Tracking control and robustness analysis for a nonlinear model of human heart rate during exercise

The control of human heart rate during exercise is an important problem that has implications for the development of protocols for athletics, assessing physical fitness, weight management, and the prevention of heart failure. Here we provide a new stabilization technique for a recently-proposed nonlinear model for human heart rate response that describes the central and peripheral local responses during and after treadmill exercise. The control input is the treadmill speed, and the control objective is to make the heart rate track a prescribed reference trajectory. We use a strict Lyapunov function analysis to design new state and output feedback tracking controllers that render the error dynamics globally exponentially stable. This allows us to prove input-to-state stability properties for our feedback stabilized systems under actuator errors. This robustness property quantifies the effects of variations of the treadmill speed from the controller values. We illustrate our feedback design through simulations.