Gaussian Processes for Improved Dynamic Modeling in the Predictive Control of an Arduino Temperature Control Lab

A practical application of Gaussian processes (GPs) as an alternative nonlinear system identification approach in model predictive control (MPC) is presented. By means of using an Arduino Temperature Control Lab, setpoint tracking accuracy for a Gaussian process-based MPC scheme is compared to state space MPC and a proportional-integral-derivative (PID) controller. Foregoing parameterized system identification, GPs are proven to offer superior accuracy, while eliminating the tedious developments plaguing first-principle nonlinear alternatives. By further utilizing GPs probabilistic framework, estimates for variance are interpreted as system-specific uncertainty and used to better select control solutions that remain in training regions. Including variance within the optimal control problem (as opposed to its exclusion), improved overall setpoint tracking and affords a more cautious controller.