Uncertainty Estimation of NMPC Horizon employing Neural Networks & MC-dropout in Safety-Critical Applications with Barrier Functions

There are cases, that models derived from first principles cannot accurately capture the system dynamics, which leads to uncertainty in model-based control. However, these nominal models are commonly used due to existence of mature methods to guaranty stability and feasibility of optimal control problems. Neural networks can be used as an alternative to approximate the dynamic model of a system directly from data. With uncertainty estimation in neural networks seeing increase in usage with regards to safety-critical applications, neural networks offer a natural way to quantify model uncertainty. Taking intuition from the above, in this work, we present an algorithm that estimates the future uncertainty of an MPC law, that combines a nominal model, derived from first principles, and a model learned with neural networks, that is employed to estimate the uncertainty of the nominal MPC horizon. The approach is based on the Monte Carlo dropout technique, aims in safety-critical applications and is general, as it can be tailored to any existing MPC strategy by gathering data from the plant. As an example, the method is applied to a simulated over- actuated marine platform that is controlled by an MPC law under realistic environmental disturbances for the task of navigation. The horizon uncertainty of the MPC, that employs Control Barrier Functions for obstacle avoidance, is used to shape the barrier of the safe set.