15,914 research outputs found
Some Applications of Polynomial Optimization in Operations Research and Real-Time Decision Making
We demonstrate applications of algebraic techniques that optimize and certify
polynomial inequalities to problems of interest in the operations research and
transportation engineering communities. Three problems are considered: (i)
wireless coverage of targeted geographical regions with guaranteed signal
quality and minimum transmission power, (ii) computing real-time certificates
of collision avoidance for a simple model of an unmanned vehicle (UV)
navigating through a cluttered environment, and (iii) designing a nonlinear
hovering controller for a quadrotor UV, which has recently been used for load
transportation. On our smaller-scale applications, we apply the sum of squares
(SOS) relaxation and solve the underlying problems with semidefinite
programming. On the larger-scale or real-time applications, we use our recently
introduced "SDSOS Optimization" techniques which result in second order cone
programs. To the best of our knowledge, this is the first study of real-time
applications of sum of squares techniques in optimization and control. No
knowledge in dynamics and control is assumed from the reader
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Using formal methods to support testing
Formal methods and testing are two important approaches that assist in the development of high quality software. While traditionally these approaches have been seen as rivals, in recent
years a new consensus has developed in which they are seen as complementary. This article reviews the state of the art regarding ways in which the presence of a formal specification can be used to assist testing
Voltage Stabilization in Microgrids via Quadratic Droop Control
We consider the problem of voltage stability and reactive power balancing in
islanded small-scale electrical networks outfitted with DC/AC inverters
("microgrids"). A droop-like voltage feedback controller is proposed which is
quadratic in the local voltage magnitude, allowing for the application of
circuit-theoretic analysis techniques to the closed-loop system. The operating
points of the closed-loop microgrid are in exact correspondence with the
solutions of a reduced power flow equation, and we provide explicit solutions
and small-signal stability analyses under several static and dynamic load
models. Controller optimality is characterized as follows: we show a one-to-one
correspondence between the high-voltage equilibrium of the microgrid under
quadratic droop control, and the solution of an optimization problem which
minimizes a trade-off between reactive power dissipation and voltage
deviations. Power sharing performance of the controller is characterized as a
function of the controller gains, network topology, and parameters. Perhaps
surprisingly, proportional sharing of the total load between inverters is
achieved in the low-gain limit, independent of the circuit topology or
reactances. All results hold for arbitrary grid topologies, with arbitrary
numbers of inverters and loads. Numerical results confirm the robustness of the
controller to unmodeled dynamics.Comment: 14 pages, 8 figure
A Survey of Symbolic Execution Techniques
Many security and software testing applications require checking whether
certain properties of a program hold for any possible usage scenario. For
instance, a tool for identifying software vulnerabilities may need to rule out
the existence of any backdoor to bypass a program's authentication. One
approach would be to test the program using different, possibly random inputs.
As the backdoor may only be hit for very specific program workloads, automated
exploration of the space of possible inputs is of the essence. Symbolic
execution provides an elegant solution to the problem, by systematically
exploring many possible execution paths at the same time without necessarily
requiring concrete inputs. Rather than taking on fully specified input values,
the technique abstractly represents them as symbols, resorting to constraint
solvers to construct actual instances that would cause property violations.
Symbolic execution has been incubated in dozens of tools developed over the
last four decades, leading to major practical breakthroughs in a number of
prominent software reliability applications. The goal of this survey is to
provide an overview of the main ideas, challenges, and solutions developed in
the area, distilling them for a broad audience.
The present survey has been accepted for publication at ACM Computing
Surveys. If you are considering citing this survey, we would appreciate if you
could use the following BibTeX entry: http://goo.gl/Hf5FvcComment: This is the authors pre-print copy. If you are considering citing
this survey, we would appreciate if you could use the following BibTeX entry:
http://goo.gl/Hf5Fv
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