Adaptive control for a class of high‐order nonlinear parameterized systems with multiple unknown control directions by switching linear controllers

Abstract

SummaryIn this paper, the adaptive control is investigated by switching linear controllers for a class of nonlinear parameterized systems with multiple unknown control directions. Parametric uncertainties entering the state equations nonlinearly can be fast time‐varying or jumping at unknown time instants, the bounds of the parametric uncertainties are not required to know a priori and the multiple control directions are unknown. Our proposed adaptive controller is a switching type controller. First, sufficient conditions for designing an adaptive stabilizer are derived. Then, a switching‐type adaptive controller is designed, in which a linear controller with two undetermined design parameters to be tuned is recursively designed by adding a power integrator, and a switching mechanism is proposed to tune these parameters online for compensating the multiple unknown control directions and the unknown bounds of the parametric uncertainties. The undetermined design parameters are based on the upper bound estimation of the unknown parameters existing not only in the nonlinear functions but also in the control directions functions. The proposed adaptive controller globally asymptotically stabilizes the system in the sense that, for any initial conditions, the state converges to the origin while all the signals of the closed‐loop system are bounded. Finally, an example is given to illustrate the effectiveness of the proposed method.