Handling Disjunctions in Signal Temporal Logic Based Control Through Nonsmooth Barrier Functions

Abstract

In this paper, we show that under mild controllability assumptions a Control Barrier Function (CBF) can be constructed based on predictions with a finite horizon. The proposed construction methodology yields a CBF that renders a prespecified subset of the state space invariant. In particular, we leverage intuitive understanding of the system dynamics to construct a subset of an unknown control-invariant set, and then apply finite horizon predictions to compute a CBF. Moreover, we provide a thorough analysis of the properties of the constructed CBF, we characterize the impact of the prediction horizon, and comment on the practical implementation. In the end, we relate our construction approach to Model Predictive Control (MPC). At the hand of a relevant application example, we demonstrate how our method is applied.

Control Barrier Functions for Disjunctions of Signal Temporal Logic Tasks

“…In the latter approaches which are closer to the work considered in this paper the satisfaction of the STL tasks is enforced using control barrier functions and/or control Lyapunov functions as in [10], [13] and feedback control laws are designed for continuous-time, nonlinear input-affine systems. Disjunctions of STL tasks have been recently considered in [11] and [12] utilizing control barrier functions and/or control Lyapunov functions. Yet, the problem of ensuring the existence of a control law over the horizon of the STL task [8] remains open.…”