Singular perturbation-based saturated adaptive control for underactuated Euler–Lagrange systems.

This paper proposes a saturated smooth adaptive controller for regulating a certain type of underactuated Euler–Lagrange systems (UELSs) with modeling uncertainties and control saturations based on a singular perturbation approach. Compared with relevent literature, the advantages of the proposed controller include: (1) it renders the UELS semiglobally asymptotically track the desired position without the violation of control input constraints; (2) high-order derivatives of positions are not required in its implementation. The Hoppensteadt's Theorem is employed to show that the proposed saturated controller renders the UELS semiglobally asymptotically stable about the desired set point with the satisfaction of control input constraints. The control effectiveness is validated by simulations on a two-link compliant robot arm. • A saturated adaptive controller is proposed for underactuated Euler–Lagrange systems. • An adaptive estimator with a prior designed bound is proposed for the gravitational torque. • A proportional-derivative control term is designed for the slow-varying subsystem. • The Hoppensteadt's Theorem is applied to prove semiglobal asymptotical stability. [ABSTRACT FROM AUTHOR]