Safe Data-Driven Model Predictive Control of Systems with Complex Dynamics

In this paper, we address the safety and efficiency of data-driven model predictive controllers (DD-MPC) for systems with complex dynamics. First, we utilize safe exploration of dynamical systems to learn an accurate model for the DD-MPC. During training, we use rapidly exploring random trees (RRT) to collect a uniform distribution of data points in the state-input space and overcome the common distribution shift in model learning. This model is also used to construct a tree offline, which at test time is used in the cost function to provide an estimate of the predicted states' distance to the target. Additionally, we show how safe sets can be approximated using demonstrations of exclusively safe trajectories, i.e. positive examples. During test time, the distances of the predicted trajectories to the safe set are used as a cost term to encourage safe inputs. We use a \emph{broken} version of the inverted pendulum problem where the friction abruptly changes in certain regions as a running example. Our results show that the proposed exploration algorithm and the two proposed cost terms lead to a controller that can effectively avoid unsafe states and displays higher success rates than the baseline controllers with models from controlled demonstrations and even random actions.QC 20211221