Iterative Gaussian Process Model Predictive Control with Application to Physiological Control Systems*

Model predictive control (MPC) is becoming one of the leading modern control approaches applied to physiological control systems. However, intra- and interpatient variability usually requires an adaptation of the model to each individual patient or otherwise deeming the controller too conservative. The incorporation of learning in model predictive control is subject to ongoing intensive research to provide tractable and safe implementation in practice. Gaussian processes (GPs) among other learning approaches have been proposed for learning uncertain or unknown system dynamics as well as time varying disturbances. However, the naïve incorporation of GPs into MPC, commonly results in complex and nonlinear optimization problems. In this paper, we propose a practical stochastic MPC implementation, that utilizes estimates of the parameter uncertainties and nonlinearities of the system as well as external additive disturbances. By using a linear nominal model augmented with two separate GPs, nonlinearities depending on the state and input as well as temporal disturbances can be considered efficiently in the MPC framework. An iterative optimization scheme is introduced using quadratic programming to circumvent solving a stochastic nonlinear program. The applicability of the proposed approach is demonstrated on a pressure controlled mechanical ventilation problem.