Adaptive architectures for control of uncertain dynamical systems with actuator and unmodeled dynamics. (10th June 2019)

• Record Type: Journal Article
• Authors: Dogan, K. Merve; Gruenwald, Benjamin C.; Yucelen, Tansel; Muse, Jonathan A.
• Is Part Of: International journal of robust and nonlinear control. Volume 29:Number 12(2019)
• Page Start: 4228
• Page End: 4249
• Publication Date: 2019-06-10
• Subjects: actuator dynamics -- adaptive control -- linear matrix inequalities -- Lyapunov stability theory -- system uncertainties -- unmodeled dynamics; Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.4624
• Languages: English
• ISSNs: 1049-8923

Abstract

Summary: In adaptive control of uncertain dynamical systems, it is well known that the presence of actuator and/or unmodeled dynamics in feedback loops can yield to unstable closed‐loop system trajectories. Motivated by this standpoint, this paper focuses on the analysis and synthesis of multiple adaptive architectures for control of uncertain dynamical systems with both actuator and unmodeled dynamics. Specifically, we first analyze model reference adaptive control architectures with standard, hedging‐based, and expanded reference models for this class of uncertain dynamical systems and develop sufficient stability conditions. We then synthesize a robustifying term for the latter architecture and analytically show that this term can allow for a relaxed sufficient stability condition. The proposed theoretical treatments involve Lyapunov stability theory, linear matrix inequalities, and matrix mathematics. Finally, we compare the resulting sufficient stability conditions of the considered adaptive control architectures on a benchmark mechanical system subject to actuator and unmodeled dynamics.