Switching Among Feedback-Linearizing Output Sets (Melds): Dwell-Time and Compatibility Guarantees

summary

The gist

The gist Switching among feedback-linearizing output sets (melds) involves studying switching among multiple square selections of output functions for nonlinear systems to derive dwell-time and

In short

The study investigates switching between different sets of output functions (melds) for nonlinear systems that can be feedback-linearized. Switching causes state-dependent coordinate mismatches not covered by standard analysis. The research provides explicit dwell-time conditions and a compatibility constant to guarantee exponential decay of tracking errors and uniform boundedness of the state error across switches.

Key concepts

Meld: A meld is a specific selection or set of output functions used for feedback linearization. When switching between different melds, the system's coordinate charts change, leading to mismatches that classical switched-system tools cannot easily handle.
Reference-Compatibility Constant: This constant measures how mismatched the desired trajectories are when comparing the reference families implied by different melds. It quantifies an inherent incompatibility between the references across different switching modes, showing that dwell time alone is insufficient to overcome this mismatch.
Cross-Chart Maps: These maps describe how a coordinate transformation defined by one meld interacts with the coordinate transformation of another meld. Analyzing their Lipschitz bounds is crucial because these bounds quantify the size of the state-dependent mismatches that arise during switching.
Dwell-Time Condition: This is a specific time constraint on how long the system must stay in one meld before switching. The derived condition depends on controller decay rates and the reference compatibility constant, ensuring that tracking errors between switches decay exponentially.

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This episode discusses

Switching Among Feedback-Linearizing Output Sets (Melds): Dwell-Time and Compatibility Guarantees · Paper Radio

The paper

Switching Among Feedback-Linearizing Output Sets (Melds): Dwell-Time and Compatibility Guarantees · Read on arXiv

Mirko Mizzoni, Pieter van Goor, Barbara Bazzana, Antonio Franchi

University of Twente · Sapienza University of Rome · University of Sydney

DOI: 10.1016/j.sysconle.2026.106618

Transcript

Introduction to the show: ident: Robotics Radio. Generated commentary on the latest robotics and control papers.

Rosa: Today's paper: "Switching Among Feedback-Linearizing Output Sets (Melds)".

Dev: The gist Switching among feedback-linearizing output sets (melds) involves studying switching among multiple square selections of output functions for nonlinear systems to derive dwell-time and compatibility guarantees for state boundedness…

Rosa: First, who's behind it and why it matters.

Paper summary: Dev: So to recap, this paper explores switching among square selections of output functions called melds for nonlinear systems that are static feedback-linearizable via outputs. The core thesis is that each meld gives a different feedback-linearizing coordinate chart in a local neighborhood, and switching between them creates state-dependent mismatches that standard switched-system analyses miss.

Rosa: They measure this effect by using Lipschitz bounds on the cross-chart maps over a compact safe set and introducing a reference-compatibility constant to gauge the mismatch between different reference families across melds.

Taro: So, what's really interesting is that they find an explicit dwell-time condition based on controller decay rates and this compatibility constant that ensures exponential tracking error decay between switches, keeps shared outputs tracking together smoothly, and keeps the state error bounded within the safe set.

Dev: It means you can design a switching schedule that guarantees this smooth transition and stability if you respect the dwell time requirement dictated by those bounds.

Rosa: This is important because it moves beyond just saying "it's stable" to giving a concrete rule on *how long* you need to wait between switches for the system to perform well under these switching conditions.

Taro: It tells us that dwell time alone isn't enough if the reference trajectories themselves are incompatible across the different melds, because they introduce this explicit reference-compatibility constant into the requirement.

Conclusion: Rosa: So looking at "Switching Among Feedback-Linearizing Output Sets (Melds): Dwell-Time and Compatibility Guarantees", the authors Mirko Mizzoni, Pieter van Goor, Barbara Bazzana, and Antonio Franchi are tackling the problem of ensuring stability when you are intentionally switching between different ways to linearize a nonlinear system using its outputs.

Dev: The implication for me is that this gives us a practical tool. We used to just rely on standard switched-system techniques, but this paper provides the mathematical framework to calculate exactly how much time we need between switches so we can guarantee that the tracking errors decay exponentially and the state stays safe.

Taro: It means for someone designing a hybrid system, you don't just pick a schedule; you have to coordinate that schedule with the compatibility of your reference trajectories across those different linearization modes.

Rosa: Right, so it’s about making sure that even when you’re switching outputs, the system doesn't get confused by which coordinate chart it’s currently operating in. It gives us a way to handle those state-dependent mismatches by quantifying them upfront.

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