Barrier Function-based Model Predictive Control under Signal Temporal Logic Specifications

In this work a continuous-time MPC scheme is presented for linear systems under Signal Temporal Logic (STL) specifications and input constraints. The satisfaction of the STL specifications is encoded by time-varying barrier functions and a least-violating control law is designed for cases when the satisfaction of the task with a given robustness value is not achieved, e.g., due to actuation limitations. The recursive feasibility of the proposed scheme is guaranteed when a time-varying terminal constraint is introduced. This constraint ensures a desired behavior for the system that guarantees the satisfaction of the task with pre-determined robustness.