Extremum Seeking Nonovershooting Control of Strict-Feedback Systems Under Unknown Control Direction

TL;DR

This paper introduces a novel control method combining extremum seeking and Lie brackets to achieve nearly nonovershooting tracking in strict-feedback nonlinear systems with unknown control directions, ensuring safety and performance.

Contribution

It presents a new approach that enables nonovershooting control for systems with unknown control directions, which was not previously achievable.

Findings

Achieves approximately nonovershooting tracking from below for any initial condition.

Overshoot can be reduced to arbitrarily small levels via parameter tuning.

Provides a mechanism for high-relative-degree nonovershooting constraints in safety-critical systems.

Abstract

This paper addresses the nonovershooting control problem for strict-feedback nonlinear systems with unknown control direction. We propose a method that integrates extremum seeking with Lie bracket-based design to achieve approximately nonovershooting tracking. The approach ensures that arbitrary reference trajectories can be tracked from below for any initial condition, with the overshoot reducible to arbitrarily small levels through parameter tuning. The method further provides a mechanism for enforcing high-relative-degree nonovershooting constraints in safety-critical scenarios involving unknown control directions.