An optimistic approach to cost-aware predictive control

Abstract

We consider continuous-time systems subject to a priori unknown state-dependent disturbance inputs. Given a target goal region, our first approach consists of a control scheme that avoids unsafe regions of the state space and observes the disturbance behavior until the goal is reachable with high probability. We leverage collected observations and the mixed monotonicity property of dynamical systems to efficiently obtain high-probability overapproximations of the system’s reachable sets. These overapproximations improve as more observations are collected. For our second approach, we consider the problem of minimizing cost while navigating toward the goal region and modify our previous formulation to allow for the estimated confidence bounds on the disturbance to be adjusted based on what would reduce the overall cost. We explicitly consider the additional cost incurred through exploration and develop a formulation wherein the amount of exploration performed can be directly tuned. We show theoretical results confirming that this confidence bound modification strategy outperforms the previously developed strategy on a simplified system. We demonstrate the first approach on an example of a motorboat navigating a river, then showcase a Monte Carlo simulation comparison of both approaches on a planar multirotor navigating toward a goal region through an unknown wind field.