Comparison of Different Gaussian Process Models and Applications in Model Predictive Control

Most advanced control methods require a sufficiently accurate model of the system to be controlled. These models are becoming increasingly difficult to generate due to the increasing complexity of the underlying systems. To address this problem, data-driven models can be used. These kind of models are trained based on data of the dynamic system. They can be used for controller design and also be applied directly to control the system. In this work, a stochastic model predictive controller (SMPC) with a Gaussian process model (GP) is utilized. The main advantage of GPs is the construction of a dynamic system model with the possibility of determining the uncertainty of its own prediction. In this contribution, three different utilizations of prediction uncertainty in SMPC are compared. Additionally, two different implementations of dynamic GPs, nonlinear autoregressive exogenous GPs (GP-NARX) and a state-space model based on GPs (GP-SSM), are considered. All six test cases are compared based on an evaluation criterion that describes the resulting control performance. A simulated inverted pendulum, a benchmark for nonlinear and unstable systems, is used as test system. In this work, the combinations of different dynamic GPs and the application of their uncertainty prediction in SMPC are evaluated and compared.