A Persistent-Excitation-Free Method for System Disturbance Estimation Using Concurrent Learning

Author: Zengjie Zhang, Fangzhou Liu

We extract the largest strongly connected subgraph containing $67$-nodes from the high school network [1] which depicts friendships between boys in a small high school in Illinois. We adjusted the adjacency matrix of the network such that it is less ill than the original version.

[1] Bonacich, Phillip, and Philip Lu. Introduction to mathematical sociology. Princeton University Press, 2012.

The experiment parameters

Load the param.mat file to pull the parameters

• $\bar{d}$, d_bar: the parameter used to generate the sinusoidal infection rates
• $\bar{\delta}$, delta_bar: the baseline curing rates
• $W$, W: the adjacency matrix of the network
• $\Lambda$, Lambda: the parameter of the disturbance model
• $x(0)$, x0: the initial condition of the system

Run experiment 0

Basic epidemic model controled by baseline curing rates $\bar{\delta}$

• Run the script exp_0_generate_data.m to generate exp_0_data.mat
• Then, run the script exp_0_draw_disturbance.m to plot the disturbance
• Then, run the script exp_0_draw_states.m to plot the states

Run experiment 1

Disturbace observation using CL-based and the conventional observers

• Run the script exp_1_infection_rate_estimation.m to generate data exp_1_data.mat
• Then, run the script exp_1_draw_disturbance_error.m to plot the estimation errors

Run experiment 2

Disturbance compensation control

• Run the script exp_2_compensation_control.m to generate data exp_2_data.mat
• Then, run the script exp_2_draw_controller.m to plot the result