SunannnSun / ds_opt_haihui

Dynamical System Optimization in Linear Parameter Varying Formulation

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.

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Input

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,
}

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Usage

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()