6,531 research outputs found
Sufficient conditions for time optimality of systems with control on the disk
International audienceThe case of time minimization for affine control systems with control on the disk is studied. After recalling the standard sufficient conditions for local optimality in the smooth case, the analysis focusses on the specific type of singularities encountered when the control is prescribed to the disk. Using a suitable stratification, the regularity of the flow is analyzed, which helps to devise verifiable sufficient conditions in terms of left and right limits of Jacobi fields at a switching point. Under the appropriate assumptions, piecewise regularity of the field of extremals is obtained
Communication-efficient Distributed Multi-resource Allocation
In several smart city applications, multiple resources must be allocated
among competing agents that are coupled through such shared resources and are
constrained --- either through limitations of communication infrastructure or
privacy considerations. We propose a distributed algorithm to solve such
distributed multi-resource allocation problems with no direct inter-agent
communication. We do so by extending a recently introduced additive-increase
multiplicative-decrease (AIMD) algorithm, which only uses very little
communication between the system and agents. Namely, a control unit broadcasts
a one-bit signal to agents whenever one of the allocated resources exceeds
capacity. Agents then respond to this signal in a probabilistic manner. In the
proposed algorithm, each agent makes decision of its resource demand locally
and an agent is unaware of the resource allocation of other agents. In
empirical results, we observe that the average allocations converge over time
to optimal allocations.Comment: To appear in IEEE International Smart Cities Conference (ISC2 2018),
Kansas City, USA, September, 2018. arXiv admin note: substantial text overlap
with arXiv:1711.0197
Convex inner approximations of nonconvex semialgebraic sets applied to fixed-order controller design
We describe an elementary algorithm to build convex inner approximations of
nonconvex sets. Both input and output sets are basic semialgebraic sets given
as lists of defining multivariate polynomials. Even though no optimality
guarantees can be given (e.g. in terms of volume maximization for bounded
sets), the algorithm is designed to preserve convex boundaries as much as
possible, while removing regions with concave boundaries. In particular, the
algorithm leaves invariant a given convex set. The algorithm is based on
Gloptipoly 3, a public-domain Matlab package solving nonconvex polynomial
optimization problems with the help of convex semidefinite programming
(optimization over linear matrix inequalities, or LMIs). We illustrate how the
algorithm can be used to design fixed-order controllers for linear systems,
following a polynomial approach
Spectral shape optimization for the Neumann traces of the Dirichlet-Laplacian eigenfunctions
We consider a spectral optimal design problem involving the Neumann traces of
the Dirichlet-Laplacian eigenfunctions on a smooth bounded open subset
of . The cost functional measures the amount of energy that Dirichlet
eigenfunctions concentrate on the boundary and that can be recovered with a
bounded density function. We first prove that, assuming a constraint on
densities, the so-called {\it Rellich functions} maximize this
functional.Motivated by several issues in shape optimization or observation
theory where it is relevant to deal with bounded densities, and noticing that
the -norm of {\it Rellich functions} may be large, depending on the
shape of , we analyze the effect of adding pointwise constraints when
maximizing the same functional. We investigate the optimality of {\it
bang-bang} functions and {\it Rellich densities} for this problem. We also deal
with similar issues for a close problem, where the cost functional is replaced
by a spectral approximation.Finally, this study is completed by the
investigation of particular geometries and is illustrated by several numerical
simulations
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