Problem Stabilization

Friction and the Inverted Pendulum Stabilization Problem

Abstract We consider an experimental system consisting of a pendulum, which is free to rotate 360 degrees, attached to a cart. The cart can move in one dimension. We study the effect of friction on the design and performance of a feedback controller, a linear quadratic regulator, that aim to stabilize the pendulum in the upright position. We show that a controller designed using a simple viscou...

Locked plate stabilization of problem fractures.

http://dx.doi.org/10.3415/VCOT-15-12-0202 Locking plates of various designs and specification are readily available commercially for fracture stabilization. All of these implants perform similarly, acting as angle stable internal fixators in regard to the plate-screw junction. There is a range of different mechanisms employed to achieve an angle stable locking connection between the plate and t...

On the stabilization problem for nonholonomic distributions

Let M be a smooth connected and complete manifold of dimension n, and ∆ be a smooth nonholonomic distribution of rank m ≤ n on M . We prove that, if there exists a smooth Riemannian metric on ∆ for which no nontrivial singular path is minimizing, then there exists a smooth repulsive stabilizing section of ∆ on M . Moreover, in dimension three, the assumption of the absence of singular minimizin...

Stabilization Problem for Nonholonomic Control Systems

An unbounded stabilization problem of bilinear systems

here the state space H is a real Hilbert with inner product <, > and corresponding norm ‖ ‖, A generates a strongly ontinuous semigroup of contractions (S(t))t≥0 on H and B is an unbounded linear operator from H to a Banach xtension X of H with a continuous injection H ↪→ X, so that ‖By ‖ X≤ M ‖ y ‖ , ∀ y ∈ H, for some M > 0. This is the ase, when for example the control is exercised over the b...