(182a) Data-Driven Discovery of Sparse Dynamical Model of Cardiac System for Model Predictive Control

Vagal Nerve Stimulation was approved in 1997 by the U.S Food and Drug Administration for reducing the frequency of seizures in patients suffering from epilepsy. In recent times, it has shown promising results in the treatment of a number of cardiovascular diseases, chronic inflammatory disorders such as sepsis, lung injury, and diabetes. In this approach, mild electrical pulses are sent to the brain via the vagus nerve in an open-loop. Because of this open-loop stimulation, various side effects have been observed due to psychological and inter-patient variability and therefore a closed-loop delivery strategy of electrical pulses that accounts for this variability is desired. Implementing closed-loop using model based control requires a mathematical model describing the system. The limited models that are already there in the literature consist of unmeasurable states, are unable to capture patient-specific variability, and are highly nonlinear for real-time applications. Therefore, to obtain a mathematical model of measurable states that is sparse, interpretable, and parameterized using patient-specific data, we use a data-driven approach called Sparse Identification of Nonlinear Dynamics (SINDy). SINDy formulates the nonlinear system identification problem as a convex optimization problem in parameter space with regularization and discovers models that balance model error and model sparsity. In order to simulate this process of discovering models, we use synthetic data generated by one of the models from the literature and then build a data-driven model. This discovered model is then used to design a controller for Model Predictive Control (MPC) and its performance is shown using the setpoint tracking example on hypertensive conditions. For MPC, we use a quadratic cost function that penalizes deviation from the setpoint and changing control inputs. In order to guarantee the stability of MPC, we use also use terminal cost in the objective function and a terminal constraint set found using the Quasi-Infinite Horizon approach. Upon interpreting the discovered model, we get the feasibility of the setpoint and the relative effect of each of the fibers at specific locations on the states of the system.