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

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.