Adaptive architectures for control of uncertain dynamical systems with actuator and unmodeled dynamics

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.

Exponentially Stable MRAC of MIMO Switched Systems with Matched Uncertainty and Completely Unknown Control Matrix

“…Nowadays, the effective synthesis procedures have been proposed that guarantee the asymptotic convergence of the plant trajectories to reference ones in all stated cases. Efficient robust modifications are developed to ensure boundedness of all signals and certain trajectory tracking quality for a system being affected by external disturbances [3], unmodeled dynamics [4], and delays [5].…”