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

TL;DR

The paper tackles nonovershooting tracking for strict-feedback nonlinear systems with unknown control direction by integrating Extremum-Seeking (ES) with Lie bracket averaging to design a controller that minimizes a positive definite function and dominates potential overshoot. The proposed ES-based controller $u=\alpha_{es}(h,t)$, together with a coordinate transformation and Lie-bracket averaged dynamics, yields conditions (Theorems 1 and 2) under which the closed-loop system is semiglobally practically uniformly bounded (SPUUB) and the tracking error $|x_1-y_r|$ can be made arbitrarily small. A safety-overrides mechanism is included to enforce high-relative-degree nonovershooting constraints in safety-critical settings, and an illustrative example demonstrates favorable performance compared with a Nussbaum-gain approach, while preserving stability guarantees. Overall, the approach enables safe, robust tracking under unknown control direction in high-relative-degree nonlinear plants and provides practical tools for safety-critical control.

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.

Figures (5)

• Figure 1: Tracking trajectories under the ES nonovershooting controller.
• Figure 2: Evolutions of the ES nonovershooting controller.
• Figure 3: Tracking trajectories under the Nussbaum controller.
• Figure 4: Safe regulation trajectories with safe initialization.
• Figure 5: Safe regulation trajectories with unsafe initialization.