104 research outputs found
Generalized Filippov solutions for systems with prescribed-time convergence
Dynamical systems with prescribed-time convergence sometimes feature a
right-hand side exhibiting a singularity at the prescribed convergence time
instant. In an open neighborhood of this singularity, classical absolutely
continuous Filippov solutions may fail to exist, preventing indefinite
continuation of such solutions. This note introduces a generalized Filippov
solution definition based on the notion of generalized absolute continuity in
the restricted sense. Conditions for the continuability of such generalized
solutions are presented and it is shown, in particular, that generalized
Filippov solutions of systems with an equilibrium that is attractive, in
prescribed time or otherwise, can always be continued indefinitely. The results
are demonstrated by applying them to a prescribed-time controller for a
perturbed second-order integrator chain
Worst-case error bounds for the super-twisting differentiator in presence of measurement noise
The super-twisting differentiator, also known as the first-order robust exact
differentiator, is a well known sliding mode differentiator. In the absence of
measurement noise, it achieves exact reconstruction of the time derivative of a
function with bounded second derivative. This note proposes an upper bound for
its worst-case differentiation error in the presence of bounded measurement
noise, based on a novel Lipschitz continuous Lyapunov function. It is shown
that the bound can be made arbitrarily tight and never exceeds the true
worst-case differentiation error by more than a factor of two. A numerical
simulation illustrates the results and also demonstrates the
non-conservativeness of the proposed bound
Optimal Robust Exact Differentiation via Linear Adaptive Techniques
The problem of differentiating a function with bounded second derivative in
the presence of bounded measurement noise is considered in both continuous-time
and sampled-data settings. Fundamental performance limitations of causal
differentiators, in terms of the smallest achievable worst-case differentiation
error, are shown. A robust exact differentiator is then constructed via the
adaptation of a single parameter of a linear differentiator. It is demonstrated
that the resulting differentiator exhibits a combination of properties that
outperforms existing continuous-time differentiators: it is robust with respect
to noise, it instantaneously converges to the exact derivative in the absence
of noise, and it attains the smallest possible -- hence optimal -- upper bound
on its differentiation error under noisy measurements. For sample-based
differentiators, the concept of quasi-exactness is introduced to classify
differentiators that achieve the lowest possible worst-case error based on
sampled measurements in the absence of noise. A straightforward sample-based
implementation of the proposed linear adaptive continuous-time differentiator
is shown to achieve quasi-exactness after a single sampling step as well as a
theoretically optimal differentiation error bound that, in addition, converges
to the continuous-time optimal one as the sampling period becomes arbitrarily
small. A numerical simulation illustrates the presented formal results
Robust exact differentiators with predefined convergence time
The problem of exactly differentiating a signal with bounded second
derivative is considered. A class of differentiators is proposed, which
converge to the derivative of such a signal within a fixed, i.e., a finite and
uniformly bounded convergence time. A tuning procedure is derived that allows
to assign an arbitrary, predefined upper bound for this convergence time. It is
furthermore shown that this bound can be made arbitrarily tight by appropriate
tuning. The usefulness of the procedure is demonstrated by applying it to the
well-known uniform robust exact differentiator, which the considered class of
differentiators includes as a special case
Organizing to Win: Introduction
[Excerpt] The American labor movement is at a watershed. For the first time since the early years of industrial unionism sixty years ago, there is near-universal agreement among union leaders that the future of the movement depends on massive new organizing. In October 1995, John Sweeney, Richard Trumka, and Linda Chavez-Thompson were swept into the top offices of the AFL-CIO, following a campaign that promised organizing at an unprecedented pace and scale. Since taking office, the new AFL-CIO leadership team has created a separate organizing department and has committed $20 million to support coordinated large-scale industry-based organizing drives. In addition, in the summer of 1996, the AFL-CIO launched the Union Summer program, which placed more than a thousand college students and young workers in organizing campaigns across the country
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