Learning-Based Iterative Optimal Control for Unknown Systems Using Gaussian Process Regression

In this paper, we propose an iterative learning-based optimal control strategy for unknown systems. The system model is assumed to be initially unknown and learned by the Gaussian process regression with the historical data collected in the previous iterations. To impose the constant improvement on the control performance and strict constraint satisfaction on the state of the system, we derive a multi-step ahead deterministic bound of the error between the prediction via a learned model and the state of the system, and then use it in the control design. The result from the numerical experiment shows the effectiveness of our method.