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

Abstract This paper proposes a saturated smooth adaptive controller for regulation of a certain type of underactuated Euler–Lagrange systems (UELSs) with modeling uncertainties and control saturations based on a singular perturbation (SP) approach. Compared with the related literature, the advantages of the proposed controller include: (1) it renders the UELS semiglobally asymptotically track the desired position without 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 UELSs semiglobally asymptotically stable about the desired set point with satisfaction of control input constraints. The control effectiveness is validated by simulations on a two-link compliant robot arm without violation of the control input constraints.