Optimal and Model Predictive Control of Cardiac Alternans

The presence of alternans, which is a persistent alternation in the cardiac action potential duration, has been linked to the onset of ventricular arrhythmia, which may lead to sudden cardiac death. In this thesis, we examine the problem of alternans annihilation in a 1D cable of cardiac cells using optimal and model predictive control strategies, through boundary and spatially distributed actuations. In the first part of the thesis, the system of parabolic partial differential equations (PDEs) describing the small amplitude of alternans and the alternation of peak intracellular Ca2+ concentration are stabilized by optimal full state feedback control. A model predictive controller (MPC) was then formulated for the small amplitude of alternans PDE. Finally, to address the issue of controller robustness with respect to model uncertainties, a robust MPC was implemented on the small amplitude of alternans PDE. Simulation studies for all three control methods demonstrate that the proposed strategies can successfully annihilate alternans in cables that are significantly longer than 1 cm, thus overcoming the limitations of earlier control efforts.