37,128 research outputs found
A Parametric Non-Convex Decomposition Algorithm for Real-Time and Distributed NMPC
A novel decomposition scheme to solve parametric non-convex programs as they
arise in Nonlinear Model Predictive Control (NMPC) is presented. It consists of
a fixed number of alternating proximal gradient steps and a dual update per
time step. Hence, the proposed approach is attractive in a real-time
distributed context. Assuming that the Nonlinear Program (NLP) is
semi-algebraic and that its critical points are strongly regular, contraction
of the sequence of primal-dual iterates is proven, implying stability of the
sub-optimality error, under some mild assumptions. Moreover, it is shown that
the performance of the optimality-tracking scheme can be enhanced via a
continuation technique. The efficacy of the proposed decomposition method is
demonstrated by solving a centralised NMPC problem to control a DC motor and a
distributed NMPC program for collaborative tracking of unicycles, both within a
real-time framework. Furthermore, an analysis of the sub-optimality error as a
function of the sampling period is proposed given a fixed computational power.Comment: 16 pages, 9 figure
Amenability of Groupoids Arising from Partial Semigroup Actions and Topological Higher Rank Graphs
We consider the amenability of groupoids equipped with a group valued
cocycle with amenable kernel . We prove a general result
which implies, in particular, that is amenable whenever is amenable and
if there is countable set such that for all . We show that our result is applicable to groupoids arising from
partial semigroup actions. We explore these actions in detail and show that
these groupoids include those arising from directed graphs, higher rank graphs
and even topological higher rank graphs. We believe our methods yield a nice
alternative groupoid approach to these important constructions.Comment: Revised as suggested by a very helpful referee. In particular, a gap
in the proof of Theorem 5.13 has been repaired resulting in a much improved
version (with fewer hypotheses
An Alternating Trust Region Algorithm for Distributed Linearly Constrained Nonlinear Programs, Application to the AC Optimal Power Flow
A novel trust region method for solving linearly constrained nonlinear
programs is presented. The proposed technique is amenable to a distributed
implementation, as its salient ingredient is an alternating projected gradient
sweep in place of the Cauchy point computation. It is proven that the algorithm
yields a sequence that globally converges to a critical point. As a result of
some changes to the standard trust region method, namely a proximal
regularisation of the trust region subproblem, it is shown that the local
convergence rate is linear with an arbitrarily small ratio. Thus, convergence
is locally almost superlinear, under standard regularity assumptions. The
proposed method is successfully applied to compute local solutions to
alternating current optimal power flow problems in transmission and
distribution networks. Moreover, the new mechanism for computing a Cauchy point
compares favourably against the standard projected search as for its activity
detection properties
Lipschitz regularity for elliptic equations with random coefficients
We develop a higher regularity theory for general quasilinear elliptic
equations and systems in divergence form with random coefficients. The main
result is a large-scale -type estimate for the gradient of a
solution. The estimate is proved with optimal stochastic integrability under a
one-parameter family of mixing assumptions, allowing for very weak mixing with
non-integrable correlations to very strong mixing (e.g., finite range of
dependence). We also prove a quenched estimate for the error in
homogenization of Dirichlet problems. The approach is based on subadditive
arguments which rely on a variational formulation of general quasilinear
divergence-form equations.Comment: 85 pages, minor revisio
A Parametric Multi-Convex Splitting Technique with Application to Real-Time NMPC
A novel splitting scheme to solve parametric multiconvex programs is
presented. It consists of a fixed number of proximal alternating minimisations
and a dual update per time step, which makes it attractive in a real-time
Nonlinear Model Predictive Control (NMPC) framework and for distributed
computing environments. Assuming that the parametric program is semi-algebraic
and that its KKT points are strongly regular, a contraction estimate is derived
and it is proven that the sub-optimality error remains stable if two key
parameters are tuned properly. Efficacy of the method is demonstrated by
solving a bilinear NMPC problem to control a DC motor.Comment: To appear in Proceedings of the 53rd IEEE Conference on Decision and
Control 201
Multiple scattering by cylinders immersed in fluid: high order approximations for the effective wavenumbers
Acoustic wave propagation in a fluid with a random assortment of identical
cylindrical scatterers is considered. While the leading order correction to the
effective wavenumber of the coherent wave is well established at dilute areal
density () of scatterers, in this paper the higher order dependence of
the coherent wavenumber on is developed in several directions. Starting
from the quasi-crystalline approximation (QCA) a consistent method is described
for continuing the Linton and Martin formula, which is second order in ,
to higher orders. Explicit formulas are provided for corrections to the
effective wavenumber up to O. Then, using the QCA theory as a basis,
generalized self consistent schemes are developed and compared with self
consistent schemes using other dynamic effective medium theories. It is shown
that the Linton and Martin formula provides a closed self-consistent scheme,
unlike some other approaches.Comment: 12 page
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