Multi-Rate Control Design Under Input Constraints via Fixed-Time Barrier Functions

In this paper, we introduce the notion of periodic safety, which requires that system trajectories periodically visit a subset forward-invariant safe set, and utilize it in multi-rate framework where high-level planner generates reference trajectory is tracked by low-level controller under input constraints. We fixed-time barrier functions leveraged proposed quadratic programming framework. Then, design model predictive control policy for planning with bound on rate change to guarantee safety achieved. demonstrate effectiveness strategy simulation example, stabilizing shows successful satisfaction objectives, whereas an exponentially fails.