15,538 research outputs found
On Necessary and Sufficient Conditions for Near-Optimal Singular Stochastic Controls
This paper is concerned with necessary and sufficient conditions for
near-optimal singular stochastic controls for systems driven by a nonlinear
stochastic differential equations (SDEs in short). The proof of our result is
based on Ekeland's variational principle and some delicate estimates of the
state and adjoint processes. This result is a generalization of Zhou's
stochastic maximum principle for near-optimality to singular control problem.Comment: 19 pages, submitted to journa
Necessary Condition for Near Optimal Control of Linear Forward-backward Stochastic Differential Equations
This paper investigates the near optimal control for a kind of linear
stochastic control systems governed by the forward backward stochastic
differential equations, where both the drift and diffusion terms are allowed to
depend on controls and the control domain is not assumed to be convex. In the
previous work (Theorem 3.1) of the second and third authors [\textit{%
Automatica} \textbf{46} (2010) 397-404], some problem of near optimal control
with the control dependent diffusion is addressed and our current paper can be
viewed as some direct response to it. The necessary condition of the
near-optimality is established within the framework of optimality variational
principle developed by Yong [\textit{SIAM J. Control Optim.} \textbf{48} (2010)
4119--4156] and obtained by the convergence technique to treat the optimal
control of FBSDEs in unbounded control domains by Wu [% \textit{Automatica}
\textbf{49} (2013) 1473--1480]. Some new estimates are given here to handle the
near optimality. In addition, an illustrating example is discussed as well.Comment: To appear in International Journal of Contro
Controlled diffusion processes
This article gives an overview of the developments in controlled diffusion
processes, emphasizing key results regarding existence of optimal controls and
their characterization via dynamic programming for a variety of cost criteria
and structural assumptions. Stochastic maximum principle and control under
partial observations (equivalently, control of nonlinear filters) are also
discussed. Several other related topics are briefly sketched.Comment: Published at http://dx.doi.org/10.1214/154957805100000131 in the
Probability Surveys (http://www.i-journals.org/ps/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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
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
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