Optimal boundary control of cardiac alternans

Alternation of normal electrical activity in the myocardium is believed to be linked to the onset of life threatening ventricular arrhythmias and sudden cardiac death. In this paper, spatially uniform unstable steady state of small amplitude of alternans described by parabolic PDEs is stabilized by boundary optimal control method. Finite dimensional linear quadratic regulator (LQR) is utilized in the full state feedback control structure and it achieves global stabilization in the finite size tissue cable length. Ability to realize such control algorithm is analyzed based on the structure of the amplitude of alternans equation and control methodology applied. Index Terms: Cardiac Alternans, Action Potential Propagation, Dissipative Parabolic PDEs, LQR, Optimal Boundary Control.