Powerbike - Model-based optimal control for cycling

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Our project connects Computer Science in Sport (Sportinformatik) with mathematical modeling, numerics, and sport science. We contribute to modeling and prediction for cycling as an example of endurance sports by- designing, calibrating, and validating mathematical physiological models that provide the means to analyze and predict cycling performance, and by- deriving methods to compute optimal pacing strategies for cycling time trials based on these models.The modeling for performance analysis in road cycling is twofold. Firstly, the mechanical aspects of cycling include the physics of the bicycle propulsion. Secondly, a physiological model of the individual athlete is required which should provide available power and energy resources at any point in time. Such a model is much more difficult to achieve than the physical one. It is impossible to accurately simulate all relevant physiological aspects because of the vast complexity of the human organism encompassing numerous subsystems with scales down to the cellular level. Thus, a compromise between the level-of-detail and the necessary abstraction of the model must be made. For this task we will use semi-physical system modeling. Basic elements of the structure of the system will be motivated by current state-of-the-art physiological models while some of the internal system details will be left for the system identification. Moreover, the parameters of such physiological models need to be estimated for individual athletes. This calibration is difficult and may render a possibly accurate but too complex model useless in practice. System identification and parameter estimation can be based best on input-output pairs. Input is a load profile in a suitably chosen ergometer test. Output is respiratory gas exchange, heart rate or variability, and lactate blood level. With models on hand we can compute minimum-time pacing strategies by solving certain mathematical optimal control problems. The physical and physiological models provide a system of constrained differential equations with a control which is the pacing strategy. Recently improved numerical algorithms designed to solve general optimal control problems efficiently are available, partly as well developed open-source software. However, the specific problem still contains some features that require additional methods to guarantee reliable convergence.Our proposed work includes an evaluation. Firstly, testing protocols must be developed to determine the parameters for physiological models to evaluate the validity and accuracy of these models. Secondly, optimal pacing strategies will be tested first on our cycling simulator, and then also in the field which requires a gps-enabled feedback device that provides the cyclist with the information about the optimal pacing in real-time. Ideally, the device should update online the optimal pacing strategy while on the road.