Stabilization of singularly perturbed systems using acceleration-dependent forces

Abstract

One of the most important properties of the Lagrange equations is their regularity, i.e. the non-singularity of their inertia matrix, as a result of which they can always be brought to normal form. However, their inertia matrix may be ill-conditioned, and the equations themselves may be singularly perturbed. As a consequence, even relatively small errors in the parameters of the control actuators and moderate perturbing actions may result in a significant difference between the calculated and the actual motions of the system. It is not always possible to remedy this situation using traditional control, which depends on the position, velocity, and time alone, thus calling for the development of special methods to control singularly perturbed systems. This paper reports a new approach to the singularly perturbed system stabilization problem, in which the effect of permanent perturbations is reduced using acceleration-dependent forces.