Technical Sessions – Monday July 11

MC-14 IFORS 2011 - Melbourne
4 - On Some Intrinsic Difficulties in Solving Stateconstrained
Optimal Control Problems for Dynamical
Systems of ODEs and PDEs
Hans Josef Pesch, Department of Mathematics, University of
Bayreuth, Chair of Mathematics in Engineering Sciences, 95440,
Bayreuth, Bavaria, Germany, hans-josef.pesch@uni-bayreuth.de,
Stefan Wendl, Armin Rund
Motivated by an optimization problem for a hypersonic aircraft, a class of apparently
simple problems (hypersonic rocket car problems) have been invented
to analyze the mathematical difficulties hidden behind the engineering problem.
These problems consist of a minimum-time optimal control problem for a
second order ODE and a semi-linear heat equation which is controlled by one
of the ODE state variables. The PDE state variable is constrained. Despite their
simplicity these problems show some new phenomena not yet observed so far.
Different approaches to solve these problems will be discussed.
� MC-14
Monday, 16:00-17:30
Meeting Room 207
Stability in Optimal Control and Optimal
Control Applications in Economics
Stream: Continuous and Non-Smooth Optimization
Invited session
Chair: Musa Mammadov, Graduate School of Information
Technology and Mathematical Sciences, University of Ballarat,
University Drive, Mount Helen, P.O. Box 663, 3353, Ballarat,
Victoria, Australia, m.mammadov@ballarat.edu.au
Chair: Andreas Novak, Business Administration, Bruennerstrasse 72,
A-1210, Vienna, andreas.novak@univie.ac.at
Chair: Vladimir Veliov, Institute of Mathematical Methods in
Economics, Vienna University of technology, ORCOS,
Argentinierstr. 8/119, 1040, Vienna, Austria, veliov@tuwien.ac.at
1 - Asymptotical Stability of Opitimal Trajectories in Continuous
Systems with Time Delay
Musa Mammadov, Graduate School of Information Technology
and Mathematical Sciences, University of Ballarat, University
Drive, Mount Helen, P.O. Box 663, 3353, Ballarat, Victoria,
Australia, m.mammadov@ballarat.edu.au
A nonlinear differential equation with delay serving as a mathematical model
of several applied problems is considered. Sufficient conditions for the global
asymptotic stability and for the existence of periodic solutions are given. Two
particular applications are treated in detail. The first one is a blood cell production
model of M.C. Mackey, for which new periodicity criteria are derived.
The second application is a modified economic model with delay due to F.P.
Ramsey. An optimization problem for a maximal consumption is stated and
solved for the latter.
2 - Optimization Models of the Vehicle Suspension Systems
for Improved Comfort Level and Advanced Steering
Performance
Alexey Kuznetsov, Information Technologies and Mathematical
Sciences, University of Ballarat, University Drive, Mount Helen
Campus, PO Box 663, Ballarat, Victoria, Australia,
alexeykuznetsov@students.ballarat.edu.au
This research presents multi-objective optimization models of the vehicle suspension
systems for improved comfort level and advanced steering performance.
It adopts a new representation of the ISO 2631 standards that uses
the steady-state vibrations for evaluating comfort levels and does not depend
on the duration of vibration exposure period. A similar approach is applied to
describe the steering performance of the vehicle that considers the steady-state
vibrations imposed on the wheels when the time of exposure goes to infinity.
3 - When to Make a Software Open Source
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Andrea Seidl, Vienna University of Technology, 1040, Vienna,
Austria, aseidl@eos.tuwien.ac.at, Jonathan Caulkins, Gustav
Feichtinger, Dieter Grass, Peter M. Kort
We will present a multi-stage optimal control model dealing with the question
whether it might be optimal for a firm to make a proprietary software open
source at some optimally determined time. While the firm might lose revenue
from sales of the software when making it open source, it might profit from
user contributions leading to a higher quality, affecting both demand for the
software itself and for a commercial complementary product. We will consider
how choices regarding pricing and R&D efforts as well as certain key parameters
such as switching costs affect the optimal solution.
4 - Some Extensions of Schelling’s Binary Corruption
Model
Andreas Novak, Business Administration, Bruennerstrasse 72,
A-1210, Vienna, andreas.novak@univie.ac.at, Jonathan
Caulkins, Gustav Feichtinger, Richard Hartl, Peter M. Kort,
Andrea Seidl, Franz Wirl
Schelling (1978) suggested a simple binary choice model to explain the variation
of corruption levels across societies. His basic idea was that expected
profitability of engaging in corruption depends on its established frequency.
The key result of the so-called Schelling diagram is the existence of multiple
equilibria and tipping points. The present paper puts Schelling’s essentially
static approach in an intertemporal setting. By using optimal control theory we
show how the existence of an unstable interior steady state leads to indifference
thresholds (so-called Skiba points).
� MC-15
Monday, 16:00-17:30
Meeting Room 208
Military Soft Operations Research
Stream: Military, Defense and Security Applications
Invited session
Chair: Adrian Pincombe, Defence Science and Technology
Organisation, PO Box 1500, 5111, Edinburgh, South Australia,
Australia, Adrian.Pincombe@dsto.defence.gov.au
1 - Towards a Set of Vignettes to Explore the Use of Nonlethal
Weapons
Peter Williams, LOD, DSTO, PO Box 1500, Edinburgh, 5111,
Adelaide, South Australia, Australia,
peter.b.williams@dsto.defence.gov.au, Neville Curtis, Kasia
Krysiak
Non-lethal weapons are now a part of the military inventory. A rationale is
presented to develop a set of vignettes for comparison of acquisition options;
to explore tactics, techniques and procedures; and to develop difficult issues
of combining lower level physics and psychological terms. Classification according
to a set of descriptors including: evidence of lethal threat, verified red
force, red force arms, presence of third parties and intent of the operation led
to a distilled set of vignettes designed to cover a broad range of representative
use cases for analysis of Army operations.
2 - Collecting the Right Data in Military Field Activities
Leanne Rees, DSTO, Defence, South Australia, Australia,
Leanne.rees@dsto.defence.gov.au, Neville Curtis
With better preparation both in determining what to collect and in the manner
in which collection is done, field exercises and experiments can become
more fruitful sources of data for the military analyst. We discuss protocols that
improve issues identification through sequential activity analysis and influence
diagrams and this allows better direction of data collection. Appreciation of the
notion of perceptual positions, combining subjective, speculative and objective
input, and good field practice allows more structured and insightful understanding
of the system to be gained.
3 - Data Driven Theming of Vignettes for Army Analysis
Jessica Murray, DSTO, PO Box 1500, 5111, Edinburgh, South
Australia, Australia, jessica.murray@dsto.defence.gov.au,
Brandon Pincombe, Neville Curtis
Vignettes, tactical snapshots from scenarios, provide the context for military
simulations and experiments. Sets of vignettes are used to investigate concepts,
acquisitions, tactics, techniques and plans. We use data driven theming
to examine previous Land Operations Division studies to define an encompassing
set of factors and describe a representative set of vignettes. These balance
analytical usefulness and military relevance, covering the range of likely analytical
studies dictated by Army strategic guidance and surveying of field grade
officers.