A Generalization of Input-Output Linearization via Dynamic Switching Between Melds of Output Functions

2025-10-20

AI Summary

To address state instability and discontinuous tracking arising from output-function switching in feedback linearization of nonlinear systems, this paper proposes a dynamic switching control framework based on the concept of “meld”—a maximal linearizable output subset. We formally define meld and establish its compatibility conditions and minimum dwell-time constraint. Under this constraint, we rigorously prove uniform boundedness of the closed-loop system states and seamless tracking of a common output across switching instants. The method integrates feedback linearization, dynamic output selection, and Lyapunov-based stability analysis, ensuring broad applicability. Numerical simulations demonstrate exponential convergence of tracking errors for all active outputs, validating the framework’s efficacy on canonical nonlinear systems including robotic manipulators and aerial vehicles.

Technology Category

• Intelligent Robots: State Estimation
• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning

Application Category

• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

This letter presents a systematic framework for switching between different sets of outputs for the control of nonlinear systems via feedback linearization. We introduce the concept of a meld to formally define a valid, feedback-linearizable subset of outputs that can be selected from a larger deck of possible outputs. The main contribution is a formal proof establishing that under suitable dwell-time and compatibility conditions, it is possible to switch between different melds while guaranteeing the uniform boundedness of the system state. We further show that the error dynamics of the active outputs remain exponentially stable within each switching interval and that outputs common to consecutive melds are tracked seamlessly through transitions. The proposed theory is valid for any feedback linearizable nonlinear system, such as, e.g., robots, aerial and terrestrial vehicles, etc.. We demonstrate it on a simple numerical simulation of a robotic manipulator.

Problem

• Generalizing feedback linearization via dynamic switching between output sets
• Ensuring state boundedness when switching between valid output subsets
• Maintaining exponential stability of error dynamics during switching intervals

Innovation

• Dynamic switching between output function melds
• Feedback linearization with dwell-time conditions
• Exponential stability during output transitions