L-CSS 2021: Multi-rate control design under input constraints via fixed-time barrier functions

Kunal Garg, Ryan K. Cosner, Ugo Rosolia, Aaron D. Ames, Dmitra Panagou. [pdf]

Abstract:

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

This is work performed in collaboration with Kunal Garg and Dmitra Panagou (U Michigan) and Ugo Rosolia and Aaron Ames (Caltech). It was originally published in the 2021 IEEE LCSS Journal.

The full publication can be found here (https://arxiv.org/pdf/2103.03695.pdf).