Optimal control of heart rate during treadmill exercise

Abstract

Feedback control of heart rate (HR) for treadmills is important for exercise intensity specification and prescription. This work aimed to formulate HR control within a stochastic optimal control framework and to experimentally evaluate controller performance. A quadratic cost function is developed and linked to quantitative performance outcome measures, namely, root-mean-square tracking error and average control signal power. An optimal polynomial systems design is combined with frequency-domain analysis of feedback loop properties, with focus on the input sensitivity function, which governs the response to broad-spectrum HR variability disturbances. These, in turn, are modelled using stochastic process theory. A simple and approximate model of HR dynamics was used for the linear time-invariant controller design. Twelve healthy male subjects were recruited for comparative experimental evaluation of 3 controllers, giving 36 tests in total. The mean root-mean-square tracking error for the optimal controllers was around 2.2 beats per minute. Significant differences were observed in average control signal power for 2 different settings of the control weighting (mean power 22.6 vs 62.5×10−4 m2/s2, high vs low setting, p=2.3×10−5). The stochastic optimal control framework provides a suitable method for attainment of high-precision, stable, and robust control of HR during treadmill exercise. The control weighting can be used to set the balance between regulation accuracy and control signal intensity, and it has a clear and systematic influence on the shape of the input sensitivity function. Future work should extend the problem formulation to encompass low-pass compensator and input sensitivity characteristics.