Abstract

The analysis and design of observed-based nonlinear control of a heartbeat tracking system is investigated in this paper. Two of Zeeman’s heartbeat models are investigated and modified by adding the control input as a pacemaker, thereby creating the control-affine nonlinear system models that capture the general heartbeat behavior of the human heart. The control objective is to force the output of the heartbeat models to track and generate a synthetic electrocardiogram (ECG) signal based on the actual patient reference data, obtained from the William Beaumont Hospitals, Michigan, and the PhysioNet database. The formulations of the proposed heartbeat tracking control systems consist of two phases: analysis and synthesis. In the analysis phase, nonlinear controls based on input-output feedback linearization are considered. This approach simplifies the difficult task of developing nonlinear controls. In the synthesis phase, observer-based controls are employed, where the unmeasured state variables are estimated for practical implementations. These observer-based nonlinear feedback control schemes may be used as a control strategy in electronic pacemakers. In addition, they could be used in a software-based approach to generate a synthetic ECG signal to assess the effectiveness of diagnostic ECG signal processing devices.

Highlights

  • The human heart is a complex yet robust system

  • The control objective is to force the output of the heartbeat models to track and generate a synthetic electrocardiogram (ECG) signal based on the actual patient reference data, obtained from the William Beaumont Hospitals, Michigan, and the PhysioNet database

  • Two Zeeman models were chosen in this study as they describe the heartbeat, and offer direct biophysical relationship to the dynamic variables

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Summary

Introduction

The human heart is a complex yet robust system. One of the most important signals that are being generated during the operation of the human heart is the electrocardiogram (ECG). Reference [7] modified the 3rd-order nonlinear ODE model in [3] by adding control parameters that affect the frequency of the oscillation to control the heart rate variability and used a neural network to produce the ECG signal. Another well-known approach to modeling the cardiac induction system is based on the van der Pol (VdP) type oscillators [8].

The Heartbeat Models
The 2nd-Order Nonlinear Heartbeat Model
Nonlinear Input-Output Feedback Linearization
A11 A12 A 21 A2 2
Application to the Heartbeat Systems
Conclusion

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