Nonlinear Static Output Feedback Control for Human Heart Rate during Treadmill Exercise

This paper presents a new control method for the nonlinear human heart beat rate dynamics during treadmill exercise. The reference trajectory represents a desired heart rate profile suggested by the physician. The goal is to design the treadmill speed input for tracking control purposes. Using Lyapunov stability arguments, we propose a parsimonious static output feedback (SOF) scheme for real-time implementation where the system nonlinearity is incorporated in the control law to guarantee the control performance. In particular, the SOF controller is robust with respect to the convex polytopic uncertainty. The design procedure is recast as an LMI-based optimization and therefore can be easily solved with available numerical solvers. Moreover, it can be extended to handle other tracking and/or disturbance rejection objectives. The proposed control method can be applied to a wide class of polytopic uncertain systems subject to a cone-bounded nonlinearity. The effectiveness of our feedback design is demonstrated with both simulation and experimental results in training exercises.