Optimal boundary control of cardiac alternans

Abstract

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, a spatially uniform unstable steady state of small amplitude of alternans described by parabolic partial differential equations (PDEs) is stabilized by boundary optimal control methods. A finite dimensional linear quadratic regulator (LQR) is utilized in both a full‐state‐feedback control structure and in a compensator design with the Luenberger observer, and it achieves global stabilization in a finite size tissue cable length. The ability to realize such control algorithm is analyzed based on the structure of the amplitude of alternans equation and the control methodology applied. Copyright © 2008 John Wiley & Sons, Ltd.

Continuous-time control of alternans in long Purkinje fibers

“…Several methods have been used to prevent and control fibrillation. [19][20][21][22][23][24][25] Echebarria and Karma 26 were the first to consider the feedback control of Purkinje fibers. They showed that alternans can be suppressed in the Noble model, using pacing interval adjustment (PIA) method which varies the pacing interval by an amount proportional to the difference between the APD on two previous intervals.…”

Optimal boundary control & estimation of diffusion-reaction PDEs

“…structural acoustics [1], fixed-bed reactors [2], multi-agent coordination control [3], and stock investment models [4]. A subset of these systems limit control and sensing to the boundaries, such as thermal/fluid flows [5], cardiovascular systems [6], chemical reactors [7], and advanced batteries [8]- [10]. Optimal control and estimation of these PDE systems is particularly challenging since actuation and sensing are limited to the boundary and the dynamics are notably more complex than ODE systems.…”