Practical Finite-/Fixed-Time Improved Command-Filtered Backstepping Control for Nonlinear Systems Via Immersion and Invariance

Abstract

Highlights1. We improve the command-filtered backstepping approach. With improved command-filtered backstepping (ICFBS), we relax the boundedness assumption of the control direction function and elevate the tunability of the design scheme, with almost no increase in computational complexity.2. We have addressed the unsolved problem: practical finite-/fixed-time ICFBS and I&I adaptive tracking control, which provides some meaningful references for future research.3. We prove with an inequality constructed by us that the proposed I&I parameter update law with the higher-power composite term of a parameter estimation can be augmented to satisfy the requirement of the practical finite-/fixed-time closed-loop stability. Therefore, this work broadens the area of application of the parameter update law based on I&I in the CFBS adaptive tracking control because only UUB and practical finite-time adaptive tracking control based on I&I and CFBS has been achieved at present.

Keywords: Improved command-filtered backstepping, practical finite/fixed time, immersion and invariance, Nonlinear systems