7,227 research outputs found
Active Sampling-based Binary Verification of Dynamical Systems
Nonlinear, adaptive, or otherwise complex control techniques are increasingly
relied upon to ensure the safety of systems operating in uncertain
environments. However, the nonlinearity of the resulting closed-loop system
complicates verification that the system does in fact satisfy those
requirements at all possible operating conditions. While analytical proof-based
techniques and finite abstractions can be used to provably verify the
closed-loop system's response at different operating conditions, they often
produce conservative approximations due to restrictive assumptions and are
difficult to construct in many applications. In contrast, popular statistical
verification techniques relax the restrictions and instead rely upon
simulations to construct statistical or probabilistic guarantees. This work
presents a data-driven statistical verification procedure that instead
constructs statistical learning models from simulated training data to separate
the set of possible perturbations into "safe" and "unsafe" subsets. Binary
evaluations of closed-loop system requirement satisfaction at various
realizations of the uncertainties are obtained through temporal logic
robustness metrics, which are then used to construct predictive models of
requirement satisfaction over the full set of possible uncertainties. As the
accuracy of these predictive statistical models is inherently coupled to the
quality of the training data, an active learning algorithm selects additional
sample points in order to maximize the expected change in the data-driven model
and thus, indirectly, minimize the prediction error. Various case studies
demonstrate the closed-loop verification procedure and highlight improvements
in prediction error over both existing analytical and statistical verification
techniques.Comment: 23 page
Autonomous search for a diffusive source in an unknown environment
The paper presents an approach to olfactory search for a diffusive emitting
source of tracer (e.g. aerosol, gas) in an environment with unknown map of
randomly placed and shaped obstacles.
The measurements of tracer concentration are sporadic, noisy and without
directional information. The search domain is discretised and modelled by a
finite two-dimensional lattice. The links is the lattice represent the
traversable paths for emitted particles and for the searcher. A missing link in
the lattice indicates a blocked paths, due to the walls or obstacles. The
searcher must simultaneously estimate the source parameters, the map of the
search domain and its own location within the map. The solution is formulated
in the sequential Bayesian framework and implemented as a Rao-Blackwellised
particle filter with information-driven motion control. The numerical results
demonstrate the concept and its performance.Comment: 11 pages, 7 figure
Sequential quasi-Monte Carlo: Introduction for Non-Experts, Dimension Reduction, Application to Partly Observed Diffusion Processes
SMC (Sequential Monte Carlo) is a class of Monte Carlo algorithms for
filtering and related sequential problems. Gerber and Chopin (2015) introduced
SQMC (Sequential quasi-Monte Carlo), a QMC version of SMC. This paper has two
objectives: (a) to introduce Sequential Monte Carlo to the QMC community, whose
members are usually less familiar with state-space models and particle
filtering; (b) to extend SQMC to the filtering of continuous-time state-space
models, where the latent process is a diffusion. A recurring point in the paper
will be the notion of dimension reduction, that is how to implement SQMC in
such a way that it provides good performance despite the high dimension of the
problem.Comment: To be published in the proceedings of MCMQMC 201
Sensor Placement for Damage Localization in Sensor Networks
The objective of this thesis is to formulate and solve the sensor placement problem for damage localization in a sensor network. A Bayesian estimation problem is formulated with the time-of-flight (ToF) measurements. In this model, ToF of lamb waves, which are generated and received by piezoelectric sensors, is the total time for each wave to be transmitted, reflected by the target, and received by the sensor. The ToF of the scattered lamb wave has characteristic information about the target location. By using the measurement model and prior information, the target location is estimated in a centralized sensor network with a Monte Carlo approach. Then we derive the Bayesian Fisher information matrix (B-FIM) and based on that posterior Cramer-Rao lower bound (PCRLB), which sets a limit on the mean squared error (MSE) of any Bayesian estimator. In addition, we develop an optimal sensor placement approach to achieve more accurate damage localization, which is based on minimizing the PCRLB. Simulation results show that the optimal sensor placement solutions lead to much lower estimation errors than some sub-optimal sensor placement solutions
Closed-Loop Statistical Verification of Stochastic Nonlinear Systems Subject to Parametric Uncertainties
This paper proposes a statistical verification framework using Gaussian
processes (GPs) for simulation-based verification of stochastic nonlinear
systems with parametric uncertainties. Given a small number of stochastic
simulations, the proposed framework constructs a GP regression model and
predicts the system's performance over the entire set of possible
uncertainties. Included in the framework is a new metric to estimate the
confidence in those predictions based on the variance of the GP's cumulative
distribution function. This variance-based metric forms the basis of active
sampling algorithms that aim to minimize prediction error through careful
selection of simulations. In three case studies, the new active sampling
algorithms demonstrate up to a 35% improvement in prediction error over other
approaches and are able to correctly identify regions with low prediction
confidence through the variance metric.Comment: 8 pages, submitted to ACC 201
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