Adaptive control for a class of uncertain nonlinear dynamical systems in the presence of high-order actuator dynamics

Abstract

Adaptive control is a powerful design methodology to achieve closed-loop system stability in the face of uncertainties resulting from modeling inaccuracies, degraded modes of operation, and changes in system dynamics. Yet, it is well known that the presence of actuator dynamics can seriously limit closed-loop system stability of any adaptive control framework. To address the problem of adaptive control design in the presence of actuator dynamics, we recently introduced a linear matrix inequalities-based adaptive control framework. The key feature of this approach is to reveal the fundamental stability interplay between the parameters of a given actuator dynamics model and the allowable uncertainties in the feedback loop. The contribution of this paper is to generalize our recent work for a class of uncertain nonlinear dynamical systems. Specifically, for a given high-order, linear time-invariant actuator dynamics model, we utilize tools and methods from Lyapunov stability and linear matrix inequalities for the computation of closed-loop system stability limits of adaptive control laws. An illustrative numerical example is also provided to demonstrate the efficacy and the practicality of the proposed design architecture.