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Mechanical systems including friction effects constitute a theoretically interesting and practically important class of nonlinear systems. Such systems are commonly described by a second-order nonlinear differential equation with a noncontinuous vector field. Under forcing conditions, a mechanical system with friction can display very complicated behavior, including noninvertible erratic trajectories. In applications, an objective is to induce a prescribed motion in spite of uncertainties (friction effects) and complicated uncontrolled behavior. This objective is attained by means of a control strategy that generates an estimate of the friction forces and counteracts them.
Álvarez‐Ramírez et al. (Thu,) studied this question.