Immersion‐ and invariance‐based adaptive stabilization of switched nonlinear systems. (30th June 2017)

• Record Type: Journal Article
• Authors: Lou, Zhi‐E; Zhao, Jun
• Is Part Of: International journal of robust and nonlinear control. Volume 28:Number 1(2018)
• Page Start: 197
• Page End: 212
• Publication Date: 2017-06-30
• Subjects: adaptive stabilization -- generalized multiple Lyapunov functions (GMLFs) -- immersion and invariance (I&I) -- switched nonlinear systems; Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.3864
• Languages: English
• ISSNs: 1049-8923

Abstract

Summary: This paper presents a novel framework to asymptotically adaptively stabilize a class of switched nonlinear systems with constant linearly parameterized uncertainty. By exploiting the generalized multiple Lyapunov functions method and the recently developed immersion and invariance (I&I) technique, which does not invoke certainty equivalence, we design the error estimator, continuous state feedback controllers for subsystems, and a switching law to ensure boundedness of all closed‐loop signals and global asymptotical regulation of the states, where the solvability of the I&I adaptive stabilization problem for individual subsystems is not required. Then, along with the backstepping method, the proposed design technique is further applied to a class of switched nonlinear systems in strict‐feedback form with an unknown constant parameter so that the I&I adaptive stabilization controllers for the system is developed. Finally, simulation results are also provided to demonstrate the effectiveness of the proposed design method.