This module is a modified rendition of Haihui Gao's Python implementation of Dynamical System Optimization in Linear Parameter Varying Formulation (DS-OPT). The module has been adapted and integrated as a part of the comprehensive pipeline: Directionality-Aware Mixture Model Parallel Sampling for Efficient Dynamical System Learning. Please refer to DAMM-LPVDS for complete usage.
The input of ds_opt consists of data dictionary of the following form:
data_dictionary = {
"Data": Data, # Data point of shape, [dimension, number_of_data]
"Data_sh": Data_sh, # Shifted attractor to 0 for 'Data' (used in Lyapunov function learning)
"att": att, # Attractor of shape, [dimension, 1]
"x0_all": x0_all, # Start points for all demonstrations of shape, [dimension, number_of_traj]
"dt": dt, # Sample time
}
and gmm parameters results, which should be saved in output.json:
{
"name": "Clustering Result",
"K": # Number of clusters,
"M": # Dimension,
"Priors": # List of Prior,
"Mu": # ravel K x M shape Mu to a list,
"Sigma": #ravel K x M x M Sigma to a list,
}
import ds_opt class and initialize the object:
ds_opt = ds_opt(data_dictionary, OUTPUT_JSON_PATH)
Train:
ds_opt.begin()
Evaluate: Return the rmse, e_dot, dwtd for learned trajectory
ds_opt.evaluate()
Plot: Make plots for Lyapunov derivative, value, and reproduced streamlines
ds_opt.make_plot()
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