Implantable Pacemakers Control and Optimization via Fractional Calculus Approaches: A Cyber-Physical Systems Perspective

Managing cardiac disease and abnormal heart rate variability remain challenging problems with an enormous economic and psychological impact worldwide. Consequently, the purpose of this paper is to introduce a fractal approach to pacemaker design based on the constrained finite horizon optimal control problem. This is achieved by modeling the heart rate dynamics via fractional differential equations. Also, by using calculus of variations, we show that the constrained finite horizon optimal control problem can be reduced to solving a linear system. Finally, we discuss the hardware complexity involved in the practical implementation of fractal controllers.