25,716 research outputs found
A Posteriori Probabilistic Bounds of Convex Scenario Programs with Validation Tests
Scenario programs have established themselves as efficient tools towards
decision-making under uncertainty. To assess the quality of scenario-based
solutions a posteriori, validation tests based on Bernoulli trials have been
widely adopted in practice. However, to reach a theoretically reliable
judgement of risk, one typically needs to collect massive validation samples.
In this work, we propose new a posteriori bounds for convex scenario programs
with validation tests, which are dependent on both realizations of support
constraints and performance on out-of-sample validation data. The proposed
bounds enjoy wide generality in that many existing theoretical results can be
incorporated as particular cases. To facilitate practical use, a systematic
approach for parameterizing a posteriori probability bounds is also developed,
which is shown to possess a variety of desirable properties allowing for easy
implementations and clear interpretations. By synthesizing comprehensive
information about support constraints and validation tests, improved risk
evaluation can be achieved for randomized solutions in comparison with existing
a posteriori bounds. Case studies on controller design of aircraft lateral
motion are presented to validate the effectiveness of the proposed a posteriori
bounds
A Statistical Learning Theory Approach for Uncertain Linear and Bilinear Matrix Inequalities
In this paper, we consider the problem of minimizing a linear functional
subject to uncertain linear and bilinear matrix inequalities, which depend in a
possibly nonlinear way on a vector of uncertain parameters. Motivated by recent
results in statistical learning theory, we show that probabilistic guaranteed
solutions can be obtained by means of randomized algorithms. In particular, we
show that the Vapnik-Chervonenkis dimension (VC-dimension) of the two problems
is finite, and we compute upper bounds on it. In turn, these bounds allow us to
derive explicitly the sample complexity of these problems. Using these bounds,
in the second part of the paper, we derive a sequential scheme, based on a
sequence of optimization and validation steps. The algorithm is on the same
lines of recent schemes proposed for similar problems, but improves both in
terms of complexity and generality. The effectiveness of this approach is shown
using a linear model of a robot manipulator subject to uncertain parameters.Comment: 19 pages, 2 figures, Accepted for Publication in Automatic
On Probabilistic Certification of Combined Cancer Therapies Using Strongly Uncertain Models
This paper proposes a general framework for probabilistic certification of
cancer therapies. The certification is defined in terms of two key issues which
are the tumor contraction and the lower admissible bound on the circulating
lymphocytes which is viewed as indicator of the patient health. The
certification is viewed as the ability to guarantee with a predefined high
probability the success of the therapy over a finite horizon despite of the
unavoidable high uncertainties affecting the dynamic model that is used to
compute the optimal scheduling of drugs injection. The certification paradigm
can be viewed as a tool for tuning the treatment parameters and protocols as
well as for getting a rational use of limited or expensive drugs. The proposed
framework is illustrated using the specific problem of combined
immunotherapy/chemotherapy of cancer.Comment: Submitted to Journal of theoretical Biolog
Formal Probabilistic Analysis of a Wireless Sensor Network for Forest Fire Detection
Wireless Sensor Networks (WSNs) have been widely explored for forest fire
detection, which is considered a fatal threat throughout the world. Energy
conservation of sensor nodes is one of the biggest challenges in this context
and random scheduling is frequently applied to overcome that. The performance
analysis of these random scheduling approaches is traditionally done by
paper-and-pencil proof methods or simulation. These traditional techniques
cannot ascertain 100% accuracy, and thus are not suitable for analyzing a
safety-critical application like forest fire detection using WSNs. In this
paper, we propose to overcome this limitation by applying formal probabilistic
analysis using theorem proving to verify scheduling performance of a real-world
WSN for forest fire detection using a k-set randomized algorithm as an energy
saving mechanism. In particular, we formally verify the expected values of
coverage intensity, the upper bound on the total number of disjoint subsets,
for a given coverage intensity, and the lower bound on the total number of
nodes.Comment: In Proceedings SCSS 2012, arXiv:1307.802
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