A Takagi-Sugeno Fuzzy-Model-Based Tracking Framework to Regulate Heart Rhythm Dynamics

Arrhythmias are conditions characterized by a faster, slower, or irregular heart rhythm. Some of them may be harmless and brief, but others can lead to sudden cardiac arrest. Thus, procedures that safely restore a normal heartbeat are a matter of interest. Laboratory experiments have evidenced that some arrhythmia exhibit nonlinear deterministic behavior, which justifies the need to build mathematical models for heartbeat description. The study of these models may contribute to a better understanding of arrhythmias mechanism and new heartbeat control treatments. This paper addresses a model-based tracking control method for heart rhythm regulation in a cardiac model. Since there is no consensus on the equations describing the heart dynamics, we leverage a nonlinear oscillator that is able to reproduce a variety of electrocardiogram-like waveforms when adjusting a parameter. First of all, the nonlinear system under study is represented as a Takagi-Sugeno fuzzy model. Due to its multiple local linear systems structure, tracking control design conditions for both nominal and uncertain slave systems are formulated as linear matrix inequalities. The simulation examples show that the proposed feedback control framework can restore the heart rhythm dynamics from a non-desirable situation to the normal behavior given by the reference system, which reveals a proof of concept to use tracking control techniques to suppress pathological behaviors.