4,073 research outputs found
On average control generating families for singularly perturbed optimal control problems with long run average optimality criteria
The paper aims at the development of tools for analysis and construction of
near optimal solutions of singularly perturbed (SP) optimal controls problems
with long run average optimality criteria. The idea that we exploit is to first
asymptotically approximate a given problem of optimal control of the SP system
by a certain averaged optimal control problem, then reformulate this averaged
problem as an infinite-dimensional (ID) linear programming (LP) problem, and
then approximate the latter by semi-infinite LP problems. We show that the
optimal solution of these semi-infinite LP problems and their duals (that can
be found with the help of a modification of an available LP software) allow one
to construct near optimal controls of the SP system. We demonstrate the
construction with a numerical example.Comment: 36 pages, 4 figures. arXiv admin note: substantial text overlap with
arXiv:1309.373
Use of approximations of Hamilton-Jacobi-Bellman inequality for solving periodic optimization problems
We show that necessary and sufficient conditions of optimality in periodic
optimization problems can be stated in terms of a solution of the corresponding
HJB inequality, the latter being equivalent to a max-min type variational
problem considered on the space of continuously differentiable functions. We
approximate the latter with a maximin problem on a finite dimensional subspace
of the space of continuously differentiable functions and show that a solution
of this problem (existing under natural controllability conditions) can be used
for construction of near optimal controls. We illustrate the construction with
a numerical example.Comment: 29 pages, 2 figure
A tutorial on recursive models for analyzing and predicting path choice behavior
The problem at the heart of this tutorial consists in modeling the path
choice behavior of network users. This problem has been extensively studied in
transportation science, where it is known as the route choice problem. In this
literature, individuals' choice of paths are typically predicted using discrete
choice models. This article is a tutorial on a specific category of discrete
choice models called recursive, and it makes three main contributions: First,
for the purpose of assisting future research on route choice, we provide a
comprehensive background on the problem, linking it to different fields
including inverse optimization and inverse reinforcement learning. Second, we
formally introduce the problem and the recursive modeling idea along with an
overview of existing models, their properties and applications. Third, we
extensively analyze illustrative examples from different angles so that a
novice reader can gain intuition on the problem and the advantages provided by
recursive models in comparison to path-based ones
Averaging and linear programming in some singularly perturbed problems of optimal control
The paper aims at the development of an apparatus for analysis and
construction of near optimal solutions of singularly perturbed (SP) optimal
controls problems (that is, problems of optimal control of SP systems)
considered on the infinite time horizon.
We mostly focus on problems with time discounting criteria but a possibility
of the extension of results to periodic optimization problems is discussed as
well. Our consideration is based on earlier results on averaging of SP control
systems and on linear programming formulations of optimal control problems. The
idea that we exploit is to first asymptotically approximate a given problem of
optimal control of the SP system by a certain averaged optimal control problem,
then reformulate this averaged problem as an infinite-dimensional (ID) linear
programming (LP) problem, and then approximate the latter by semi-infinite LP
problems. We show that the optimal solution of these semi-infinite LP problems
and their duals (that can be found with the help of a modification of an
available LP software) allow one to construct near optimal controls of the SP
system. We demonstrate the construction with two numerical examples.Comment: 53 pages, 10 figure
Conditions for the discovery of solution horizons
We present necessary and sufficient conditions for discrete infinite horizon optimization problems with unique solutions to be solvable. These problems can be equivalently viewed as the task of finding a shortest path in an infinite directed network. We provide general forward algorithms with stopping rules for their solution. The key condition required is that of weak reachability, which roughly requires that for any sequence of nodes or states, it must be possible from optimal states to reach states close in cost to states along this sequence. Moreover the costs to reach these states must converge to zero. Applications are considered in optimal search, undiscounted Markov decision processes, and deterministic infinite horizon optimization.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47927/1/10107_2005_Article_BF01581244.pd
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