80,415 research outputs found
On the control of max-plus linear system subject to state restriction
This paper deals with the control of discrete event systems subject to synchronization and time delay phenomena, which can be described by using the max-plus algebra. The objective is to design a feedback controller to guarantee that the system evolves without violating time restrictions imposed on the state. To this end an equation is derived, which involves the system, the feedback and the restriction matrices. Conditions concerning the existence of a feedback are discussed and sufficient conditions that ensure the computation of a causal feedback are presented. To illustrate the results of this paper, a workshop control problem is presented
Duality and interval analysis over idempotent semirings
In this paper semirings with an idempotent addition are considered. These
algebraic structures are endowed with a partial order. This allows to consider
residuated maps to solve systems of inequalities . The
purpose of this paper is to consider a dual product, denoted , and the
dual residuation of matrices, in order to solve the following inequality . Sufficient conditions ensuring the
existence of a non-linear projector in the solution set are proposed. The
results are extended to semirings of intervals
Power Aware Wireless File Downloading: A Constrained Restless Bandit Approach
This paper treats power-aware throughput maximization in a multi-user file
downloading system. Each user can receive a new file only after its previous
file is finished. The file state processes for each user act as coupled Markov
chains that form a generalized restless bandit system. First, an optimal
algorithm is derived for the case of one user. The algorithm maximizes
throughput subject to an average power constraint. Next, the one-user algorithm
is extended to a low complexity heuristic for the multi-user problem. The
heuristic uses a simple online index policy and its effectiveness is shown via
simulation. For simple 3-user cases where the optimal solution can be computed
offline, the heuristic is shown to be near-optimal for a wide range of
parameters
Spectral Theorem for Convex Monotone Homogeneous Maps, and Ergodic Control
We consider convex maps f:R^n -> R^n that are monotone (i.e., that preserve
the product ordering of R^n), and nonexpansive for the sup-norm. This includes
convex monotone maps that are additively homogeneous (i.e., that commute with
the addition of constants). We show that the fixed point set of f, when it is
non-empty, is isomorphic to a convex inf-subsemilattice of R^n, whose dimension
is at most equal to the number of strongly connected components of a critical
graph defined from the tangent affine maps of f. This yields in particular an
uniqueness result for the bias vector of ergodic control problems. This
generalizes results obtained previously by Lanery, Romanovsky, and Schweitzer
and Federgruen, for ergodic control problems with finite state and action
spaces, which correspond to the special case of piecewise affine maps f. We
also show that the length of periodic orbits of f is bounded by the cyclicity
of its critical graph, which implies that the possible orbit lengths of f are
exactly the orders of elements of the symmetric group on n letters.Comment: 38 pages, 13 Postscript figure
DYNAMICALLY OPTIMAL AND APPROXIMATELY OPTIMAL BEEF CATTLE DIETS FORMULATED BY NONLINEAR PROGRAMMING
Cattle purchasing, feeding, and selling decisions are described by a free-time optimal control model. The nutrient constraints of the National Research Council and a recently published dry matter intake constraint augment the model and make it nonlinear in the feed ingredients, the daily gain, and the weight of the cattle. Optimal feeding programs are calculated by nonlinear programming under two scenarios: first, when the feedlot has excess capacity and, second, when animals must be sold to make room in the feedlot before more can be purchased. An approximately optimal feeding program is calculated by nonlinear programming and is all but identical to the dynamically optimal programs.Livestock Production/Industries,
Vandermonde-subspace Frequency Division Multiplexing for Two-Tiered Cognitive Radio Networks
Vandermonde-subspace frequency division multiplexing (VFDM) is an overlay
spectrum sharing technique for cognitive radio. VFDM makes use of a precoder
based on a Vandermonde structure to transmit information over a secondary
system, while keeping an orthogonal frequency division multiplexing
(OFDM)-based primary system interference-free. To do so, VFDM exploits
frequency selectivity and the use of cyclic prefixes by the primary system.
Herein, a global view of VFDM is presented, including also practical aspects
such as linear receivers and the impact of channel estimation. We show that
VFDM provides a spectral efficiency increase of up to 1 bps/Hz over cognitive
radio systems based on unused band detection. We also present some key design
parameters for its future implementation and a feasible channel estimation
protocol. Finally we show that, even when some of the theoretical assumptions
are relaxed, VFDM provides non-negligible rates while protecting the primary
system.Comment: 9 pages, accepted for publication in IEEE Transactions on
Communication
Multigrid methods for two-player zero-sum stochastic games
We present a fast numerical algorithm for large scale zero-sum stochastic
games with perfect information, which combines policy iteration and algebraic
multigrid methods. This algorithm can be applied either to a true finite state
space zero-sum two player game or to the discretization of an Isaacs equation.
We present numerical tests on discretizations of Isaacs equations or
variational inequalities. We also present a full multi-level policy iteration,
similar to FMG, which allows to improve substantially the computation time for
solving some variational inequalities.Comment: 31 page
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