robust synergistic hybrid feedback

TL;DR

This paper introduces advanced synergistic hybrid feedback controllers that enable global stabilization and obstacle avoidance, even under parametric uncertainties, through innovative switching logic and adaptive backstepping techniques.

Contribution

It presents a novel synergistic controller design with dynamic logic variables, addresses parametric uncertainties, and extends to adaptive backstepping and obstacle avoidance.

Findings

Successful stabilization on compact manifolds

Effective obstacle avoidance demonstrated

Robustness to parametric uncertainties achieved

Abstract

Synergistic hybrid feedback refers to a collection of feedback laws that allow for global asymptotic stabilization of a compact set through the following switching logic: given a collection of Lyapunov functions that are indexed by a logic variable, whenever the currently selected Lyapunov function exceeds the value of another function in the collection by a given margin, then a switch to the corresponding feedback law is triggered. This kind of feedback has been under development over the past decade and it has led to multiple solutions for global asymptotic stabilization on compact manifolds. The contributions of this paper include a synergistic controller design in which the logic variable is not necessarily constant between jumps, a synergistic hybrid feedback that is able to tackle the presence of parametric uncertainty, backstepping of adaptive synergistic hybrid feedbacks, and a demonstration of the proposed solutions to the problem of global obstacle avoidance.