Y','U ','T','X0 ','X_test','Ytest ','ub','lb '] Are they using parameters obtained from real robotic arm operation or dynamic equations? If possible, could you please provide the code to generate the data.npz file? Also, according to the paper, I believe that x data=x k and y data=x k+1, but based on this code, y data is x k. Am I a bit confused? y data shouldn't be the predicted state for the next moment? There are a lot of questions, and if you could answer them, I would really, really, really appreciate it!!

Hi,

the data is generated from dynamic equations, but this equations are identified from a real robotic arm.
unfortunately, I can't provide you the code to generate the data.npz, since I do not work on this project anymore.
the function you quoted is only used to generate initial conditions, i.e., data points for which the time $t = 0$. We do not need any other data obtained by solving the system dynamics for the training (the data.npz is just used for evaluation of the trained model)! The model learns the dynamics via the PINN approach. That is why Y_data is a part of X_data in this case, in this way we tell the model that it should map any input where $t=0$ to just the state $x_0$ (which is contained in [1:5] entry).

I hope this clarifies everything for you.

Jonas-Nicodemus / PINNs-based-MPC

About the data.npz file (resources) #2