Authors:
Tyrone E. Duncan,
Yaozhong Hu,
Bozenna Pasik-Duncan,
Volume: 1, Page 212 Paper number 6
Abstract:
This paper describes some of the results in a paper by the same authors
in SIAM J. Control Optim. 38(2000), 582-612, for a stochastic calculus
for a fractional Brownian motion with the Hurst parameter in the interval
(1/2,1). Two stochastic integrals are defined with explicit expressions
for their first two moments. Multiple and iterated integrals of a
fractional Brownian motion are defined and various properties of these
integrals are given. A square integrable functional on a probability
space of a fractional Brownian motion is expressed as an infinite series
of multiple integrals.
Authors:
Valery A. Ugrinovskii,
Ian R. Petersen,
Volume: 1, Page 217 Paper number 1245
Abstract:
In this paper, we consider a robust stability problem for continuous
time stochastic uncertain systems. The uncertainty in the system is
characterized in terms of an uncertain probability distribution on
the noise input. This uncertainty is assumed to satisfy a certain relative
entropy constraint. The solution to a specially parametrized risk-sensitive
performance analysis problem is used to estimate the level of guaranteed
performance for the stochastic uncertain system under consideration.
This solution is obtained by solving an algebraic Riccati equation.
The corresponding performance bound holds for all admissible uncertainties
and is nonconservative.
Authors:
Kate Duckworth,
Mihail Zervos,
Volume: 1, Page 222 Paper number 2056
Abstract:
We consider a stochastic control problem that has emerged in the economics
literature as an investment model under uncertainty. This problem combines
some of the features of stochastic impulse control with optimal stopping.
The aim is to discover the form of the optimal strategy. The results
that we establish are of an explicit nature.
Authors:
Andrew E.B. Lim,
Xun Yu Zhou,
Volume: 1, Page 228 Paper number 1320
Abstract:
In this paper, a control methodology based on the HARA utility function
is presented as an alternative to the exponential-of-an-integral approach
to finding robust controllers. This work is inspired by the intuition
that HARA controllers, while being robust, may give better performance
than exponential controllers in normal situations. The HARA problem
is shown to be equivalent to a certain differential game and the asymptotic
properties of the HARA problem and this differential game are studied.
As an example, a linear-quadratic HARA problem is studied, where the
problem of finding a robust HARA controller is proved to be equivalent
to solving a standard linear-quadratic problem for a system with a
higher noise intensity. This reveals an interesting relationship between
robustness and uncertainty.
Authors:
Nathaniel Keohane,
Benjamin Van Roy,
Richard Zeckhauser,
Volume: 1, Page 234 Paper number 1786
Abstract:
Our analysis melds two traditional approaches to promoting quality.
The first is restoring the stock of quality. The second is curbing
its flow of deterioration. Although both approaches are widely used
in real world settings, analytic models have tended to focus on one
strategy or the other. We consider a class of problems, which we call
``SFQ'' problems, in which both stocks and flows can be controlled
to promote quality. We develop our results in the context of environmental
quality, drawing on real-world examples from atomic wastes to zebra
mussels. But the lessons are general, and we show how they apply to
promoting the quality of both physical and human capital. We first
study optimal policies in the limiting cases when only abatement or
restoration is possible. We then focus on the full SFQ world, where
both approaches can be used. We show that the optimal policy employs
both instruments. Moreover, when combined optimally, neither strategy
takes the form it would in the absence of the other.
Authors:
Valery A. Ugrinovskii,
Volume: 1, Page 240 Paper number 1089
Abstract:
This paper is concerned with the existence of a guaranteed cost controller
for an uncertain system which is subject to structured uncertainty.
The uncertainty in the system is assumed to have a stochastic character
and satisfy certain stochastic integral quadratic constraints. It is
shown that a guaranteed cost output feedback controller for a stochastic
system can be synthesized as an output feedback controller absolutely
stabilizing this system.
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