Distributed predictive control of spiral wave in cardiac excitable media

In this paper, we propose the distributed predictivecontrol strategies of spiral wave in cardiac excitable media. Themodified FitzHugh--Nagumo model was used to express the cardiacexcitable media approximately. Based on the control-Lyapunov theory,we obtained the distributed control equation, which consists of apositive control-Lyapunov function and a positive cost function.Using the equation, we investigate two kinds of robust controlstrategies: the time-dependent distributed control strategy and thespace-time dependent distributed control strategy. The feasibilityof the strategies was demonstrated via an illustrative example, inwhich the spiral wave was prevented to occur, and the possibilityfor inducing ventricular fibrillation was eliminated. The strategiesare helpful in designing various cardiac devices. Since the secondstrategy is more efficient and robust than the first one, and theresponse time in the second strategy is far less than that in thefirst one, the former is suitable for the quick-response controlsystems. In addition, our spatiotemporal control strategies,especially the second strategy, can be applied to other cardiacmodels, even to other reaction-diffusion systems.